Version: Next

Trial-level early stopping

Trial-level early stopping aims to monitor the results of expensive evaluations with timeseries-like data and terminate those that are unlikely to produce promising results prior to completing that evaluation. This reduces computational waste, and enables the same amount of resources to explore more configurations. Early stopping is useful for expensive to evaluate problems where stepwise information is available on the way to the final measurement.

Like the Getting Started tutorial we'll be minimizing the Hartmann6 function, but this time we've modified it to incorporate a new parameter $t$ which allows the function to produce timeseries-like data where the value returned is closer and closer to Hartmann6's true value as $t$ increases. At $t = 100$ the function will simply return Hartmann6's unaltered value.

f(x, t) = hartmann6(x) - log_2(t/100)

While the function is synthetic, the workflow captures the intended principles for this tutorial and is similar to the process of training typical machine learning models.

Learning Objectives

Understand when time-series-like data can be used in an optimization experiment
Run a simple optimization experiment with early stopping
Configure details of an early stopping strategy
Analyze the results of the optimization

Prerequisites

Familiarity with Python and basic programming concepts
Understanding of adaptive experimentation and Bayesian optimization
Getting Started with Ax

Step 1: Import Necessary Modules

First, ensure you have all the necessary imports:

import numpy as np
from ax.api.client import Client
from ax.api.configs import  RangeParameterConfig

Step 2: Initialize the Client

Create an instance of the Client to manage the state of your experiment.

client = Client()

Step 3: Configure the Experiment

The Client instance can be configured with a series of Configs that define how the experiment will be run.

The Hartmann6 problem is usually evaluated on the hypercube $x_i \in (0, 1)$ , so we will define six identical RangeParameterConfigs with these bounds.

You may specify additional features like parameter constraints to further refine the search space and parameter scaling to help navigate parameters with nonuniform effects.

# Define six float parameters for the Hartmann6 function
parameters = [
    RangeParameterConfig(
        name=f"x{i + 1}", parameter_type="float", bounds=(0, 1)
    )
    for i in range(6)
]

client.configure_experiment(parameters=parameters)

Step 4: Configure Optimization

Now, we must configure the objective for this optimization, which we do using Client.configure_optimization. This method expects a string objective, an expression containing either a single metric to maximize, a linear combination of metrics to maximize, or a tuple of multiple metrics to jointly maximize. These expressions are parsed using SymPy. For example:

"score" would direct Ax to maximize a metric named score
"-loss" would direct Ax to Ax to minimize a metric named loss
"task_0 + 0.5 * task_1" would direct Ax to maximize the sum of two task scores, downweighting task_1 by a factor of 0.5
"score, -flops" would direct Ax to simultaneously maximize score while minimizing flops

See these recipes for more information on configuring objectives and outcome constraints.

client.configure_optimization(objective="-hartmann6")

Step 5: Run Trials with early stopping

Here, we will configure the ask-tell loop.

We begin by defining our Hartmann6 function as written above. Remember, this is just an example problem and any Python function can be substituted here.

Then we will iteratively do the following:

Call client.get_next_trials to "ask" Ax for a parameterization to evaluate
Evaluate hartmann6_curve using those parameters in an inner loop to simulate the generation of timeseries data
"Tell" Ax the partial result using client.attach_data
Query whether the trial should be stopped via client.should_stop_trial_early
Stop the underperforming trial and report back to Ax that is has been stopped

This loop will run multiple trials to optimize the function.

Ax will configure an EarlyStoppingStrategy when should_stop_trial_early is called for the first time. By default Ax uses a Percentile early stopping strategy which will terminate a trial early if its performance falls below a percentile threshold when compared to other trials at the same step. Early stopping can only occur after a minimum number of progressions to prevent premature early stopping. This validates that both enough data is gathered to make a decision and there is a minimum number of completed trials with curve data; these completed trials establish a baseline.

# Hartmann6 function
def hartmann6(x1, x2, x3, x4, x5, x6):
    alpha = np.array([1.0, 1.2, 3.0, 3.2])
    A = np.array(
        [
            [10, 3, 17, 3.5, 1.7, 8],
            [0.05, 10, 17, 0.1, 8, 14],
            [3, 3.5, 1.7, 10, 17, 8],
            [17, 8, 0.05, 10, 0.1, 14],
        ]
    )
    P = 10**-4 * np.array(
        [
            [1312, 1696, 5569, 124, 8283, 5886],
            [2329, 4135, 8307, 3736, 1004, 9991],
            [2348, 1451, 3522, 2883, 3047, 6650],
            [4047, 8828, 8732, 5743, 1091, 381],
        ]
    )

    outer = 0.0
    for i in range(4):
        inner = 0.0
        for j, x in enumerate([x1, x2, x3, x4, x5, x6]):
            inner += A[i, j] * (x - P[i, j]) ** 2
        outer += alpha[i] * np.exp(-inner)
    return -outer


# Hartmann6 function with additional t term such that
# hartmann6(X) == hartmann6_curve(X, t=100)
def hartmann6_curve(x1, x2, x3, x4, x5, x6, t):
    return hartmann6(x1, x2, x3, x4, x5, x6) - np.log2(t / 100)


(
    hartmann6(0.1, 0.45, 0.8, 0.25, 0.552, 1.0),
    hartmann6_curve(0.1, 0.45, 0.8, 0.25, 0.552, 1.0, 100),
)

Output:
(np.float64(-0.4878737485613134), np.float64(-0.4878737485613134))

maximum_progressions = 100  # Observe hartmann6_curve over 100 progressions

for _ in range(30):  # Run 30 rounds of trials
    trials = client.get_next_trials(max_trials=3)
    for trial_index, parameters in trials.items():
        for t in range(1, maximum_progressions + 1):
            raw_data = {"hartmann6": hartmann6_curve(t=t, **parameters)}

            # On the final reading call complete_trial and break, else call attach_data
            if t == maximum_progressions:
                client.complete_trial(
                    trial_index=trial_index, raw_data=raw_data, progression=t
                )
                break

            client.attach_data(
                trial_index=trial_index, raw_data=raw_data, progression=t
            )

            # If the trial is underperforming, stop it
            if client.should_stop_trial_early(trial_index=trial_index):
                client.mark_trial_early_stopped(trial_index=trial_index)
                break

Output:
[INFO 10-12 05:04:54] ax.api.client: GenerationStrategy(name='Center+Sobol+MBM:fast', nodes=[CenterGenerationNode(next_node_name='Sobol'), GenerationNode(node_name='Sobol', generator_specs=[GeneratorSpec(generator_enum=Sobol, model_key_override=None)], transition_criteria=[MinTrials(transition_to='MBM'), MinTrials(transition_to='MBM')]), GenerationNode(node_name='MBM', generator_specs=[GeneratorSpec(generator_enum=BoTorch, model_key_override=None)], transition_criteria=[])]) chosen based on user input and problem structure.
[INFO 10-12 05:04:54] ax.api.client: Generated new trial 0 with parameters {'x1': 0.5, 'x2': 0.5, 'x3': 0.5, 'x4': 0.5, 'x5': 0.5, 'x6': 0.5} using GenerationNode CenterOfSearchSpace.
[INFO 10-12 05:04:54] ax.api.client: Generated new trial 1 with parameters {'x1': 0.569844, 'x2': 0.207419, 'x3': 0.090854, 'x4': 0.407376, 'x5': 0.920197, 'x6': 0.988185} using GenerationNode Sobol.
[INFO 10-12 05:04:54] ax.api.client: Generated new trial 2 with parameters {'x1': 0.29014, 'x2': 0.507271, 'x3': 0.647595, 'x4': 0.724803, 'x5': 0.426718, 'x6': 0.480608} using GenerationNode Sobol.
[INFO 10-12 05:04:55] ax.api.client: Trial 0 marked COMPLETED.
[INFO 10-12 05:04:57] ax.api.client: Trial 1 marked COMPLETED.
[INFO 10-12 05:04:58] ax.api.client: Trial 2 marked COMPLETED.
[INFO 10-12 05:04:58] ax.api.client: Generated new trial 3 with parameters {'x1': 0.160273, 'x2': 0.384106, 'x3': 0.347328, 'x4': 0.121946, 'x5': 0.113965, 'x6': 0.224867} using GenerationNode Sobol.
[INFO 10-12 05:04:58] ax.api.client: Generated new trial 4 with parameters {'x1': 0.947761, 'x2': 0.838153, 'x3': 0.915537, 'x4': 0.80839, 'x5': 0.607479, 'x6': 0.743657} using GenerationNode Sobol.
[WARNING 10-12 05:04:58] ax.api.client: 3 trials requested but only 2 could be generated.
[INFO 10-12 05:05:00] ax.api.client: Trial 3 marked COMPLETED.
[INFO 10-12 05:05:01] ax.api.client: Trial 4 marked COMPLETED.
[INFO 10-12 05:05:02] ax.api.client: Generated new trial 5 with parameters {'x1': 0.740901, 'x2': 0.582752, 'x3': 0.465543, 'x4': 0.341851, 'x5': 0.521128, 'x6': 0.377314} using GenerationNode MBM.
[WARNING 10-12 05:05:02] ax.api.client: 3 trials requested but only 1 could be generated.
[INFO 10-12 05:05:02] ax.early_stopping.strategies.percentile: Early stopping trial 5: Trial objective value 3.1334438661172035 is worse than 50.0-th percentile (3.104256585051232) across comparable trials..
[INFO 10-12 05:05:02] ax.api.client: Trial 5 should be stopped early: Trial objective value 3.1334438661172035 is worse than 50.0-th percentile (3.104256585051232) across comparable trials.
[INFO 10-12 05:05:02] ax.api.client: Trial 5 marked EARLY_STOPPED.
[INFO 10-12 05:05:03] ax.api.client: Generated new trial 6 with parameters {'x1': 0.82089, 'x2': 0.611023, 'x3': 0.463807, 'x4': 0.309329, 'x5': 0.537708, 'x6': 0.363185} using GenerationNode MBM.
[INFO 10-12 05:05:03] ax.api.client: Generated new trial 7 with parameters {'x1': 0.458261, 'x2': 0.472112, 'x3': 0.478715, 'x4': 0.309868, 'x5': 0.351339, 'x6': 0.789451} using GenerationNode MBM.
[INFO 10-12 05:05:03] ax.api.client: Generated new trial 8 with parameters {'x1': 0.448569, 'x2': 0.41021, 'x3': 0.372014, 'x4': 0.586224, 'x5': 0.664376, 'x6': 0.264964} using GenerationNode MBM.
[INFO 10-12 05:05:03] ax.early_stopping.strategies.percentile: Early stopping trial 6: Trial objective value 3.216293838962652 is worse than 50.0-th percentile (3.1334438661172035) across comparable trials..
[INFO 10-12 05:05:03] ax.api.client: Trial 6 should be stopped early: Trial objective value 3.216293838962652 is worse than 50.0-th percentile (3.1334438661172035) across comparable trials.
[INFO 10-12 05:05:03] ax.api.client: Trial 6 marked EARLY_STOPPED.
[INFO 10-12 05:05:06] ax.api.client: Trial 7 marked COMPLETED.
[INFO 10-12 05:05:09] ax.api.client: Trial 8 marked COMPLETED.
[INFO 10-12 05:05:10] ax.api.client: Generated new trial 9 with parameters {'x1': 0.429068, 'x2': 0.436964, 'x3': 0.417412, 'x4': 0.168036, 'x5': 0.277864, 'x6': 0.853455} using GenerationNode MBM.
[INFO 10-12 05:05:10] ax.api.client: Generated new trial 10 with parameters {'x1': 0.465443, 'x2': 0.439612, 'x3': 0.33566, 'x4': 0.439129, 'x5': 0.29029, 'x6': 0.883182} using GenerationNode MBM.
[INFO 10-12 05:05:10] ax.api.client: Generated new trial 11 with parameters {'x1': 0.230281, 'x2': 0.416253, 'x3': 0.645273, 'x4': 0.147288, 'x5': 0.358182, 'x6': 0.839843} using GenerationNode MBM.
[INFO 10-12 05:05:13] ax.api.client: Trial 9 marked COMPLETED.
[INFO 10-12 05:05:16] ax.api.client: Trial 10 marked COMPLETED.
[INFO 10-12 05:05:18] ax.api.client: Trial 11 marked COMPLETED.
[INFO 10-12 05:05:20] ax.api.client: Generated new trial 12 with parameters {'x1': 0.51689, 'x2': 0.131775, 'x3': 0.646985, 'x4': 0.0, 'x5': 0.785929, 'x6': 0.783954} using GenerationNode MBM.
[INFO 10-12 05:05:20] ax.api.client: Generated new trial 13 with parameters {'x1': 0.0, 'x2': 0.474072, 'x3': 0.590582, 'x4': 0.0, 'x5': 1.0, 'x6': 0.813107} using GenerationNode MBM.
[INFO 10-12 05:05:20] ax.api.client: Generated new trial 14 with parameters {'x1': 0.0, 'x2': 0.227729, 'x3': 0.626499, 'x4': 1.0, 'x5': 0.0, 'x6': 0.796293} using GenerationNode MBM.
[INFO 10-12 05:05:20] ax.early_stopping.strategies.percentile: Early stopping trial 12: Trial objective value 3.1589235786777374 is worse than 50.0-th percentile (3.04280231969693) across comparable trials..
[INFO 10-12 05:05:20] ax.api.client: Trial 12 should be stopped early: Trial objective value 3.1589235786777374 is worse than 50.0-th percentile (3.04280231969693) across comparable trials.
[INFO 10-12 05:05:20] ax.api.client: Trial 12 marked EARLY_STOPPED.
[INFO 10-12 05:05:23] ax.api.client: Trial 13 marked COMPLETED.
[INFO 10-12 05:05:23] ax.early_stopping.strategies.percentile: Early stopping trial 14: Trial objective value 3.10584624740548 is worse than 50.0-th percentile (3.04280231969693) across comparable trials..
[INFO 10-12 05:05:23] ax.api.client: Trial 14 should be stopped early: Trial objective value 3.10584624740548 is worse than 50.0-th percentile (3.04280231969693) across comparable trials.
[INFO 10-12 05:05:23] ax.api.client: Trial 14 marked EARLY_STOPPED.
[INFO 10-12 05:05:24] ax.api.client: Generated new trial 15 with parameters {'x1': 0.061146, 'x2': 0.168429, 'x3': 1.0, 'x4': 0.0, 'x5': 0.365378, 'x6': 1.0} using GenerationNode MBM.
[INFO 10-12 05:05:24] ax.api.client: Generated new trial 16 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 0.749632, 'x4': 0.0, 'x5': 0.364407, 'x6': 1.0} using GenerationNode MBM.
[INFO 10-12 05:05:24] ax.api.client: Generated new trial 17 with parameters {'x1': 1.0, 'x2': 0.0, 'x3': 1.0, 'x4': 0.0, 'x5': 0.351984, 'x6': 1.0} using GenerationNode MBM.
[INFO 10-12 05:05:27] ax.api.client: Trial 15 marked COMPLETED.
[INFO 10-12 05:05:28] ax.early_stopping.strategies.percentile: Early stopping trial 16: Trial objective value 3.2672712125755123 is worse than 50.0-th percentile (3.04280231969693) across comparable trials..
[INFO 10-12 05:05:28] ax.api.client: Trial 16 should be stopped early: Trial objective value 3.2672712125755123 is worse than 50.0-th percentile (3.04280231969693) across comparable trials.
[INFO 10-12 05:05:28] ax.api.client: Trial 16 marked EARLY_STOPPED.
[INFO 10-12 05:05:28] ax.early_stopping.strategies.percentile: Early stopping trial 17: Trial objective value 3.2046938197080546 is worse than 50.0-th percentile (3.058935811841095) across comparable trials..
[INFO 10-12 05:05:28] ax.api.client: Trial 17 should be stopped early: Trial objective value 3.2046938197080546 is worse than 50.0-th percentile (3.058935811841095) across comparable trials.
[INFO 10-12 05:05:28] ax.api.client: Trial 17 marked EARLY_STOPPED.
[INFO 10-12 05:05:29] ax.api.client: Generated new trial 18 with parameters {'x1': 1.0, 'x2': 0.788651, 'x3': 0.611847, 'x4': 0.0, 'x5': 0.096319, 'x6': 1.0} using GenerationNode MBM.
[INFO 10-12 05:05:29] ax.api.client: Generated new trial 19 with parameters {'x1': 0.0, 'x2': 0.0, 'x3': 0.556424, 'x4': 0.0, 'x5': 0.153423, 'x6': 1.0} using GenerationNode MBM.
[INFO 10-12 05:05:29] ax.api.client: Generated new trial 20 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 0.602961, 'x4': 0.0, 'x5': 0.036605, 'x6': 1.0} using GenerationNode MBM.
[INFO 10-12 05:05:29] ax.early_stopping.strategies.percentile: Early stopping trial 18: Trial objective value 3.188141773320342 is worse than 50.0-th percentile (3.0750693039852606) across comparable trials..
[INFO 10-12 05:05:29] ax.api.client: Trial 18 should be stopped early: Trial objective value 3.188141773320342 is worse than 50.0-th percentile (3.0750693039852606) across comparable trials.
[INFO 10-12 05:05:29] ax.api.client: Trial 18 marked EARLY_STOPPED.
[INFO 10-12 05:05:33] ax.api.client: Trial 19 marked COMPLETED.
[INFO 10-12 05:05:33] ax.early_stopping.strategies.percentile: Early stopping trial 20: Trial objective value 3.288379541450405 is worse than 50.0-th percentile (3.0750693039852606) across comparable trials..
[INFO 10-12 05:05:33] ax.api.client: Trial 20 should be stopped early: Trial objective value 3.288379541450405 is worse than 50.0-th percentile (3.0750693039852606) across comparable trials.
[INFO 10-12 05:05:33] ax.api.client: Trial 20 marked EARLY_STOPPED.
[INFO 10-12 05:05:34] ax.api.client: Generated new trial 21 with parameters {'x1': 0.077414, 'x2': 1.0, 'x3': 0.76588, 'x4': 0.248323, 'x5': 0.0, 'x6': 1.0} using GenerationNode MBM.
[INFO 10-12 05:05:34] ax.api.client: Generated new trial 22 with parameters {'x1': 1.0, 'x2': 0.0, 'x3': 0.78993, 'x4': 0.2569, 'x5': 0.0, 'x6': 1.0} using GenerationNode MBM.
[INFO 10-12 05:05:34] ax.api.client: Generated new trial 23 with parameters {'x1': 1.0, 'x2': 1.0, 'x3': 0.745616, 'x4': 0.234137, 'x5': 0.0, 'x6': 1.0} using GenerationNode MBM.
[INFO 10-12 05:05:35] ax.early_stopping.strategies.percentile: Early stopping trial 21: Trial objective value 3.2717533683882873 is worse than 50.0-th percentile (3.0904577756953704) across comparable trials..
[INFO 10-12 05:05:35] ax.api.client: Trial 21 should be stopped early: Trial objective value 3.2717533683882873 is worse than 50.0-th percentile (3.0904577756953704) across comparable trials.
[INFO 10-12 05:05:35] ax.api.client: Trial 21 marked EARLY_STOPPED.
[INFO 10-12 05:05:35] ax.early_stopping.strategies.percentile: Early stopping trial 22: Trial objective value 2.966720778085125 is worse than 50.0-th percentile (2.7782501313086687) across comparable trials..
[INFO 10-12 05:05:35] ax.api.client: Trial 22 should be stopped early: Trial objective value 2.966720778085125 is worse than 50.0-th percentile (2.7782501313086687) across comparable trials.
[INFO 10-12 05:05:35] ax.api.client: Trial 22 marked EARLY_STOPPED.
[INFO 10-12 05:05:35] ax.early_stopping.strategies.percentile: Early stopping trial 23: Trial objective value 3.2889862456854493 is worse than 50.0-th percentile (3.1050352746202696) across comparable trials..
[INFO 10-12 05:05:35] ax.api.client: Trial 23 should be stopped early: Trial objective value 3.2889862456854493 is worse than 50.0-th percentile (3.1050352746202696) across comparable trials.
[INFO 10-12 05:05:35] ax.api.client: Trial 23 marked EARLY_STOPPED.
[INFO 10-12 05:05:37] ax.api.client: Generated new trial 24 with parameters {'x1': 0.0, 'x2': 0.0, 'x3': 0.749599, 'x4': 0.0, 'x5': 0.115083, 'x6': 0.708391} using GenerationNode MBM.
[INFO 10-12 05:05:37] ax.api.client: Generated new trial 25 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 0.0, 'x4': 0.0, 'x5': 0.146799, 'x6': 0.719504} using GenerationNode MBM.
[INFO 10-12 05:05:37] ax.api.client: Generated new trial 26 with parameters {'x1': 0.0, 'x2': 0.0, 'x3': 0.0, 'x4': 0.0, 'x5': 0.287412, 'x6': 0.729348} using GenerationNode MBM.
[INFO 10-12 05:05:41] ax.api.client: Trial 24 marked COMPLETED.
[INFO 10-12 05:05:41] ax.early_stopping.strategies.percentile: Early stopping trial 25: Trial objective value 3.277298925414536 is worse than 50.0-th percentile (3.1050352746202696) across comparable trials..
[INFO 10-12 05:05:41] ax.api.client: Trial 25 should be stopped early: Trial objective value 3.277298925414536 is worse than 50.0-th percentile (3.1050352746202696) across comparable trials.
[INFO 10-12 05:05:41] ax.api.client: Trial 25 marked EARLY_STOPPED.
[INFO 10-12 05:05:44] ax.api.client: Trial 26 marked COMPLETED.
[INFO 10-12 05:05:46] ax.api.client: Generated new trial 27 with parameters {'x1': 0.350026, 'x2': 1.0, 'x3': 0.0, 'x4': 0.0, 'x5': 0.008206, 'x6': 0.892041} using GenerationNode MBM.
[INFO 10-12 05:05:46] ax.api.client: Generated new trial 28 with parameters {'x1': 1.0, 'x2': 0.808347, 'x3': 0.0, 'x4': 0.0, 'x5': 0.148417, 'x6': 0.815312} using GenerationNode MBM.
[INFO 10-12 05:05:46] ax.api.client: Generated new trial 29 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 1.0, 'x4': 0.07237, 'x5': 0.0, 'x6': 0.908594} using GenerationNode MBM.
[INFO 10-12 05:05:46] ax.early_stopping.strategies.percentile: Early stopping trial 27: Trial objective value 3.31016207009424 is worse than 50.0-th percentile (3.1050352746202696) across comparable trials..
[INFO 10-12 05:05:46] ax.api.client: Trial 27 should be stopped early: Trial objective value 3.31016207009424 is worse than 50.0-th percentile (3.1050352746202696) across comparable trials.
[INFO 10-12 05:05:46] ax.api.client: Trial 27 marked EARLY_STOPPED.
[INFO 10-12 05:05:46] ax.early_stopping.strategies.percentile: Early stopping trial 28: Trial objective value 3.3003388447343274 is worse than 50.0-th percentile (3.10584624740548) across comparable trials..
[INFO 10-12 05:05:46] ax.api.client: Trial 28 should be stopped early: Trial objective value 3.3003388447343274 is worse than 50.0-th percentile (3.10584624740548) across comparable trials.
[INFO 10-12 05:05:46] ax.api.client: Trial 28 marked EARLY_STOPPED.
[INFO 10-12 05:05:46] ax.early_stopping.strategies.percentile: Early stopping trial 29: Trial objective value 3.294426399909312 is worse than 50.0-th percentile (3.1196450567613416) across comparable trials..
[INFO 10-12 05:05:46] ax.api.client: Trial 29 should be stopped early: Trial objective value 3.294426399909312 is worse than 50.0-th percentile (3.1196450567613416) across comparable trials.
[INFO 10-12 05:05:46] ax.api.client: Trial 29 marked EARLY_STOPPED.
[INFO 10-12 05:05:48] ax.api.client: Generated new trial 30 with parameters {'x1': 0.268931, 'x2': 1.0, 'x3': 0.0, 'x4': 0.038624, 'x5': 0.004666, 'x6': 0.876752} using GenerationNode MBM.
[INFO 10-12 05:05:48] ax.api.client: Generated new trial 31 with parameters {'x1': 1.0, 'x2': 1.0, 'x3': 0.0, 'x4': 0.0, 'x5': 0.146689, 'x6': 0.830708} using GenerationNode MBM.
[INFO 10-12 05:05:48] ax.api.client: Generated new trial 32 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 1.0, 'x4': 0.163288, 'x5': 0.0, 'x6': 0.939755} using GenerationNode MBM.
[INFO 10-12 05:05:48] ax.early_stopping.strategies.percentile: Early stopping trial 30: Trial objective value 3.306630805507493 is worse than 50.0-th percentile (3.1334438661172035) across comparable trials..
[INFO 10-12 05:05:48] ax.api.client: Trial 30 should be stopped early: Trial objective value 3.306630805507493 is worse than 50.0-th percentile (3.1334438661172035) across comparable trials.
[INFO 10-12 05:05:48] ax.api.client: Trial 30 marked EARLY_STOPPED.
[INFO 10-12 05:05:48] ax.early_stopping.strategies.percentile: Early stopping trial 31: Trial objective value 3.3144970712784185 is worse than 50.0-th percentile (3.1461837223974705) across comparable trials..
[INFO 10-12 05:05:48] ax.api.client: Trial 31 should be stopped early: Trial objective value 3.3144970712784185 is worse than 50.0-th percentile (3.1461837223974705) across comparable trials.
[INFO 10-12 05:05:48] ax.api.client: Trial 31 marked EARLY_STOPPED.
[INFO 10-12 05:05:48] ax.early_stopping.strategies.percentile: Early stopping trial 32: Trial objective value 3.2915999014883908 is worse than 50.0-th percentile (3.1589235786777374) across comparable trials..
[INFO 10-12 05:05:48] ax.api.client: Trial 32 should be stopped early: Trial objective value 3.2915999014883908 is worse than 50.0-th percentile (3.1589235786777374) across comparable trials.
[INFO 10-12 05:05:48] ax.api.client: Trial 32 marked EARLY_STOPPED.
[INFO 10-12 05:05:49] ax.api.client: Generated new trial 33 with parameters {'x1': 0.02635, 'x2': 1.0, 'x3': 0.0, 'x4': 0.057689, 'x5': 0.020905, 'x6': 0.868279} using GenerationNode MBM.
[INFO 10-12 05:05:49] ax.api.client: Generated new trial 34 with parameters {'x1': 1.0, 'x2': 1.0, 'x3': 0.0, 'x4': 0.006212, 'x5': 0.06857, 'x6': 0.849839} using GenerationNode MBM.
[INFO 10-12 05:05:49] ax.api.client: Generated new trial 35 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 1.0, 'x4': 0.18294, 'x5': 0.0, 'x6': 0.915} using GenerationNode MBM.
[INFO 10-12 05:05:50] ax.early_stopping.strategies.percentile: Early stopping trial 33: Trial objective value 3.304089127347284 is worse than 50.0-th percentile (3.1735326759990397) across comparable trials..
[INFO 10-12 05:05:50] ax.api.client: Trial 33 should be stopped early: Trial objective value 3.304089127347284 is worse than 50.0-th percentile (3.1735326759990397) across comparable trials.
[INFO 10-12 05:05:50] ax.api.client: Trial 33 marked EARLY_STOPPED.
[INFO 10-12 05:05:50] ax.early_stopping.strategies.percentile: Early stopping trial 34: Trial objective value 3.3176046635406893 is worse than 50.0-th percentile (3.188141773320342) across comparable trials..
[INFO 10-12 05:05:50] ax.api.client: Trial 34 should be stopped early: Trial objective value 3.3176046635406893 is worse than 50.0-th percentile (3.188141773320342) across comparable trials.
[INFO 10-12 05:05:50] ax.api.client: Trial 34 marked EARLY_STOPPED.
[INFO 10-12 05:05:50] ax.early_stopping.strategies.percentile: Early stopping trial 35: Trial objective value 3.291037696916534 is worse than 50.0-th percentile (3.196417796514198) across comparable trials..
[INFO 10-12 05:05:50] ax.api.client: Trial 35 should be stopped early: Trial objective value 3.291037696916534 is worse than 50.0-th percentile (3.196417796514198) across comparable trials.
[INFO 10-12 05:05:50] ax.api.client: Trial 35 marked EARLY_STOPPED.
[INFO 10-12 05:05:51] ax.api.client: Generated new trial 36 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 0.0, 'x4': 0.066081, 'x5': 0.035541, 'x6': 0.860339} using GenerationNode MBM.
[INFO 10-12 05:05:51] ax.api.client: Generated new trial 37 with parameters {'x1': 1.0, 'x2': 1.0, 'x3': 0.0, 'x4': 0.012007, 'x5': 0.081174, 'x6': 0.843911} using GenerationNode MBM.
[INFO 10-12 05:05:51] ax.api.client: Generated new trial 38 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 1.0, 'x4': 0.167727, 'x5': 0.0, 'x6': 0.906763} using GenerationNode MBM.
[INFO 10-12 05:05:52] ax.early_stopping.strategies.percentile: Early stopping trial 36: Trial objective value 3.3008885146330136 is worse than 50.0-th percentile (3.2046938197080546) across comparable trials..
[INFO 10-12 05:05:52] ax.api.client: Trial 36 should be stopped early: Trial objective value 3.3008885146330136 is worse than 50.0-th percentile (3.2046938197080546) across comparable trials.
[INFO 10-12 05:05:52] ax.api.client: Trial 36 marked EARLY_STOPPED.
[INFO 10-12 05:05:52] ax.early_stopping.strategies.percentile: Early stopping trial 37: Trial objective value 3.316914585492188 is worse than 50.0-th percentile (3.2104938293353533) across comparable trials..
[INFO 10-12 05:05:52] ax.api.client: Trial 37 should be stopped early: Trial objective value 3.316914585492188 is worse than 50.0-th percentile (3.2104938293353533) across comparable trials.
[INFO 10-12 05:05:52] ax.api.client: Trial 37 marked EARLY_STOPPED.
[INFO 10-12 05:05:52] ax.early_stopping.strategies.percentile: Early stopping trial 38: Trial objective value 3.2914378357144445 is worse than 50.0-th percentile (3.216293838962652) across comparable trials..
[INFO 10-12 05:05:52] ax.api.client: Trial 38 should be stopped early: Trial objective value 3.2914378357144445 is worse than 50.0-th percentile (3.216293838962652) across comparable trials.
[INFO 10-12 05:05:52] ax.api.client: Trial 38 marked EARLY_STOPPED.
[INFO 10-12 05:05:54] ax.api.client: Generated new trial 39 with parameters {'x1': 0.0, 'x2': 0.0, 'x3': 1.0, 'x4': 0.224031, 'x5': 0.342665, 'x6': 0.770337} using GenerationNode MBM.
[INFO 10-12 05:05:54] ax.api.client: Generated new trial 40 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 1.0, 'x4': 0.220425, 'x5': 0.340552, 'x6': 0.785289} using GenerationNode MBM.
[INFO 10-12 05:05:54] ax.api.client: Generated new trial 41 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 1.0, 'x4': 1.0, 'x5': 1.0, 'x6': 0.0} using GenerationNode MBM.
[INFO 10-12 05:05:58] ax.api.client: Trial 39 marked COMPLETED.
[INFO 10-12 05:05:58] ax.early_stopping.strategies.percentile: Early stopping trial 40: Trial objective value 3.232187366835228 is worse than 50.0-th percentile (3.216293838962652) across comparable trials..
[INFO 10-12 05:05:58] ax.api.client: Trial 40 should be stopped early: Trial objective value 3.232187366835228 is worse than 50.0-th percentile (3.216293838962652) across comparable trials.
[INFO 10-12 05:05:58] ax.api.client: Trial 40 marked EARLY_STOPPED.
[INFO 10-12 05:05:59] ax.early_stopping.strategies.percentile: Early stopping trial 41: Trial objective value 3.2957661652743133 is worse than 50.0-th percentile (3.22424060289894) across comparable trials..
[INFO 10-12 05:05:59] ax.api.client: Trial 41 should be stopped early: Trial objective value 3.2957661652743133 is worse than 50.0-th percentile (3.22424060289894) across comparable trials.
[INFO 10-12 05:05:59] ax.api.client: Trial 41 marked EARLY_STOPPED.
[INFO 10-12 05:06:00] ax.api.client: Generated new trial 42 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 0.0, 'x4': 0.205988, 'x5': 0.170499, 'x6': 0.83184} using GenerationNode MBM.
[INFO 10-12 05:06:00] ax.api.client: Generated new trial 43 with parameters {'x1': 1.0, 'x2': 1.0, 'x3': 1.0, 'x4': 0.209791, 'x5': 0.164295, 'x6': 0.836504} using GenerationNode MBM.
[INFO 10-12 05:06:00] ax.api.client: Generated new trial 44 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 0.0, 'x4': 1.0, 'x5': 1.0, 'x6': 0.0} using GenerationNode MBM.
[INFO 10-12 05:06:00] ax.early_stopping.strategies.percentile: Early stopping trial 42: Trial objective value 3.2339396461644863 is worse than 50.0-th percentile (3.232187366835228) across comparable trials..
[INFO 10-12 05:06:00] ax.api.client: Trial 42 should be stopped early: Trial objective value 3.2339396461644863 is worse than 50.0-th percentile (3.232187366835228) across comparable trials.
[INFO 10-12 05:06:00] ax.api.client: Trial 42 marked EARLY_STOPPED.
[INFO 10-12 05:06:00] ax.early_stopping.strategies.percentile: Early stopping trial 43: Trial objective value 3.2961764519228036 is worse than 50.0-th percentile (3.233063506499857) across comparable trials..
[INFO 10-12 05:06:00] ax.api.client: Trial 43 should be stopped early: Trial objective value 3.2961764519228036 is worse than 50.0-th percentile (3.233063506499857) across comparable trials.
[INFO 10-12 05:06:00] ax.api.client: Trial 43 marked EARLY_STOPPED.
[INFO 10-12 05:06:01] ax.early_stopping.strategies.percentile: Early stopping trial 44: Trial objective value 3.2967305906390476 is worse than 50.0-th percentile (3.2339396461644863) across comparable trials..
[INFO 10-12 05:06:01] ax.api.client: Trial 44 should be stopped early: Trial objective value 3.2967305906390476 is worse than 50.0-th percentile (3.2339396461644863) across comparable trials.
[INFO 10-12 05:06:01] ax.api.client: Trial 44 marked EARLY_STOPPED.
[INFO 10-12 05:06:02] ax.api.client: Generated new trial 45 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 0.191121, 'x4': 0.152576, 'x5': 0.29497, 'x6': 0.790555} using GenerationNode MBM.
[INFO 10-12 05:06:02] ax.api.client: Generated new trial 46 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 0.0, 'x4': 0.79824, 'x5': 0.0, 'x6': 0.0} using GenerationNode MBM.
[INFO 10-12 05:06:02] ax.api.client: Generated new trial 47 with parameters {'x1': 1.0, 'x2': 1.0, 'x3': 1.0, 'x4': 0.139933, 'x5': 0.292383, 'x6': 0.78923} using GenerationNode MBM.
[INFO 10-12 05:06:03] ax.early_stopping.strategies.percentile: Early stopping trial 45: Trial objective value 3.0418979303579246 is worse than 50.0-th percentile (2.748858685066134) across comparable trials..
[INFO 10-12 05:06:03] ax.api.client: Trial 45 should be stopped early: Trial objective value 3.0418979303579246 is worse than 50.0-th percentile (2.748858685066134) across comparable trials.
[INFO 10-12 05:06:03] ax.api.client: Trial 45 marked EARLY_STOPPED.
[INFO 10-12 05:06:03] ax.early_stopping.strategies.percentile: Early stopping trial 46: Trial objective value 3.083304457416975 is worse than 50.0-th percentile (2.7697981404380756) across comparable trials..
[INFO 10-12 05:06:03] ax.api.client: Trial 46 should be stopped early: Trial objective value 3.083304457416975 is worse than 50.0-th percentile (2.7697981404380756) across comparable trials.
[INFO 10-12 05:06:03] ax.api.client: Trial 46 marked EARLY_STOPPED.
[INFO 10-12 05:06:03] ax.early_stopping.strategies.percentile: Early stopping trial 47: Trial objective value 3.298845929367043 is worse than 50.0-th percentile (3.233063506499857) across comparable trials..
[INFO 10-12 05:06:03] ax.api.client: Trial 47 should be stopped early: Trial objective value 3.298845929367043 is worse than 50.0-th percentile (3.233063506499857) across comparable trials.
[INFO 10-12 05:06:03] ax.api.client: Trial 47 marked EARLY_STOPPED.
[INFO 10-12 05:06:04] ax.api.client: Generated new trial 48 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 0.0, 'x4': 0.203012, 'x5': 0.198286, 'x6': 0.826911} using GenerationNode MBM.
[INFO 10-12 05:06:04] ax.api.client: Generated new trial 49 with parameters {'x1': 1.0, 'x2': 1.0, 'x3': 0.0, 'x4': 0.195558, 'x5': 0.227855, 'x6': 0.812139} using GenerationNode MBM.
[INFO 10-12 05:06:04] ax.api.client: Generated new trial 50 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 1.0, 'x4': 0.235361, 'x5': 0.0, 'x6': 0.909535} using GenerationNode MBM.
[INFO 10-12 05:06:05] ax.early_stopping.strategies.percentile: Early stopping trial 48: Trial objective value 3.0850615527789427 is worse than 50.0-th percentile (2.7782501313086687) across comparable trials..
[INFO 10-12 05:06:05] ax.api.client: Trial 48 should be stopped early: Trial objective value 3.0850615527789427 is worse than 50.0-th percentile (2.7782501313086687) across comparable trials.
[INFO 10-12 05:06:05] ax.api.client: Trial 48 marked EARLY_STOPPED.
[INFO 10-12 05:06:05] ax.early_stopping.strategies.percentile: Early stopping trial 49: Trial objective value 3.2992513469411398 is worse than 50.0-th percentile (3.233063506499857) across comparable trials..
[INFO 10-12 05:06:05] ax.api.client: Trial 49 should be stopped early: Trial objective value 3.2992513469411398 is worse than 50.0-th percentile (3.233063506499857) across comparable trials.
[INFO 10-12 05:06:05] ax.api.client: Trial 49 marked EARLY_STOPPED.
[INFO 10-12 05:06:05] ax.early_stopping.strategies.percentile: Early stopping trial 50: Trial objective value 3.2900905024311786 is worse than 50.0-th percentile (3.2339396461644863) across comparable trials..
[INFO 10-12 05:06:05] ax.api.client: Trial 50 should be stopped early: Trial objective value 3.2900905024311786 is worse than 50.0-th percentile (3.2339396461644863) across comparable trials.
[INFO 10-12 05:06:05] ax.api.client: Trial 50 marked EARLY_STOPPED.
[WARNING 10-12 05:06:08] ax.generation_strategy.generation_node: gen failed with error GenerationStrategy exceeded MAX_GEN_ATTEMPTS of 5 while trying to generate a unique parameterization. This indicates that the search space has likely been fully explored, or that the sweep has converged., switching to fallback model with generator_enum Generators.SOBOL
[INFO 10-12 05:06:08] ax.api.client: Generated new trial 51 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 0.0, 'x4': 0.204881, 'x5': 0.222437, 'x6': 0.825388} using GenerationNode MBM.
[INFO 10-12 05:06:08] ax.api.client: Generated new trial 52 with parameters {'x1': 1.0, 'x2': 1.0, 'x3': 1.0, 'x4': 0.204141, 'x5': 0.231726, 'x6': 0.823064} using GenerationNode MBM.
[INFO 10-12 05:06:08] ax.api.client: Generated new trial 53 with parameters {'x1': 0.810142, 'x2': 0.889322, 'x3': 0.464992, 'x4': 0.413748, 'x5': 0.417588, 'x6': 0.667784} using GenerationNode MBM.
[INFO 10-12 05:06:08] ax.early_stopping.strategies.percentile: Early stopping trial 51: Trial objective value 3.0763010526648746 is worse than 50.0-th percentile (2.786702122179262) across comparable trials..
[INFO 10-12 05:06:08] ax.api.client: Trial 51 should be stopped early: Trial objective value 3.0763010526648746 is worse than 50.0-th percentile (2.786702122179262) across comparable trials.
[INFO 10-12 05:06:08] ax.api.client: Trial 51 marked EARLY_STOPPED.
[INFO 10-12 05:06:09] ax.early_stopping.strategies.percentile: Early stopping trial 52: Trial objective value 3.2953089060387337 is worse than 50.0-th percentile (3.2339396461644863) across comparable trials..
[INFO 10-12 05:06:09] ax.api.client: Trial 52 should be stopped early: Trial objective value 3.2953089060387337 is worse than 50.0-th percentile (3.2339396461644863) across comparable trials.
[INFO 10-12 05:06:09] ax.api.client: Trial 52 marked EARLY_STOPPED.
[INFO 10-12 05:06:09] ax.early_stopping.strategies.percentile: Early stopping trial 53: Trial objective value 3.0742231466542544 is worse than 50.0-th percentile (2.8407314909377614) across comparable trials..
[INFO 10-12 05:06:09] ax.api.client: Trial 53 should be stopped early: Trial objective value 3.0742231466542544 is worse than 50.0-th percentile (2.8407314909377614) across comparable trials.
[INFO 10-12 05:06:09] ax.api.client: Trial 53 marked EARLY_STOPPED.
[INFO 10-12 05:06:12] ax.api.client: Generated new trial 54 with parameters {'x1': 0.0, 'x2': 0.293696, 'x3': 1.0, 'x4': 1.0, 'x5': 0.0, 'x6': 0.715458} using GenerationNode MBM.
[INFO 10-12 05:06:12] ax.api.client: Generated new trial 55 with parameters {'x1': 1.0, 'x2': 0.289205, 'x3': 1.0, 'x4': 1.0, 'x5': 0.0, 'x6': 0.703032} using GenerationNode MBM.
[INFO 10-12 05:06:12] ax.api.client: Generated new trial 56 with parameters {'x1': 0.0, 'x2': 0.291638, 'x3': 1.0, 'x4': 0.0, 'x5': 0.0, 'x6': 0.704859} using GenerationNode MBM.
[INFO 10-12 05:06:12] ax.early_stopping.strategies.percentile: Early stopping trial 54: Trial objective value 2.9995330359897614 is worse than 50.0-th percentile (2.8947608596962615) across comparable trials..
[INFO 10-12 05:06:12] ax.api.client: Trial 54 should be stopped early: Trial objective value 2.9995330359897614 is worse than 50.0-th percentile (2.8947608596962615) across comparable trials.
[INFO 10-12 05:06:12] ax.api.client: Trial 54 marked EARLY_STOPPED.
[INFO 10-12 05:06:13] ax.early_stopping.strategies.percentile: Early stopping trial 55: Trial objective value 3.0246536828255337 is worse than 50.0-th percentile (2.900029827821628) across comparable trials..
[INFO 10-12 05:06:13] ax.api.client: Trial 55 should be stopped early: Trial objective value 3.0246536828255337 is worse than 50.0-th percentile (2.900029827821628) across comparable trials.
[INFO 10-12 05:06:13] ax.api.client: Trial 55 marked EARLY_STOPPED.
[INFO 10-12 05:06:13] ax.early_stopping.strategies.percentile: Early stopping trial 56: Trial objective value 2.776809883703673 is worse than 50.0-th percentile (2.6023883476103333) across comparable trials..
[INFO 10-12 05:06:13] ax.api.client: Trial 56 should be stopped early: Trial objective value 2.776809883703673 is worse than 50.0-th percentile (2.6023883476103333) across comparable trials.
[INFO 10-12 05:06:13] ax.api.client: Trial 56 marked EARLY_STOPPED.
[INFO 10-12 05:06:14] ax.api.client: Generated new trial 57 with parameters {'x1': 0.0, 'x2': 0.28315, 'x3': 1.0, 'x4': 1.0, 'x5': 0.405767, 'x6': 0.704439} using GenerationNode MBM.
[INFO 10-12 05:06:14] ax.api.client: Generated new trial 58 with parameters {'x1': 1.0, 'x2': 0.286236, 'x3': 1.0, 'x4': 0.0, 'x5': 0.418607, 'x6': 0.706036} using GenerationNode MBM.
[INFO 10-12 05:06:14] ax.api.client: Generated new trial 59 with parameters {'x1': 1.0, 'x2': 0.279998, 'x3': 1.0, 'x4': 1.0, 'x5': 0.286044, 'x6': 0.687713} using GenerationNode MBM.
[INFO 10-12 05:06:15] ax.early_stopping.strategies.percentile: Early stopping trial 57: Trial objective value 3.231306416991417 is worse than 50.0-th percentile (3.226935746760147) across comparable trials..
[INFO 10-12 05:06:15] ax.api.client: Trial 57 should be stopped early: Trial objective value 3.231306416991417 is worse than 50.0-th percentile (3.226935746760147) across comparable trials.
[INFO 10-12 05:06:15] ax.api.client: Trial 57 marked EARLY_STOPPED.
[INFO 10-12 05:06:15] ax.early_stopping.strategies.percentile: Early stopping trial 58: Trial objective value 3.0226041837872026 is worse than 50.0-th percentile (2.9038197808672637) across comparable trials..
[INFO 10-12 05:06:15] ax.api.client: Trial 58 should be stopped early: Trial objective value 3.0226041837872026 is worse than 50.0-th percentile (2.9038197808672637) across comparable trials.
[INFO 10-12 05:06:15] ax.api.client: Trial 58 marked EARLY_STOPPED.
[INFO 10-12 05:06:15] ax.early_stopping.strategies.percentile: Early stopping trial 59: Trial objective value 3.0704586813906203 is worse than 50.0-th percentile (2.905298795946995) across comparable trials..
[INFO 10-12 05:06:15] ax.api.client: Trial 59 should be stopped early: Trial objective value 3.0704586813906203 is worse than 50.0-th percentile (2.905298795946995) across comparable trials.
[INFO 10-12 05:06:15] ax.api.client: Trial 59 marked EARLY_STOPPED.
[INFO 10-12 05:06:17] ax.api.client: Generated new trial 60 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 0.483388, 'x4': 0.149106, 'x5': 0.303706, 'x6': 0.785781} using GenerationNode MBM.
[INFO 10-12 05:06:17] ax.api.client: Generated new trial 61 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 1.0, 'x4': 0.793894, 'x5': 0.0, 'x6': 0.0} using GenerationNode MBM.
[INFO 10-12 05:06:17] ax.api.client: Generated new trial 62 with parameters {'x1': 1.0, 'x2': 1.0, 'x3': 1.0, 'x4': 0.131196, 'x5': 0.297311, 'x6': 0.782251} using GenerationNode MBM.
[INFO 10-12 05:06:17] ax.early_stopping.strategies.percentile: Early stopping trial 60: Trial objective value 3.000608957841883 is worse than 50.0-th percentile (2.9214322880911605) across comparable trials..
[INFO 10-12 05:06:17] ax.api.client: Trial 60 should be stopped early: Trial objective value 3.000608957841883 is worse than 50.0-th percentile (2.9214322880911605) across comparable trials.
[INFO 10-12 05:06:17] ax.api.client: Trial 60 marked EARLY_STOPPED.
[INFO 10-12 05:06:17] ax.early_stopping.strategies.percentile: Early stopping trial 61: Trial objective value 3.0774390972862995 is worse than 50.0-th percentile (2.937565780235326) across comparable trials..
[INFO 10-12 05:06:17] ax.api.client: Trial 61 should be stopped early: Trial objective value 3.0774390972862995 is worse than 50.0-th percentile (2.937565780235326) across comparable trials.
[INFO 10-12 05:06:17] ax.api.client: Trial 61 marked EARLY_STOPPED.
[INFO 10-12 05:06:17] ax.early_stopping.strategies.percentile: Early stopping trial 62: Trial objective value 3.299517886257113 is worse than 50.0-th percentile (3.2208079811669097) across comparable trials..
[INFO 10-12 05:06:17] ax.api.client: Trial 62 should be stopped early: Trial objective value 3.299517886257113 is worse than 50.0-th percentile (3.2208079811669097) across comparable trials.
[INFO 10-12 05:06:17] ax.api.client: Trial 62 marked EARLY_STOPPED.
[INFO 10-12 05:06:19] ax.api.client: Generated new trial 63 with parameters {'x1': 0.0, 'x2': 0.283487, 'x3': 1.0, 'x4': 1.0, 'x5': 0.407921, 'x6': 0.71388} using GenerationNode MBM.
[INFO 10-12 05:06:19] ax.api.client: Generated new trial 64 with parameters {'x1': 1.0, 'x2': 0.283882, 'x3': 1.0, 'x4': 0.0, 'x5': 0.415103, 'x6': 0.717018} using GenerationNode MBM.
[INFO 10-12 05:06:19] ax.api.client: Generated new trial 65 with parameters {'x1': 1.0, 'x2': 0.280762, 'x3': 1.0, 'x4': 1.0, 'x5': 0.2924, 'x6': 0.691238} using GenerationNode MBM.
[INFO 10-12 05:06:20] ax.early_stopping.strategies.percentile: Early stopping trial 63: Trial objective value 3.225595167727201 is worse than 50.0-th percentile (3.2216865288478935) across comparable trials..
[INFO 10-12 05:06:20] ax.api.client: Trial 63 should be stopped early: Trial objective value 3.225595167727201 is worse than 50.0-th percentile (3.2216865288478935) across comparable trials.
[INFO 10-12 05:06:20] ax.api.client: Trial 63 marked EARLY_STOPPED.
[INFO 10-12 05:06:20] ax.early_stopping.strategies.percentile: Early stopping trial 64: Trial objective value 3.01354052810781 is worse than 50.0-th percentile (2.952143279160225) across comparable trials..
[INFO 10-12 05:06:20] ax.api.client: Trial 64 should be stopped early: Trial objective value 3.01354052810781 is worse than 50.0-th percentile (2.952143279160225) across comparable trials.
[INFO 10-12 05:06:20] ax.api.client: Trial 64 marked EARLY_STOPPED.
[INFO 10-12 05:06:20] ax.early_stopping.strategies.percentile: Early stopping trial 65: Trial objective value 3.0689400448970017 is worse than 50.0-th percentile (2.966720778085125) across comparable trials..
[INFO 10-12 05:06:20] ax.api.client: Trial 65 should be stopped early: Trial objective value 3.0689400448970017 is worse than 50.0-th percentile (2.966720778085125) across comparable trials.
[INFO 10-12 05:06:20] ax.api.client: Trial 65 marked EARLY_STOPPED.
[INFO 10-12 05:06:23] ax.api.client: Generated new trial 66 with parameters {'x1': 0.0, 'x2': 0.284598, 'x3': 1.0, 'x4': 1.0, 'x5': 0.421342, 'x6': 0.701972} using GenerationNode MBM.
[INFO 10-12 05:06:23] ax.api.client: Generated new trial 67 with parameters {'x1': 1.0, 'x2': 0.283834, 'x3': 1.0, 'x4': 0.0, 'x5': 0.42276, 'x6': 0.705064} using GenerationNode MBM.
[INFO 10-12 05:06:23] ax.api.client: Generated new trial 68 with parameters {'x1': 0.0, 'x2': 0.272128, 'x3': 1.0, 'x4': 0.0, 'x5': 0.536195, 'x6': 0.669368} using GenerationNode MBM.
[INFO 10-12 05:06:23] ax.early_stopping.strategies.percentile: Early stopping trial 66: Trial objective value 3.2392121847700754 is worse than 50.0-th percentile (3.2208079811669097) across comparable trials..
[INFO 10-12 05:06:23] ax.api.client: Trial 66 should be stopped early: Trial objective value 3.2392121847700754 is worse than 50.0-th percentile (3.2208079811669097) across comparable trials.
[INFO 10-12 05:06:23] ax.api.client: Trial 66 marked EARLY_STOPPED.
[INFO 10-12 05:06:23] ax.early_stopping.strategies.percentile: Early stopping trial 67: Trial objective value 3.026483292103228 is worse than 50.0-th percentile (2.983126907037443) across comparable trials..
[INFO 10-12 05:06:23] ax.api.client: Trial 67 should be stopped early: Trial objective value 3.026483292103228 is worse than 50.0-th percentile (2.983126907037443) across comparable trials.
[INFO 10-12 05:06:23] ax.api.client: Trial 67 marked EARLY_STOPPED.
[INFO 10-12 05:06:24] ax.early_stopping.strategies.percentile: Early stopping trial 68: Trial objective value 2.8005827766599922 is worse than 50.0-th percentile (2.623327802982275) across comparable trials..
[INFO 10-12 05:06:24] ax.api.client: Trial 68 should be stopped early: Trial objective value 2.8005827766599922 is worse than 50.0-th percentile (2.623327802982275) across comparable trials.
[INFO 10-12 05:06:24] ax.api.client: Trial 68 marked EARLY_STOPPED.
[INFO 10-12 05:06:27] ax.api.client: Generated new trial 69 with parameters {'x1': 0.0, 'x2': 0.0, 'x3': 0.464057, 'x4': 0.0, 'x5': 0.521489, 'x6': 0.813659} using GenerationNode MBM.
[INFO 10-12 05:06:27] ax.api.client: Generated new trial 70 with parameters {'x1': 0.0, 'x2': 1.0, 'x3': 0.45473, 'x4': 0.0, 'x5': 0.519232, 'x6': 0.810462} using GenerationNode MBM.
[INFO 10-12 05:06:27] ax.api.client: Generated new trial 71 with parameters {'x1': 0.0, 'x2': 0.0, 'x3': 1.0, 'x4': 0.0, 'x5': 0.42825, 'x6': 0.0} using GenerationNode MBM.
[INFO 10-12 05:06:33] ax.api.client: Trial 69 marked COMPLETED.
[INFO 10-12 05:06:34] ax.early_stopping.strategies.percentile: Early stopping trial 70: Trial objective value 3.2378343738769884 is worse than 50.0-th percentile (3.216293838962652) across comparable trials..
[INFO 10-12 05:06:34] ax.api.client: Trial 70 should be stopped early: Trial objective value 3.2378343738769884 is worse than 50.0-th percentile (3.216293838962652) across comparable trials.
[INFO 10-12 05:06:34] ax.api.client: Trial 70 marked EARLY_STOPPED.
[INFO 10-12 05:06:34] ax.early_stopping.strategies.percentile: Early stopping trial 71: Trial objective value 3.3093006081389045 is worse than 50.0-th percentile (3.218550910064781) across comparable trials..
[INFO 10-12 05:06:34] ax.api.client: Trial 71 should be stopped early: Trial objective value 3.3093006081389045 is worse than 50.0-th percentile (3.218550910064781) across comparable trials.
[INFO 10-12 05:06:34] ax.api.client: Trial 71 marked EARLY_STOPPED.
[INFO 10-12 05:06:36] ax.api.client: Generated new trial 72 with parameters {'x1': 0.0, 'x2': 0.327079, 'x3': 1.0, 'x4': 0.0, 'x5': 0.44122, 'x6': 0.788186} using GenerationNode MBM.
[INFO 10-12 05:06:36] ax.api.client: Generated new trial 73 with parameters {'x1': 1.0, 'x2': 0.70921, 'x3': 1.0, 'x4': 0.0, 'x5': 0.294228, 'x6': 0.0} using GenerationNode MBM.
[INFO 10-12 05:06:36] ax.api.client: Generated new trial 74 with parameters {'x1': 1.0, 'x2': 0.323438, 'x3': 1.0, 'x4': 0.0, 'x5': 0.442593, 'x6': 0.789255} using GenerationNode MBM.
[INFO 10-12 05:06:37] ax.early_stopping.strategies.percentile: Early stopping trial 72: Trial objective value 2.47350257570065 is worse than 50.0-th percentile (2.4558020278160244) across comparable trials..
[INFO 10-12 05:06:37] ax.api.client: Trial 72 should be stopped early: Trial objective value 2.47350257570065 is worse than 50.0-th percentile (2.4558020278160244) across comparable trials.
[INFO 10-12 05:06:37] ax.api.client: Trial 72 marked EARLY_STOPPED.
[INFO 10-12 05:06:37] ax.early_stopping.strategies.percentile: Early stopping trial 73: Trial objective value 3.3206551906490707 is worse than 50.0-th percentile (3.218550910064781) across comparable trials..
[INFO 10-12 05:06:37] ax.api.client: Trial 73 should be stopped early: Trial objective value 3.3206551906490707 is worse than 50.0-th percentile (3.218550910064781) across comparable trials.
[INFO 10-12 05:06:37] ax.api.client: Trial 73 marked EARLY_STOPPED.
[INFO 10-12 05:06:38] ax.early_stopping.strategies.percentile: Early stopping trial 74: Trial objective value 2.9834638810991456 is worse than 50.0-th percentile (2.952143279160225) across comparable trials..
[INFO 10-12 05:06:38] ax.api.client: Trial 74 should be stopped early: Trial objective value 2.9834638810991456 is worse than 50.0-th percentile (2.952143279160225) across comparable trials.
[INFO 10-12 05:06:38] ax.api.client: Trial 74 marked EARLY_STOPPED.
[INFO 10-12 05:06:40] ax.api.client: Generated new trial 75 with parameters {'x1': 0.504642, 'x2': 0.270848, 'x3': 1.0, 'x4': 1.0, 'x5': 0.387978, 'x6': 0.756626} using GenerationNode MBM.
[INFO 10-12 05:06:40] ax.api.client: Generated new trial 76 with parameters {'x1': 0.0, 'x2': 0.275154, 'x3': 1.0, 'x4': 0.0, 'x5': 0.39599, 'x6': 0.75736} using GenerationNode MBM.
[INFO 10-12 05:06:40] ax.api.client: Generated new trial 77 with parameters {'x1': 1.0, 'x2': 0.271187, 'x3': 1.0, 'x4': 0.0, 'x5': 0.389502, 'x6': 0.757434} using GenerationNode MBM.
[INFO 10-12 05:06:40] ax.early_stopping.strategies.percentile: Early stopping trial 75: Trial objective value 3.0478438868189883 is worse than 50.0-th percentile (2.966720778085125) across comparable trials..
[INFO 10-12 05:06:40] ax.api.client: Trial 75 should be stopped early: Trial objective value 3.0478438868189883 is worse than 50.0-th percentile (2.966720778085125) across comparable trials.
[INFO 10-12 05:06:40] ax.api.client: Trial 75 marked EARLY_STOPPED.
[INFO 10-12 05:06:47] ax.api.client: Trial 76 marked COMPLETED.
[INFO 10-12 05:06:47] ax.early_stopping.strategies.percentile: Early stopping trial 77: Trial objective value 2.967613342958811 is worse than 50.0-th percentile (2.966720778085125) across comparable trials..
[INFO 10-12 05:06:47] ax.api.client: Trial 77 should be stopped early: Trial objective value 2.967613342958811 is worse than 50.0-th percentile (2.966720778085125) across comparable trials.
[INFO 10-12 05:06:47] ax.api.client: Trial 77 marked EARLY_STOPPED.
[INFO 10-12 05:06:52] ax.api.client: Generated new trial 78 with parameters {'x1': 0.0, 'x2': 0.581803, 'x3': 0.0, 'x4': 0.275639, 'x5': 1.0, 'x6': 1.0} using GenerationNode MBM.
[INFO 10-12 05:06:52] ax.api.client: Generated new trial 79 with parameters {'x1': 0.0, 'x2': 0.636317, 'x3': 0.0, 'x4': 0.283806, 'x5': 0.0, 'x6': 1.0} using GenerationNode MBM.
[INFO 10-12 05:06:52] ax.api.client: Generated new trial 80 with parameters {'x1': 0.0, 'x2': 0.698447, 'x3': 1.0, 'x4': 0.299271, 'x5': 1.0, 'x6': 1.0} using GenerationNode MBM.
[INFO 10-12 05:06:52] ax.early_stopping.strategies.percentile: Early stopping trial 78: Trial objective value 3.321312109662194 is worse than 50.0-th percentile (3.214942621036234) across comparable trials..
[INFO 10-12 05:06:52] ax.api.client: Trial 78 should be stopped early: Trial objective value 3.321312109662194 is worse than 50.0-th percentile (3.214942621036234) across comparable trials.
[INFO 10-12 05:06:52] ax.api.client: Trial 78 marked EARLY_STOPPED.
[INFO 10-12 05:06:52] ax.early_stopping.strategies.percentile: Early stopping trial 79: Trial objective value 3.247398137185191 is worse than 50.0-th percentile (3.215618229999443) across comparable trials..
[INFO 10-12 05:06:52] ax.api.client: Trial 79 should be stopped early: Trial objective value 3.247398137185191 is worse than 50.0-th percentile (3.215618229999443) across comparable trials.
[INFO 10-12 05:06:52] ax.api.client: Trial 79 marked EARLY_STOPPED.
[INFO 10-12 05:06:52] ax.early_stopping.strategies.percentile: Early stopping trial 80: Trial objective value 3.3189988303161018 is worse than 50.0-th percentile (3.216293838962652) across comparable trials..
[INFO 10-12 05:06:52] ax.api.client: Trial 80 should be stopped early: Trial objective value 3.3189988303161018 is worse than 50.0-th percentile (3.216293838962652) across comparable trials.
[INFO 10-12 05:06:52] ax.api.client: Trial 80 marked EARLY_STOPPED.
[INFO 10-12 05:06:55] ax.api.client: Generated new trial 81 with parameters {'x1': 0.0, 'x2': 0.637267, 'x3': 1.0, 'x4': 0.306276, 'x5': 0.0, 'x6': 1.0} using GenerationNode MBM.
[INFO 10-12 05:06:55] ax.api.client: Generated new trial 82 with parameters {'x1': 0.0, 'x2': 0.807545, 'x3': 1.0, 'x4': 0.307704, 'x5': 0.0, 'x6': 1.0} using GenerationNode MBM.
[INFO 10-12 05:06:55] ax.api.client: Generated new trial 83 with parameters {'x1': 1.0, 'x2': 0.573925, 'x3': 1.0, 'x4': 0.308556, 'x5': 1.0, 'x6': 1.0} using GenerationNode MBM.
[INFO 10-12 05:06:55] ax.early_stopping.strategies.percentile: Early stopping trial 81: Trial objective value 2.602379453523953 is worse than 50.0-th percentile (2.59567962332227) across comparable trials..
[INFO 10-12 05:06:55] ax.api.client: Trial 81 should be stopped early: Trial objective value 2.602379453523953 is worse than 50.0-th percentile (2.59567962332227) across comparable trials.
[INFO 10-12 05:06:55] ax.api.client: Trial 81 marked EARLY_STOPPED.
[INFO 10-12 05:06:55] ax.early_stopping.strategies.percentile: Early stopping trial 82: Trial objective value 3.0179456766947577 is worse than 50.0-th percentile (2.966720778085125) across comparable trials..
[INFO 10-12 05:06:55] ax.api.client: Trial 82 should be stopped early: Trial objective value 3.0179456766947577 is worse than 50.0-th percentile (2.966720778085125) across comparable trials.
[INFO 10-12 05:06:55] ax.api.client: Trial 82 marked EARLY_STOPPED.
[INFO 10-12 05:06:56] ax.early_stopping.strategies.percentile: Early stopping trial 83: Trial objective value 3.321058133661577 is worse than 50.0-th percentile (3.215618229999443) across comparable trials..
[INFO 10-12 05:06:56] ax.api.client: Trial 83 should be stopped early: Trial objective value 3.321058133661577 is worse than 50.0-th percentile (3.215618229999443) across comparable trials.
[INFO 10-12 05:06:56] ax.api.client: Trial 83 marked EARLY_STOPPED.
[INFO 10-12 05:06:58] ax.api.client: Generated new trial 84 with parameters {'x1': 0.0, 'x2': 0.636397, 'x3': 1.0, 'x4': 0.306322, 'x5': 0.0, 'x6': 1.0} using GenerationNode MBM.
[INFO 10-12 05:06:58] ax.api.client: Generated new trial 85 with parameters {'x1': 1.0, 'x2': 0.781149, 'x3': 1.0, 'x4': 0.308449, 'x5': 1.0, 'x6': 1.0} using GenerationNode MBM.
[INFO 10-12 05:06:58] ax.api.client: Generated new trial 86 with parameters {'x1': 1.0, 'x2': 0.553375, 'x3': 1.0, 'x4': 0.306994, 'x5': 1.0, 'x6': 1.0} using GenerationNode MBM.
[INFO 10-12 05:06:59] ax.early_stopping.strategies.percentile: Early stopping trial 84: Trial objective value 2.485165796413682 is worse than 50.0-th percentile (2.4558020278160244) across comparable trials..
[INFO 10-12 05:06:59] ax.api.client: Trial 84 should be stopped early: Trial objective value 2.485165796413682 is worse than 50.0-th percentile (2.4558020278160244) across comparable trials.
[INFO 10-12 05:06:59] ax.api.client: Trial 84 marked EARLY_STOPPED.
[INFO 10-12 05:06:59] ax.early_stopping.strategies.percentile: Early stopping trial 85: Trial objective value 3.321634585361375 is worse than 50.0-th percentile (3.215618229999443) across comparable trials..
[INFO 10-12 05:06:59] ax.api.client: Trial 85 should be stopped early: Trial objective value 3.321634585361375 is worse than 50.0-th percentile (3.215618229999443) across comparable trials.
[INFO 10-12 05:06:59] ax.api.client: Trial 85 marked EARLY_STOPPED.
[INFO 10-12 05:07:00] ax.early_stopping.strategies.percentile: Early stopping trial 86: Trial objective value 3.321002811853987 is worse than 50.0-th percentile (3.216293838962652) across comparable trials..
[INFO 10-12 05:07:00] ax.api.client: Trial 86 should be stopped early: Trial objective value 3.321002811853987 is worse than 50.0-th percentile (3.216293838962652) across comparable trials.
[INFO 10-12 05:07:00] ax.api.client: Trial 86 marked EARLY_STOPPED.

Step 6: Analyze Results

After running trials, you can analyze the results. Most commonly this means extracting the parameterization from the best performing trial you conducted.

best_parameters, prediction, index, name = client.get_best_parameterization()
print("Best Parameters:", best_parameters)
print("Prediction (mean, variance):", prediction)

Output:
Best Parameters: {'x1': 0.23028146273475225, 'x2': 0.4162534138427786, 'x3': 0.6452726719210254, 'x4': 0.14728802601386914, 'x5': 0.3581820475301774, 'x6': 0.8398428676262572}
Prediction (mean, variance): {'hartmann6': (np.float64(-1.7469827768302797), np.float64(0.00024918464054083056))}

Step 7: Compute Analyses

Ax can also produce a number of analyses to help interpret the results of the experiment via client.compute_analyses. Users can manually select which analyses to run, or can allow Ax to select which would be most relevant. In this case Ax selects the following:

Arm Effects Plots show the metric value for each arm on the experiment. Ax produces one plot using values from its internal surrogate model (this can be helpful for seeing the true effect of an arm when evaluations are noisy) and another using the raw metric values as observed.
Summary lists all trials generated along with their parameterizations, observations, and miscellaneous metadata
Sensitivity Analysis Plot shows which parameters have the largest affect on the objective using Sobol Indicies
Slice Plot shows how the model predicts a single parameter effects the objective along with a confidence interval
Contour Plot shows how the model predicts a pair of parameters effects the objective as a 2D surface
Cross Validation helps to visualize how well the surrogate model is able to predict out of sample points

# display=True instructs Ax to sort then render the resulting analyses
cards = client.compute_analyses(display=True)

Modeled Arm Effects on hartmann6

Modeled effects on hartmann6. This plot visualizes predictions of the true metric changes for each arm based on Ax's model. This is the expected delta you would expect if you (re-)ran that arm. This plot helps in anticipating the outcomes and performance of arms based on the model's predictions. Note, flat predictions across arms indicate that the model predicts that there is no effect, meaning if you were to re-run the experiment, the delta you would see would be small and fall within the confidence interval indicated in the plot.

Observed Arm Effects on hartmann6

Observed effects on hartmann6. This plot visualizes the effects from previously-run arms on a specific metric, providing insights into their performance. This plot allows one to compare and contrast the effectiveness of different arms, highlighting which configurations have yielded the most favorable outcomes.

Summary for Experiment

High-level summary of the Trial-s in this Experiment

	trial_index	arm_name	trial_status	generation_node	hartmann6	x1	x2	x3	x4	x5	x6
0	0	0_0	COMPLETED	CenterOfSearchSpace	-0.505315	0.500000	0.500000	0.500000	0.500000	0.500000	0.500000
1	1	1_0	COMPLETED	Sobol	-0.001707	0.569844	0.207419	0.090854	0.407376	0.920197	0.988185
2	2	2_0	COMPLETED	Sobol	-0.246859	0.290140	0.507271	0.647595	0.724803	0.426718	0.480608
3	3	3_0	COMPLETED	Sobol	-0.279126	0.160273	0.384106	0.347328	0.121946	0.113965	0.224867
4	4	4_0	COMPLETED	Sobol	-0.009543	0.947761	0.838153	0.915537	0.808390	0.607479	0.743657
...	...	...	...	...	...	...	...	...	...	...	...
82	82	82_0	EARLY_STOPPED	MBM	3.017946	0.000000	0.807545	1.000000	0.307704	0.000000	1.000000
83	83	83_0	EARLY_STOPPED	MBM	3.321058	1.000000	0.573925	1.000000	0.308556	1.000000	1.000000
84	84	84_0	EARLY_STOPPED	MBM	2.485166	0.000000	0.636397	1.000000	0.306322	0.000000	1.000000
85	85	85_0	EARLY_STOPPED	MBM	3.321635	1.000000	0.781149	1.000000	0.308449	1.000000	1.000000
86	86	86_0	EARLY_STOPPED	MBM	3.321003	1.000000	0.553375	1.000000	0.306994	1.000000	1.000000

Sensitivity Analysis for hartmann6

Understand how each parameter affects hartmann6 according to a second-order sensitivity analysis.

x2 vs. hartmann6

The slice plot provides a one-dimensional view of predicted outcomes for hartmann6 as a function of a single parameter, while keeping all other parameters fixed at their status_quo value (or mean value if status_quo is unavailable). This visualization helps in understanding the sensitivity and impact of changes in the selected parameter on the predicted metric outcomes.

x6 vs. hartmann6

x4, x6 vs. hartmann6

The contour plot visualizes the predicted outcomes for hartmann6 across a two-dimensional parameter space, with other parameters held fixed at their status_quo value (or mean value if status_quo is unavailable). This plot helps in identifying regions of optimal performance and understanding how changes in the selected parameters influence the predicted outcomes. Contour lines represent levels of constant predicted values, providing insights into the gradient and potential optima within the parameter space.

Cross Validation for hartmann6

The cross-validation plot displays the model fit for each metric in the experiment. It employs a leave-one-out approach, where the model is trained on all data except one sample, which is used for validation. The plot shows the predicted outcome for the validation set on the y-axis against its actual value on the x-axis. Points that align closely with the dotted diagonal line indicate a strong model fit, signifying accurate predictions. Additionally, the plot includes 95% confidence intervals that provide insight into the noise in observations and the uncertainty in model predictions. A horizontal, flat line of predictions indicates that the model has not picked up on sufficient signal in the data, and instead is just predicting the mean.

Conclusion

This tutorial demonstates Ax's early stopping capabilities, which utilize timeseries-like data to monitor the results of expensive evaluations and terminate those that are unlikely to produce promising results, freeing up resources to explore more configurations. This can be used in a number of applications, and is especially useful in machine learning contexts.

Learning Objectives​

Prerequisites​

Step 1: Import Necessary Modules​

Step 2: Initialize the Client​

Step 3: Configure the Experiment​

Step 4: Configure Optimization​

Step 5: Run Trials with early stopping​

Step 6: Analyze Results​

Step 7: Compute Analyses​

Conclusion​