The loop API is the most lightweight way to do optimization in Ax. The user makes one call to `optimize`

, which performs all of the optimization under the hood and returns the optimized parameters.

For more customizability of the optimization procedure, consider the Service or Developer API.

In [ ]:

```
import numpy as np
from ax.metrics.branin import branin
from ax.plot.contour import plot_contour
from ax.plot.trace import optimization_trace_single_method
from ax.service.managed_loop import optimize
from ax.utils.measurement.synthetic_functions import hartmann6
from ax.utils.notebook.plotting import init_notebook_plotting, render
init_notebook_plotting()
```

First, we define an evaluation function that is able to compute all the metrics needed for this experiment. This function needs to accept a set of parameter values and can also accept a weight. It should produce a dictionary of metric names to tuples of mean and standard error for those metrics.

In [ ]:

```
def hartmann_evaluation_function(parameterization):
x = np.array([parameterization.get(f"x{i+1}") for i in range(6)])
# In our case, standard error is 0, since we are computing a synthetic function.
return {"hartmann6": (hartmann6(x), 0.0), "l2norm": (np.sqrt((x**2).sum()), 0.0)}
```

If there is only one metric in the experiment – the objective – then evaluation function can return a single tuple of mean and SEM, in which case Ax will assume that evaluation corresponds to the objective. It can also return only the mean as a float, in which case Ax will treat SEM as unknown and use a model that can infer it. For more details on evaluation function, refer to the "Trial Evaluation" section in the docs.

The setup for the loop is fully compatible with JSON. The optimization algorithm is selected based on the properties of the problem search space.

In [ ]:

```
best_parameters, values, experiment, model = optimize(
parameters=[
{
"name": "x1",
"type": "range",
"bounds": [0.0, 1.0],
"value_type": "float", # Optional, defaults to inference from type of "bounds".
"log_scale": False, # Optional, defaults to False.
},
{
"name": "x2",
"type": "range",
"bounds": [0.0, 1.0],
},
{
"name": "x3",
"type": "range",
"bounds": [0.0, 1.0],
},
{
"name": "x4",
"type": "range",
"bounds": [0.0, 1.0],
},
{
"name": "x5",
"type": "range",
"bounds": [0.0, 1.0],
},
{
"name": "x6",
"type": "range",
"bounds": [0.0, 1.0],
},
],
experiment_name="test",
objective_name="hartmann6",
evaluation_function=hartmann_evaluation_function,
minimize=True, # Optional, defaults to False.
parameter_constraints=["x1 + x2 <= 20"], # Optional.
outcome_constraints=["l2norm <= 1.25"], # Optional.
total_trials=30, # Optional.
)
```

And we can introspect optimization results:

In [ ]:

```
best_parameters
```

In [ ]:

```
means, covariances = values
means
```

For comparison, minimum of Hartmann6 is:

In [ ]:

```
hartmann6.fmin
```

Here we arbitrarily select "x1" and "x2" as the two parameters to plot for both metrics, "hartmann6" and "l2norm".

In [ ]:

```
render(plot_contour(model=model, param_x="x1", param_y="x2", metric_name="hartmann6"))
```

In [ ]:

```
render(plot_contour(model=model, param_x="x1", param_y="x2", metric_name="l2norm"))
```

We also plot optimization trace, which shows best hartmann6 objective value seen by each iteration of the optimization:

In [ ]:

```
# `plot_single_method` expects a 2-d array of means, because it expects to average means from multiple
# optimization runs, so we wrap out best objectives array in another array.
best_objectives = np.array(
[[trial.objective_mean for trial in experiment.trials.values()]]
)
best_objective_plot = optimization_trace_single_method(
y=np.minimum.accumulate(best_objectives, axis=1),
optimum=hartmann6.fmin,
title="Model performance vs. # of iterations",
ylabel="Hartmann6",
)
render(best_objective_plot)
```

Total runtime of script: 2 minutes, 15.12 seconds.