#!/usr/bin/env python3
# Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.
import hashlib
import json
from typing import Dict, List, Optional, Tuple
import numpy as np
from ax.core.types import TConfig, TParamValue, TParamValueList
from ax.models.discrete_base import DiscreteModel
from ax.utils.common.docutils import copy_doc
[docs]class ThompsonSampler(DiscreteModel):
"""Generator for Thompson sampling.
The generator performs Thompson sampling on the data passed in via `fit`.
Arms are given weight proportional to the probability that they are
winners, according to Monte Carlo simulations.
"""
def __init__(
self,
num_samples: int = 10000,
min_weight: Optional[float] = None,
uniform_weights: bool = False,
) -> None:
"""
Args:
num_samples: The number of samples to draw from the posterior.
min_weight: The minimum weight a arm must be
given in order for it to be returned from the gernerator. If not
specified, will be set to 2 / (number of arms).
uniform_weights: If True, the arms returned from the
generator will each be given a weight of 1 / (number of arms).
"""
self.num_samples = num_samples
self.min_weight = min_weight
self.uniform_weights = uniform_weights
self.X = None
self.Ys = None
self.Yvars = None
self.X_to_Ys_and_Yvars = None
[docs] @copy_doc(DiscreteModel.fit)
def fit(
self,
Xs: List[List[TParamValueList]],
Ys: List[List[float]],
Yvars: List[List[float]],
parameter_values: List[TParamValueList],
outcome_names: List[str],
) -> None:
self.X = self._fit_X(Xs=Xs)
self.Ys, self.Yvars = self._fit_Ys_and_Yvars(
Ys=Ys, Yvars=Yvars, outcome_names=outcome_names
)
self.X_to_Ys_and_Yvars = self._fit_X_to_Ys_and_Yvars(
X=self.X, Ys=self.Ys, Yvars=self.Yvars
)
[docs] @copy_doc(DiscreteModel.gen)
def gen(
self,
n: int,
parameter_values: List[TParamValueList],
objective_weights: Optional[np.ndarray],
outcome_constraints: Optional[Tuple[np.ndarray, np.ndarray]] = None,
fixed_features: Optional[Dict[int, TParamValue]] = None,
pending_observations: Optional[List[List[TParamValueList]]] = None,
model_gen_options: Optional[TConfig] = None,
) -> Tuple[List[TParamValueList], List[float]]:
if objective_weights is None:
raise ValueError("ThompsonSampler requires objective weights.")
arms = self.X
# pyre: Expected `typing.Sized` for 1st anonymous parameter to call
# pyre-fixme[6]: `len` but got `typing.Type[None]`.
k = len(arms)
weights = self._generate_weights(
objective_weights=objective_weights, outcome_constraints=outcome_constraints
)
min_weight = self.min_weight if self.min_weight is not None else 2.0 / k
# Second entry is used for tie-breaking
weighted_arms = [
# pyre-fixme[16]: Optional type has no attribute `__getitem__`.
(weights[i], np.random.random(), arms[i])
for i in range(k)
# pyre-fixme[6]: Expected `float` for 1st param but got `Optional[float]`.
if weights[i] > min_weight
]
if len(weighted_arms) == 0:
raise ValueError(
"No arms generated by Thompson Sampling had weight > min_weight. "
+ f"The minimum weight required is {min_weight:2.4}, "
+ "and the maximum weight of any arm generated "
+ f"is {max(weights):2.4}."
)
weighted_arms.sort(reverse=True)
top_weighted_arms = weighted_arms[:n] if n > 0 else weighted_arms
top_arms = [arm for _, _, arm in top_weighted_arms]
top_weights = [weight for weight, _, _ in top_weighted_arms]
if self.uniform_weights:
top_weights = [1 / len(top_arms) for _ in top_arms]
return top_arms, [x / sum(top_weights) for x in top_weights]
[docs] @copy_doc(DiscreteModel.predict)
def predict(self, X: List[TParamValueList]) -> Tuple[np.ndarray, np.ndarray]:
n = len(X) # number of parameterizations at which to make predictions
# pyre: Expected `typing.Sized` for 1st anonymous parameter to call
# pyre-fixme[6]: `len` but got `typing.Type[None]`.
m = len(self.Ys) # number of outcomes
f = np.zeros((n, m)) # array of outcome predictions
cov = np.zeros((n, m, m)) # array of predictive covariances
predictX = [self._hash_TParamValueList(x) for x in X]
# pyre-fixme[6]: Expected `Iterable[_T]` for 1st param but got `None`.
for i, (X_to_Y_and_Yvar) in enumerate(self.X_to_Ys_and_Yvars):
# iterate through outcomes
for j, x in enumerate(predictX):
# iterate through parameterizations at which to make predictions
if x not in X_to_Y_and_Yvar:
raise ValueError(
"ThompsonSampler does not support out-of-sample prediction."
)
f[j, i], cov[j, i, i] = X_to_Y_and_Yvar[x]
return f, cov
def _generate_weights(
self,
objective_weights: np.ndarray,
outcome_constraints: Optional[Tuple[np.ndarray, np.ndarray]] = None,
) -> List[float]:
samples, fraction_all_infeasible = self._produce_samples(
num_samples=self.num_samples,
objective_weights=objective_weights,
outcome_constraints=outcome_constraints,
)
if fraction_all_infeasible > 0.99:
raise ValueError(
"Less than 1% of samples have a feasible arm. "
"Check your outcome constraints."
)
num_valid_samples = samples.shape[1]
while num_valid_samples < self.num_samples:
num_additional_samples = (self.num_samples - num_valid_samples) / (
1 - fraction_all_infeasible
)
num_additional_samples = int(np.maximum(num_additional_samples, 100))
new_samples, _ = self._produce_samples(
num_samples=num_additional_samples,
objective_weights=objective_weights,
outcome_constraints=outcome_constraints,
)
samples = np.concatenate([samples, new_samples], axis=1)
num_valid_samples = samples.shape[1]
winner_indices = np.argmax(samples, axis=0) # (num_samples,)
# pyre: Expected `typing.Sized` for 1st anonymous parameter to call
# pyre-fixme[6]: `len` but got `typing.Type[None]`.
winner_counts = np.zeros(len(self.X)) # (k,)
for index in winner_indices:
winner_counts[index] += 1
weights = winner_counts / winner_counts.sum()
return weights.tolist()
def _produce_samples(
self,
num_samples: int,
objective_weights: np.ndarray,
outcome_constraints: Optional[Tuple[np.ndarray, np.ndarray]],
) -> Tuple[np.ndarray, float]:
# pyre: Expected `typing.Sized` for 1st anonymous parameter to call
# pyre-fixme[6]: `len` but got `typing.Type[None]`.
k = len(self.X)
samples_per_metric = np.zeros(
# pyre: Expected `typing.Sized` for 1st anonymous parameter to
# pyre-fixme[6]: call `len` but got `typing.Type[None]`.
(k, num_samples, len(self.Ys))
) # k x num_samples x m
# pyre-fixme[6]: Expected `Iterable[_T]` for 1st param but got `None`.
for i, Y in enumerate(self.Ys): # (k x 1)
# pyre-fixme[16]: Optional type has no attribute `__getitem__`.
Yvar = self.Yvars[i] # (k x 1)
cov = np.diag(Yvar) # (k x k)
samples = np.random.multivariate_normal(
Y, cov, num_samples
).T # (k x num_samples)
samples_per_metric[:, :, i] = samples
any_violation = np.zeros((k, num_samples), dtype=bool) # (k x num_samples)
if outcome_constraints:
# A is (num_constraints x m)
# b is (num_constraints x 1)
A, b = outcome_constraints
# (k x num_samples x m) dot (num_constraints x m)^T
# = (k x num_samples x m) dot (m x num_constraints)
# ==> (k x num_samples x num_constraints)
constraint_values = np.dot(samples_per_metric, A.T)
violations = constraint_values > b.T
any_violation = np.max(violations, axis=2) # (k x num_samples)
objective_values = np.dot(
samples_per_metric, objective_weights
) # (k x num_samples)
objective_values[any_violation] = -np.Inf
best_arm = objective_values.max(axis=0) # (num_samples,)
all_arms_infeasible = best_arm == -np.Inf # (num_samples,)
fraction_all_infeasible = all_arms_infeasible.mean()
filtered_objective = objective_values[:, ~all_arms_infeasible] # (k x ?)
return filtered_objective, fraction_all_infeasible
def _validate_Xs(self, Xs: List[List[TParamValueList]]) -> None:
"""
1. Require that all Xs have the same arms, i.e. we have observed
all arms for all metrics. If so, we can safely use Xs[0] exclusively.
2. Require that all rows of X are unique, i.e. only one observation
per parameterization.
"""
if not all(x == Xs[0] for x in Xs[1:]):
raise ValueError(
"ThompsonSampler requires that all elements of Xs are identical; "
"i.e. that we have observed all arms for all metrics."
)
X = Xs[0]
uniqueX = {self._hash_TParamValueList(x) for x in X}
if len(uniqueX) != len(X):
raise ValueError(
"ThompsonSampler requires all rows of X to be unique; "
"i.e. that there is only one observation per parameterization."
)
def _fit_X(self, Xs: List[List[TParamValueList]]) -> List[TParamValueList]:
"""After validation has been performed, it's safe to use Xs[0]."""
self._validate_Xs(Xs=Xs)
return Xs[0]
def _fit_Ys_and_Yvars(
self, Ys: List[List[float]], Yvars: List[List[float]], outcome_names: List[str]
) -> Tuple[List[List[float]], List[List[float]]]:
"""For plain Thompson Sampling, there's nothing to be done here.
EmpiricalBayesThompsonSampler will overwrite this method to perform
shrinkage.
"""
return Ys, Yvars
def _fit_X_to_Ys_and_Yvars(
self, X: List[TParamValueList], Ys: List[List[float]], Yvars: List[List[float]]
) -> List[Dict[TParamValueList, Tuple[float, float]]]:
"""Construct lists of mappings, one per outcome, of parameterizations
to the a tuple of their mean and variance.
"""
X_to_Ys_and_Yvars = []
hashableX = [self._hash_TParamValueList(x) for x in X]
for (Y, Yvar) in zip(Ys, Yvars):
X_to_Ys_and_Yvars.append(dict(zip(hashableX, zip(Y, Yvar))))
return X_to_Ys_and_Yvars
def _hash_TParamValueList(self, x: TParamValueList) -> str:
"""Hash a list of parameter values. This is safer than converting the
list to a tuple because of int/floats.
"""
param_values_str = json.dumps(x)
return hashlib.md5(param_values_str.encode("utf-8")).hexdigest()
