def fit(self, X, a, r, p):
"""
Fits the Doubly-Robust estimator to partially-labeled data collected from a different policy.
Parameters
----------
X : array (n_samples, n_features)
Matrix of covariates for the available data.
a : array (n_samples), int type
Arms or actions that were chosen for each observations.
r : array (n_samples), {0,1}
Rewards that were observed for the chosen actions. Must be binary rewards 0/1.
p : array (n_samples)
Reward estimates for the actions that were chosen by the policy.
"""
try:
from costsensitive import RegressionOneVsRest, WeightedAllPairs
except:
raise ValueError(
"This functionality requires package 'costsensitive'.\nCan be installed with 'pip install costsensitive'."
)
p = _check_1d_inp(p)
assert p.shape[0] == X.shape[0]
l = -r
if type(self.reward_estimator) == np.ndarray:
C = self.reward_estimator
elif 'predict_proba_separate' in dir(self.reward_estimator):
C = -self.reward_estimator.predict_proba_separate(X)
elif 'predict_proba' in dir(self.reward_estimator):
reward_estimator = SeparateClassifiers(self.reward_estimator,
self.nchoices,
beta_prior=self.beta_prior,
smoothing=self.smoothing)
reward_estimator.fit(X, a, r)
C = -reward_estimator.predict_proba_separate(X)
else:
raise ValueError(
"Error: couldn't obtain reward estimates. Are you passing the right input to 'reward_estimator'?"
)
if self.handle_invalid:
C[C == 1] = np.random.beta(3, 1, size=C.shape)[C == 1]
C[C == 0] = np.random.beta(1, 3, size=C.shape)[C == 0]
if self.c is not None:
p = self.c * p
if self.pmin is not None:
p = np.clip(p, a_min=self.pmin, a_max=None)
C[np.arange(C.shape[0]),
a] += (l - C[np.arange(C.shape[0]), a]) / p.reshape(-1)
if self.method == 'rovr':
self.oracle = RegressionOneVsRest(self.base_algorithm,
**self.kwargs_costsens)
else:
self.oracle = WeightedAllPairs(self.base_algorithm,
**self.kwargs_costsens)
self.oracle.fit(X, C)
class DoublyRobustEstimator:
"""
Doubly-Robust Estimator
Estimates the expected reward for each arm, applies a correction for the actions that
were chosen, and converts the problem to const-sensitive classification, on which the
base algorithm is then fit.
Note
----
This technique converts the problem into a cost-sensitive classification problem
by calculating a matrix of expected rewards and turning it into costs. The base
algorithm is then fit to this data, using either the Weighted All-Pairs approach,
which requires a binary classifier with sample weights as base algorithm, or the
Regression One-Vs-Rest approach, which requires a regressor as base algorithm.
In the Weighted All-Pairs approach, this technique will fail if there are actions that
were never taken by the exploration policy, as it cannot construct a model for them.
The expected rewards are estimated with the imputer algorithm passed here, which should
output a number in the range [0,1].
This technique is meant for the case of contiunous rewards in the [0,1] interval,
but here it is used for the case of discrete rewards {0,1}, under which it performs
poorly. It is not recommended to use, but provided for comparison purposes.
Alo important: this method requires to form reward estimates of all arms for each observation. In order to
do so, you can either provide estimates as an array (see Parameters), or pass a model.
One method to obtain reward estimates is to fit a model to the data and use its predictions as
reward estimates. You can do so by passing an object of class
`contextualbandits.online.SeparateClassifiers` which should be already fitted, or by passing a
classifier with a 'predict_proba' method, which will be put into a 'SeparateClassifiers'
object and fit to the same data passed to this function to obtain reward estimates.
The estimates can make invalid predictions if there are some arms for which every time
they were chosen they resulted in a reward, or never resulted in a reward. In such cases,
this function includes the option to impute the "predictions" for them (which would otherwise
always be exactly zero or one regardless of the context) by replacing them with random
numbers ~Beta(3,1) or ~Beta(1,3) for the cases of always good and always bad.
This is just a wild idea though, and doesn't guarantee reasonable results in such siutation.
Note that, if you are using the 'SeparateClassifiers' class from the online module in this
same package, it comes with a method 'predict_proba_separate' that can be used to get reward
estimates. It still can suffer from the same problem of always-one and always-zero predictions though.
Parameters
----------
base_algorithm : obj
Base algorithm to be used for cost-sensitive classification.
reward_estimator : obj or array (n_samples, n_choices)
One of the following:
* An array with the first column corresponding to the reward estimates for the action chosen
by the new policy, and the second column corresponding to the reward estimates for the
action chosen in the data (see Note for details).
* An already-fit object of class 'contextualbandits.online.SeparateClassifiers', which will
be used to make predictions on the actions chosen and the actions that the new
policy would choose.
* A classifier with a 'predict_proba' method, which will be fit to the same test data
passed here in order to obtain reward estimates (see Note 2 for details).
nchoices : int
Number of arms/labels to choose from.
Only used when passing a classifier object to 'reward_estimator'.
method : str, either 'rovr' or 'wap'
Whether to use Regression One-Vs-Rest or Weighted All-Pairs (see Note 1)
handle_invalid : bool
Whether to replace 0/1 estimated rewards with randomly-generated numbers (see Note 2)
c : None or float
Constant by which to multiply all scores from the exploration policy.
pmin : None or float
Scores (from the exploration policy) will be converted to the minimum between
pmin and the original estimate.
beta_prior : tuple((a, b), n), str "auto", or None
Beta prior to pass to 'SeparateClassifiers'. Only used when passing to 'reward_estimator'
a classifier with 'predict_proba'.
smoothing : tuple(a, b) or None
Smoothing parameter to pass to 'SeparateClassifiers' Only used when passing to 'reward_estimator'
a classifier with 'predict_proba'.
kwargs_costsens
Additional keyword arguments to pass to the cost-sensitive classifier.
References
----------
[1] Dudík, Miroslav, John Langford, and Lihong Li. "Doubly robust policy evaluation and learning."
arXiv preprint arXiv:1103.4601 (2011).
[2] Dudík, Miroslav, et al. "Doubly robust policy evaluation and optimization."
Statistical Science 29.4 (2014): 485-511.
"""
def __init__(self, base_algorithm, reward_estimator, nchoices, method='rovr',
handle_invalid=True, c=None, pmin=1e-5, beta_prior=None, smoothing=(1,2), **kwargs_costsens):
assert (method == 'rovr') or (method == 'wap')
self.method = method
if method == 'wap':
_check_constructor_input(base_algorithm, nchoices)
else:
assert isinstance(nchoices, int)
assert nchoices > 2
assert ('fit' in dir(base_algorithm)) and ('predict' in dir(base_algorithm))
if c is not None:
assert isinstance(c, float)
if pmin is not None:
assert isinstance(pmin, float)
assert isinstance(handle_invalid, bool)
if type(reward_estimator) == np.ndarray:
assert reward_estimator.shape[1] == nchoices
assert reward_estimator.shape[0] == X.shape[0]
else:
assert ('predict_proba_separate' in dir(reward_estimator)) or ('predict_proba' in dir(reward_estimator))
if beta_prior is not None:
beta_prior = _check_beta_prior(beta_prior, nchoices, 2)
self.base_algorithm = base_algorithm
self.reward_estimator = reward_estimator
self.nchoices = nchoices
self.c = c
self.pmin = pmin
self.handle_invalid = handle_invalid
self.beta_prior = beta_prior
self.smoothing = _check_smoothing(smoothing)
self.kwargs_costsens = kwargs_costsens
def fit(self, X, a, r, p):
"""
Fits the Doubly-Robust estimator to partially-labeled data collected from a different policy.
Parameters
----------
X : array (n_samples, n_features)
Matrix of covariates for the available data.
a : array (n_samples), int type
Arms or actions that were chosen for each observations.
r : array (n_samples), {0,1}
Rewards that were observed for the chosen actions. Must be binary rewards 0/1.
p : array (n_samples)
Reward estimates for the actions that were chosen by the policy.
"""
p = _check_1d_inp(p)
assert p.shape[0] == X.shape[0]
l = -r
if type(self.reward_estimator) == np.ndarray:
C = self.reward_estimator
elif 'predict_proba_separate' in dir(self.reward_estimator):
C = -self.reward_estimator.predict_proba_separate(X)
elif 'predict_proba' in dir(self.reward_estimator):
reward_estimator = SeparateClassifiers(self.reward_estimator, self.nchoices, beta_prior = self.beta_prior, smoothing = self.smoothing)
reward_estimator.fit(X, a, r)
C = -reward_estimator.predict_proba_separate(X)
else:
raise ValueError("Error: couldn't obtain reward estimates. Are you passing the right input to 'reward_estimator'?")
if self.handle_invalid:
C[C == 1] = np.random.beta(3, 1, size = C.shape)[C == 1]
C[C == 0] = np.random.beta(1, 3, size = C.shape)[C == 0]
if self.c is not None:
p = self.c * p
if self.pmin is not None:
p = np.clip(p, a_min = self.pmin, a_max = None)
C[np.arange(C.shape[0]), a] += (l - C[np.arange(C.shape[0]), a]) / p.reshape(-1)
if self.method == 'rovr':
self.oracle = RegressionOneVsRest(self.base_algorithm, **self.kwargs_costsens)
else:
self.oracle = WeightedAllPairs(self.base_algorithm, **self.kwargs_costsens)
self.oracle.fit(X, C)
def predict(self, X):
"""
Predict best arm for new data.
Parameters
----------
X : array (n_samples, n_features)
New observations for which to choose an action.
Returns
-------
pred : array (n_samples,)
Actions chosen by this technique.
"""
X = _check_X_input(X)
return self.oracle.predict(X)
def decision_function(self, X):
"""
Get score distribution for the arm's rewards
Note
----
For details on how this is calculated, see the documentation of the
RegressionOneVsRest and WeightedAllPairs classes in the costsensitive package.
Parameters
----------
X : array (n_samples, n_features)
New observations for which to evaluate actions.
Returns
-------
pred : array (n_samples, n_choices)
Score assigned to each arm for each observation (see Note).
"""
X = _check_X_input(X)
return self.oracle.decision_function(X)