MySyntheticDataset.py

from dataclasses import dataclass
from typing import Optional, Callable

from obp.dataset import BaseBanditDataset
from obp.dataset.reward_type import RewardType
import numpy as np
from obp.types import BanditFeedback
from obp.utils import check_array, softmax, sample_action_fast

from scipy.stats import truncnorm
from sklearn.utils import check_random_state
from sklearn.utils import check_scalar


@dataclass
class SyntheticBanditDataset(BaseBanditDataset):
    """Class for synthesizing bandit data.

    Note
    -----
    By calling the `obtain_batch_bandit_feedback` method several times,
    we can resample logged bandit data from the same data generating distribution.
    This can be used to estimate confidence intervals of the performances of OPE estimators.

    If None is given as `behavior_policy_function`, the behavior policy will be generated from the true expected reward function. See the description of the `beta` argument, which controls the behavior policy.

    Parameters
    -----------
    n_actions: int
        Number of actions.

    dim_context: int, default=1
        Number of dimensions of context vectors.

    reward_type: str, default='binary'
        Type of reward variable, which must be either 'binary' or 'continuous'.
        When 'binary', rewards are sampled from the Bernoulli distribution.
        When 'continuous', rewards are sampled from the truncated Normal distribution with `scale=1`.
        The mean parameter of the reward distribution is determined by the `reward_function` specified by the next argument.

    reward_function: Callable[[np.ndarray, np.ndarray], np.ndarray]], default=None
        Function defining the expected reward for each given action-context pair,
        i.e., :math:`q: \\mathcal{X} \\times \\mathcal{A} \\rightarrow \\mathbb{R}`.
        If None, context **independent** expected rewards will be
        sampled from the uniform distribution automatically.

    reward_std: float, default=1.0
        Standard deviation of the reward distribution.
        A larger value leads to a noisier reward distribution.
        This argument is valid only when `reward_type="continuous"`.

    action_context: np.ndarray, default=None
         Vector representation of (discrete) actions.
         If None, one-hot representation will be used.

    behavior_policy_function: Callable[[np.ndarray, np.ndarray], np.ndarray], default=None
        Function generating logit values, which will be used to define the behavior policy via softmax transformation.
        If None, behavior policy will be generated by applying the softmax function to the expected reward.
        Thus, in this case, it is possible to control the optimality of the behavior policy by customizing `beta`.
        If `beta` is large, the behavior policy becomes near-deterministic/near-optimal,
        while a small or negative value of `beta` leads to a sub-optimal behavior policy.

    beta: int or float, default=1.0
        Inverse temperature parameter, which controls the optimality and entropy of the behavior policy.
        A large value leads to a near-deterministic behavior policy,
        while a small value leads to a near-uniform behavior policy.
        A positive value leads to a near-optimal behavior policy,
        while a negative value leads to a sub-optimal behavior policy.

    n_deficient_actions: int, default=0
        Number of deficient actions having zero probability of being selected in the logged bandit data.
        If there are some deficient actions, the full/common support assumption is very likely to be violated,
        leading to some bias for IPW-type estimators. See Sachdeva et al.(2020) for details.
        `n_deficient_actions` should be an integer smaller than `n_actions - 1` so that there exists at least one action
        that have a positive probability of being selected by the behavior policy.

    random_state: int, default=12345
        Controls the random seed in sampling synthetic bandit data.

    dataset_name: str, default='synthetic_bandit_dataset'
        Name of the dataset.

    Examples
    ----------

    .. code-block:: python

        >>> from obp.dataset import (
            SyntheticBanditDataset,
            logistic_reward_function
        )

        # generate synthetic contextual bandit feedback with 10 actions.
        >>> dataset = SyntheticBanditDataset(
                n_actions=5,
                dim_context=3,
                reward_function=logistic_reward_function,
                beta=3,
                random_state=12345
            )
        >>> bandit_feedback = dataset.obtain_batch_bandit_feedback(n_rounds=100000)
        >>> bandit_feedback
        {
            'n_rounds': 10000,
            'n_actions': 5,
            'context': array([[-0.20470766,  0.47894334, -0.51943872],
                    [-0.5557303 ,  1.96578057,  1.39340583],
                    [ 0.09290788,  0.28174615,  0.76902257],
                    ...,
                    [ 0.42468038,  0.48214752, -0.57647866],
                    [-0.51595888, -1.58196174, -1.39237837],
                    [-0.74213546, -0.93858948,  0.03919589]]),
            'action_context': array([[1, 0, 0, 0, 0],
                    [0, 1, 0, 0, 0],
                    [0, 0, 1, 0, 0],
                    [0, 0, 0, 1, 0],
                    [0, 0, 0, 0, 1]]),
            'action': array([4, 2, 0, ..., 0, 0, 3]),
            'position': None,
            'reward': array([1, 0, 1, ..., 1, 1, 1]),
            'expected_reward': array([[0.58447584, 0.42261239, 0.28884131, 0.40610288, 0.59416389],
                    [0.13543381, 0.06309101, 0.3696813 , 0.69883145, 0.19717306],
                    [0.52369136, 0.30840555, 0.45036116, 0.59873096, 0.4294134 ],
                    ...,
                    [0.68953133, 0.55893616, 0.34955984, 0.45572919, 0.67187002],
                    [0.88247154, 0.76355595, 0.25545932, 0.19939877, 0.78578675],
                    [0.67637136, 0.42096732, 0.33178027, 0.36439361, 0.52300522]]),
            'pi_b': array([[[0.27454777],
                    [0.16342857],
                    [0.12506266],
                    [0.13791739],
                    [0.22195834]]]),
            'pscore': array([0.28264435, 0.19326617, 0.23079467, ..., 0.28729378, 0.36637549,
                    0.13791739])
        }

    References
    ------------
    Miroslav Dudík, Dumitru Erhan, John Langford, and Lihong Li.
    "Doubly Robust Policy Evaluation and Optimization.", 2014.

    Noveen Sachdeva, Yi Su, and Thorsten Joachims.
    "Off-policy Bandits with Deficient Support.", 2020.

    """

    n_actions: int
    dim_context: int = 1
    reward_type: str = RewardType.BINARY.value
    reward_function: Optional[Callable[[np.ndarray, np.ndarray], np.ndarray]] = None
    reward_std: float = 1.0
    action_context: Optional[np.ndarray] = None
    behavior_policy_function: Optional[
        Callable[[np.ndarray, np.ndarray], np.ndarray]
    ] = None
    beta: float = 1.0
    n_deficient_actions: int = 0
    random_state: int = 12345
    dataset_name: str = "synthetic_bandit_dataset"

    def __post_init__(self) -> None:
        """Initialize Class."""
        check_scalar(self.n_actions, "n_actions", int, min_val=2)
        check_scalar(self.dim_context, "dim_context", int, min_val=1)
        check_scalar(self.beta, "beta", (int, float))
        check_scalar(
            self.n_deficient_actions,
            "n_deficient_actions",
            int,
            min_val=0,
            max_val=self.n_actions - 1,
        )

        if self.random_state is None:
            raise ValueError("`random_state` must be given")
        self.random_ = check_random_state(self.random_state)

        if RewardType(self.reward_type) not in [
            RewardType.BINARY,
            RewardType.CONTINUOUS,
        ]:
            raise ValueError(
                f"`reward_type` must be either '{RewardType.BINARY.value}' or '{RewardType.CONTINUOUS.value}',"
                f"but {self.reward_type} is given.'"
            )
        check_scalar(self.reward_std, "reward_std", (int, float), min_val=0)
        if self.reward_function is None:
            self.expected_reward = self.sample_contextfree_expected_reward()
        if RewardType(self.reward_type) == RewardType.CONTINUOUS:
            self.reward_min = 0
            self.reward_max = 1e10

        # one-hot encoding characterizing actions.
        if self.action_context is None:
            self.action_context = np.eye(self.n_actions, dtype=int)
        else:
            check_array(
                array=self.action_context, name="action_context", expected_dim=2
            )
            if self.action_context.shape[0] != self.n_actions:
                raise ValueError(
                    "Expected `action_context.shape[0] == n_actions`, but found it False."
                )

    @property
    def len_list(self) -> int:
        """Length of recommendation lists, slate size."""
        return 1

    def sample_contextfree_expected_reward(self) -> np.ndarray:
        """Sample expected reward for each action from the uniform distribution."""
        return self.random_.uniform(size=self.n_actions)

    def calc_expected_reward(self, context: np.ndarray) -> np.ndarray:
        """Sample expected rewards given contexts"""
        # sample reward for each round based on the reward function
        if self.reward_function is None:
            expected_reward_ = np.tile(self.expected_reward, (context.shape[0], 1))
        else:
            expected_reward_ = self.reward_function(
                context=context,
                action_context=self.action_context,
                random_state=self.random_state,
            )

        return expected_reward_

    def sample_reward_given_expected_reward(
            self,
            expected_reward: np.ndarray,
            action: np.ndarray,
    ) -> np.ndarray:
        """Sample reward given expected rewards"""
        expected_reward_factual = expected_reward[np.arange(action.shape[0]), action]
        if RewardType(self.reward_type) == RewardType.BINARY:
            reward = self.random_.binomial(n=1, p=expected_reward_factual)
        elif RewardType(self.reward_type) == RewardType.CONTINUOUS:
            mean = expected_reward_factual
            a = (self.reward_min - mean) / self.reward_std
            b = (self.reward_max - mean) / self.reward_std
            reward = truncnorm.rvs(
                a=a,
                b=b,
                loc=mean,
                scale=self.reward_std,
                random_state=self.random_state,
            )
        else:
            raise NotImplementedError

        return reward

    def sample_reward(self, context: np.ndarray, action: np.ndarray) -> np.ndarray:
        """Sample rewards given contexts and actions, i.e., :math:`r \\sim p(r | x, a)`.

        Parameters
        -----------
        context: array-like, shape (n_rounds, dim_context)
            Context vectors characterizing each data (such as user information).

        action: array-like, shape (n_rounds,)
            Actions chosen by the behavior policy for each context.

        Returns
        ---------
        reward: array-like, shape (n_rounds,)
            Sampled rewards given contexts and actions.

        """
        check_array(array=context, name="context", expected_dim=2)
        check_array(array=action, name="action", expected_dim=1)
        if context.shape[0] != action.shape[0]:
            raise ValueError(
                "Expected `context.shape[0] == action.shape[0]`, but found it False"
            )
        if not np.issubdtype(action.dtype, np.integer):
            raise ValueError("the dtype of action must be a subdtype of int")

        expected_reward_ = self.calc_expected_reward(context)

        return self.sample_reward_given_expected_reward(expected_reward_, action)

    def obtain_batch_bandit_feedback(self, n_rounds: int) -> BanditFeedback:
        """Obtain batch logged bandit data.

        Parameters
        ----------
        n_rounds: int
            Data size of the synthetic logged bandit data.

        Returns
        ---------
        bandit_feedback: BanditFeedback
            Synthesized logged bandit data.

        """
        check_scalar(n_rounds, "n_rounds", int, min_val=1)
        contexts = self.random_.normal(size=(n_rounds, self.dim_context))

        # calc expected reward given context and action
        expected_reward_ = self.calc_expected_reward(contexts)
        if RewardType(self.reward_type) == RewardType.CONTINUOUS:
            # correct expected_reward_, as we use truncated normal distribution here
            mean = expected_reward_
            a = (self.reward_min - mean) / self.reward_std
            b = (self.reward_max - mean) / self.reward_std
            expected_reward_ = truncnorm.stats(
                a=a, b=b, loc=mean, scale=self.reward_std, moments="m"
            )

        # calculate the action choice probabilities of the behavior policy
        if self.behavior_policy_function is None:
            pi_b_logits = expected_reward_
        else:
            pi_b_logits = self.behavior_policy_function(
                context=contexts,
                action_context=self.action_context,
                random_state=self.random_state,
            )
        # create some deficient actions based on the value of `n_deficient_actions`
        if self.n_deficient_actions > 0:
            pi_b = np.zeros_like(pi_b_logits)
            n_supported_actions = self.n_actions - self.n_deficient_actions
            supported_actions = np.argsort(
                self.random_.gumbel(size=(n_rounds, self.n_actions)), axis=1
            )[:, ::-1][:, :n_supported_actions]

            supported_actions_idx = (
                np.tile(np.arange(n_rounds), (n_supported_actions, 1)).T,
                supported_actions,
            )
            self.supported_actions = supported_actions
            self.supported_actions_idx = supported_actions_idx

            pi_b[supported_actions_idx] = softmax(
                self.beta * pi_b_logits[supported_actions_idx]
            )

        else:
            pi_b = softmax(self.beta * pi_b_logits)
        # sample actions for each round based on the behavior policy
        actions = sample_action_fast(pi_b, random_state=self.random_state)

        # sample rewards based on the context and action
        rewards = self.sample_reward_given_expected_reward(expected_reward_, actions)

        return dict(
            n_rounds=n_rounds,
            n_actions=self.n_actions,
            context=contexts,
            action_context=self.action_context,
            action=actions,
            position=None,  # position effect is not considered in synthetic data
            reward=rewards,
            expected_reward=expected_reward_,
            pi_b=pi_b[:, :, np.newaxis],
            pscore=pi_b[np.arange(n_rounds), actions],
        )

    def calc_ground_truth_policy_value(
            self, expected_reward: np.ndarray, action_dist: np.ndarray
    ) -> float:
        """Calculate the policy value of given action distribution on the given expected_reward.

        Parameters
        -----------
        expected_reward: array-like, shape (n_rounds, n_actions)
            Expected reward given context (:math:`x`) and action (:math:`a`), i.e., :math:`q(x,a):=\\mathbb{E}[r|x,a]`.
            This is often the `expected_reward` of the test set of logged bandit data.

        action_dist: array-like, shape (n_rounds, n_actions, len_list)
            Action choice probabilities of evaluation policy (can be deterministic), i.e., :math:`\\pi_e(a_i|x_i)`.

        Returns
        ----------
        policy_value: float
            The policy value of the given action distribution on the given logged bandit data.

        """
        check_array(array=expected_reward, name="expected_reward", expected_dim=2)
        check_array(array=action_dist, name="action_dist", expected_dim=3)
        if expected_reward.shape[0] != action_dist.shape[0]:
            raise ValueError(
                "Expected `expected_reward.shape[0] = action_dist.shape[0]`, but found it False"
            )
        if expected_reward.shape[1] != action_dist.shape[1]:
            raise ValueError(
                "Expected `expected_reward.shape[1] = action_dist.shape[1]`, but found it False"
            )

        return np.average(expected_reward, weights=action_dist[:, :, 0], axis=1).mean()