scope_rl.ope.discrete.basic_estimators.PerDecisionImportanceSampling#
- class scope_rl.ope.discrete.basic_estimators.PerDecisionImportanceSampling[source]#
Per-Decision Importance Sampling (PDIS) for discrete action spaces.
Bases:
scope_rl.ope.BaseOffPolicyEstimatorImported as:
scope_rl.ope.discrete.PerDecisionImportanceSamplingNote
PDIS estimates the policy value via step-wise importance weighting as follows.
\[\hat{J}_{\mathrm{PDIS}} (\pi; \mathcal{D}) := \frac{1}{n} \sum_{i=1}^n \sum_{t=0}^{T-1} \gamma^t w_{0:t}^{(i)} r_t^{(i)},\]where \(w_{0:t} := \prod_{t'=0}^t (\pi(a_{t'} | s_{t'}) / \pi_0(a_{t'} | s_{t'}))\) is the importance weight for each time step wrt the previous actions (referred to as the per-decision or step-wise importance weight).
By using per-decision importance weighting instead of trajectory-wise importance weighting of TIS, PDIS has lower variance than TIS while remaining unbiased. However, when the trajectory length (\(T\)) is large, PDIS still suffers from high variance.
- Parameters:
estimator_name (str, default="pdis") – Name of the estimator.
References
Doina Precup, Richard S. Sutton, and Satinder P. Singh. “Eligibility Traces for Off-Policy Policy Evaluation.” 2000.
Methods
estimate_interval(step_per_trajectory, ...)Estimate the confidence interval of the policy value by nonparametric bootstrap.
estimate_policy_value(step_per_trajectory, ...)Estimate the policy value of the evaluation policy.
- estimate_policy_value(step_per_trajectory, action, reward, pscore, evaluation_policy_action_dist, gamma=1.0, **kwargs)[source]#
Estimate the policy value of the evaluation policy.
- Parameters:
step_per_trajectory (int (> 0)) – Number of timesteps in an episode.
action (array-like of shape (n_trajectories * step_per_trajectory, )) – Action chosen by the behavior policy.
reward (array-like of shape (n_trajectories * step_per_trajectory, )) – Observed immediate rewards.
pscore (array-like of shape (n_trajectories * step_per_trajectory, )) – Conditional action choice probability of the behavior policy, i.e., \(\pi_b(a | s)\)
evaluation_policy_action_dist (array-like of shape (n_trajectories * step_per_trajectory, n_action)) – Conditional action distribution induced by the evaluation policy, i.e., \(\pi(a | s_t) \forall a \in \mathcal{A}\)
gamma (float, default=1.0) – Discount factor. The value should be within (0, 1].
- Returns:
V_hat – Estimated policy value.
- Return type:
- estimate_interval(step_per_trajectory, action, reward, pscore, evaluation_policy_action_dist, gamma=1.0, alpha=0.05, ci='bootstrap', n_bootstrap_samples=10000, random_state=None, **kwargs)[source]#
Estimate the confidence interval of the policy value by nonparametric bootstrap.
- Parameters:
step_per_trajectory (int (> 0)) – Number of timesteps in an episode.
action (array-like of shape (n_trajectories * step_per_trajectory, )) – Action chosen by the behavior policy.
reward (array-like of shape (n_trajectories * step_per_trajectory, )) – Observed immediate rewards.
pscore (array-like of shape (n_trajectories * step_per_trajectory, )) – Conditional action choice probability of the behavior policy, i.e., \(\pi_b(a | s)\)
evaluation_policy_action_dist (array-like of shape (n_trajectories * step_per_trajectory, n_action)) – Conditional action distribution induced by the evaluation policy, i.e., \(\pi(a | s_t) \forall a \in \mathcal{A}\)
gamma (float, default=1.0) – Discount factor. The value should be within (0, 1].
alpha (float, default=0.05) – Significance level. The value should be within [0, 1).
ci ({"bootstrap", "hoeffding", "bernstein", "ttest"}, default="bootstrap") – Name of the method to estimate the confidence interval.
n_bootstrap_samples (int, default=10000 (> 0)) – Number of resampling performed in the bootstrap procedure.
random_state (int, default=None (>= 0)) – Random state.
- Returns:
estimated_confidence_interval – Dictionary storing the estimated mean and upper-lower confidence bounds.
key: [ mean, {100 * (1. - alpha)}% CI (lower), {100 * (1. - alpha)}% CI (upper), ]
- Return type:
Methods