scope_rl.ope.discrete.marginal_estimators.StateMarginalIS#
- class scope_rl.ope.discrete.marginal_estimators.StateMarginalIS(estimator_name='sm_is')[source]#
State Marginal Importance Sampling (SM-IS) for discrete action spaces.
Bases:
scope_rl.ope.BaseStateMarginalOPEEstimator->scope_rl.ope.BaseOffPolicyEstimatorImported as:
scope_rl.ope.discrete.StateMarginalISNote
SM-IS estimates the policy value using state marginal importance weighting. Following SOPE (Yuan et al., 2021), we combine state-marginal importance weighting and \(k\)-step PDIS as follows.
\[\hat{J}_{\mathrm{SM-IS}} (\pi; \mathcal{D}) := \frac{1}{n} \sum_{i=1}^n \sum_{t=0}^{k-1} \gamma^t w_{0:t}^{(i)} r_t^{(i)} + \frac{1}{n} \sum_{i=1}^n \sum_{t=k}^{T-1} \gamma^t \rho(s_{t-k}^{(i)}) w_{t-k:t}^{(i)} r_t^{(i)},\]where \(w_{t_1:t_2} := \prod_{t=t_1}^{t_2} (\pi(a_t | s_t) / \pi_0(a_t | s_t))\) and \(\rho(s) \approx d^{\pi}(s) / d^{\pi_b}(s)\) is the state-marginal importance weight, where \(d^{\pi}(s)\) is the marginal visitation probability of the policy \(\pi\) on \(s\). When \(k=0\), this estimator is reduced to the vanilla state marginal IS.
SM-IS is unbiased when the marginal importance weight is estimated correctly. Moreover, SM-IS reduces the variance caused by trajectory-wise or per-decision importance weighting by considering the marginal distribution across various timesteps.
There are several ways to estimate the state(-action) marginal importance weight such as Augmented Lagrangian Method (ALM) (Yang et al., 2020) and Minimax Weight Learning (MWL) (Uehara et al., 2020).
See also
The implementations of such weight learning methods are available at
scope_rl.ope.weight_value_learning.- Parameters:
estimator_name (str, default="sm_is") – Name of the estimator.
References
Christina J. Yuan, Yash Chandak, Stephen Giguere, Philip S. Thomas, and Scott Niekum. “SOPE: Spectrum of Off-Policy Estimators.” 2021.
Masatoshi Uehara, Jiawei Huang, and Nan Jiang. “Minimax Weight and Q-Function Learning for Off-Policy Evaluation.” 2020.
Mengjiao Yang, Ofir Nachum, Bo Dai, Lihong Li, and Dale Schuurmans. “Off-Policy Evaluation via the Regularized Lagrangian.” 2020.
Qiang Liu, Lihong Li, Ziyang Tang, and Dengyong Zhou. “Breaking the Curse of Horizon: Infinite-Horizon Off-Policy Estimation.” 2018
Doina Precup, Richard S. Sutton, and Satinder P. Singh. “Eligibility Traces for Off-Policy Policy Evaluation.” 2000.
Methods
estimate_interval(n_step_pdis, ...[, gamma, ...])Estimate the confidence interval of the policy value by nonparametric bootstrap.
estimate_policy_value(n_step_pdis, ...[, gamma])Estimate the policy value of the evaluation policy.
- estimate_policy_value(n_step_pdis, step_per_trajectory, action, reward, state_marginal_importance_weight, pscore, evaluation_policy_action_dist, gamma=1.0, **kwargs)[source]#
Estimate the policy value of the evaluation policy.
- Parameters:
n_step_pdis (int (>= 0)) – Number of initial steps whose rewards are estimated by step-wise importance weighting. When set to zero, the estimator is reduced to the vanilla state marginal IS.
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.
state_marginal_importance_weight (array-like of shape (n_trajectories * step_per_trajectory, )) – Importance weight wrt the state marginal distribution, i.e., \(d^{\pi}(s) / d^{\pi_b}(s)\)
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., \(\pi(a | s) \forall a \in \mathcal{A}\)
gamma (float, default=1.0) – Discount factor. The value should be within (0, 1].
- Returns:
V_hat – Estimated policy value.
- Return type:
- estimate_interval(n_step_pdis, step_per_trajectory, action, reward, state_marginal_importance_weight, 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:
n_step_pdis (int (>= 0)) – Number of initial steps whose rewards are estimated by step-wise importance weighting. When set to zero, the estimator is reduced to the vanilla state marginal IS.
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.
state_marginal_importance_weight (array-like of shape (n_trajectories * step_per_trajectory, )) – Importance weight wrt the state marginal distribution, i.e., \(d^{\pi}(s) / d^{\pi_b}(s)\)
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., \(\pi(a | s) \forall a \in \mathcal{A}\)
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") – 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