Reducing Sampling Error in Batch Temporal Difference Learning

TL;DR

This paper introduces PSEC-TD(0), a modified batch TD learning algorithm that corrects sampling bias using importance sampling, resulting in more accurate value function estimates in reinforcement learning.

Contribution

The paper proposes PSEC-TD(0), a novel correction method for sampling errors in batch TD learning, improving data efficiency and accuracy over standard TD(0).

Findings

PSEC-TD(0) reduces mean squared error in value estimates.

Empirical results show improved accuracy over TD(0).

Method is more data-efficient in batch reinforcement learning.

Abstract

Temporal difference (TD) learning is one of the main foundations of modern reinforcement learning. This paper studies the use of TD(0), a canonical TD algorithm, to estimate the value function of a given policy from a batch of data. In this batch setting, we show that TD(0) may converge to an inaccurate value function because the update following an action is weighted according to the number of times that action occurred in the batch -- not the true probability of the action under the given policy. To address this limitation, we introduce \textit{policy sampling error corrected}-TD(0) (PSEC-TD(0)). PSEC-TD(0) first estimates the empirical distribution of actions in each state in the batch and then uses importance sampling to correct for the mismatch between the empirical weighting and the correct weighting for updates following each action. We refine the concept of a certainty-equivalence estimate and argue that PSEC-TD(0) is a more data efficient estimator than TD(0) for a fixed batch of data. Finally, we conduct an empirical evaluation of PSEC-TD(0) on three batch value function learning tasks, with a hyperparameter sensitivity analysis, and show that PSEC-TD(0) produces value function estimates with lower mean squared error than TD(0).