Trajectory-Aware Eligibility Traces for Off-Policy Reinforcement Learning

TL;DR

This paper introduces a new multistep operator for off-policy reinforcement learning that unifies and analyzes per-decision and trajectory-aware methods, providing convergence guarantees and a robust sampling technique.

Contribution

It proposes a novel multistep operator that encompasses existing methods, proves their convergence in tabular settings, and introduces RBIS for improved off-policy control.

Findings

Proves convergence conditions for the new operator and existing methods.

Introduces RBIS, a trajectory-aware sampling method with robust performance.

Unifies per-decision and trajectory-aware approaches under a common framework.

Abstract

Off-policy learning from multistep returns is crucial for sample-efficient reinforcement learning, but counteracting off-policy bias without exacerbating variance is challenging. Classically, off-policy bias is corrected in a per-decision manner: past temporal-difference errors are re-weighted by the instantaneous Importance Sampling (IS) ratio after each action via eligibility traces. Many off-policy algorithms rely on this mechanism, along with differing protocols for cutting the IS ratios to combat the variance of the IS estimator. Unfortunately, once a trace has been fully cut, the effect cannot be reversed. This has led to the development of credit-assignment strategies that account for multiple past experiences at a time. These trajectory-aware methods have not been extensively analyzed, and their theoretical justification remains uncertain. In this paper, we propose a multistep operator that can express both per-decision and trajectory-aware methods. We prove convergence conditions for our operator in the tabular setting, establishing the first guarantees for several existing methods as well as many new ones. Finally, we introduce Recency-Bounded Importance Sampling (RBIS), which leverages trajectory awareness to perform robustly across $\lambda$-values in an off-policy control task.