Trajectory-Aware Eligibility Traces for Off-Policy Reinforcement Learning

Off-policy learning from multistep returns is crucial for sample-efficient reinforcement learning, but counteracting off-policy bias without exacerbating variance is challenging. Classically, offpolicy 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 offpolicy 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 perdecision 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 λ-values in several off-policy control tasks. Introduction Reinforcement learning concerns an agent interacting with its environment through trial and error to maximize its expected cumulative reward. One of the great challenges of re-