Regularized Emphatic Temporal-Difference Learning: Stability under Constant Stepsizes

2026-09-13

AI Summary

论文提出正则化强调时序差分学习（RETD）方法，解决ETD在常数步长下稳定性问题，通过引入延迟修正机制改善了采样动态。

Abstract

Emphatic temporal-difference learning (ETD) stabilizes the expected off-policy TD update and changes its projection geometry, but neither property determines constant-stepsize sampled dynamics. We construct an ergodic two-state counterexample in which the ETD mean map contracts while the sampled product has a positive top Lyapunov exponent. Regenerative-cycle analysis separates this sign from the infinite variance of the follow-on trace. We introduce regularized emphatic TD (RETD), a normalized first-order post-shock repair that leaves the trace and importance ratios unchanged, stores the emphatic TD signal in a leaky scalar state, and releases a delayed correction. RETD's raw equilibrium is an affine shift of the ETD equilibrium; single- and two-regularization readouts recover the ETD fixed point exactly. We prove almost-sure convergence for harmonic diminishing stepsizes and a conditional constant-stepsize moment-contraction result from a Markovian random-product bound. RETD has certified negative exponents on the two-state construction and one Baird point, whereas the positive Baird ETD sign remains numerical. Paired 10,000-run experiments validate both separations, fixed-point recovery, a nonmonotone stability region, and task dependence. RETD changes post-shock dynamics; it does not reduce the shared follow-on-trace variance.

Problem

• Emphatic Temporal-Difference Learning
• Constant Stepsizes
• Sampled Dynamics

Innovation

• Regularized Emphatic TD (RETD)
• Leaky Scalar State
• Negative Lyapunov Exponents
• Almost-sure Convergence