[Submitted on 14 Sep 2026]
Title:Regularized Emphatic Temporal-Difference Learning: Stability under Constant Stepsizes
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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.
Subjects:
Artificial Intelligence (cs.AI)
Cite as: arXiv:2609.19170 [cs.AI]
(or arXiv:2609.19170v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2609.19170
arXiv-issued DOI via DataCite
Submission history
From: Xingguo Chen [view email] [v1] Mon, 14 Sep 2026 01:42:49 UTC (608 KB)
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