Extensions of Robbins-Siegmund Theorem with Applications in Reinforcement Learning

arXiv:2509.26442v2 Announce Type: replace Abstract: The Robbins-Siegmund theorem establishes the convergence of stochastic processes that are almost supermartingales and is one of the most commonly used approaches for analyzing stochastic iterative algorithms in stochastic approximation and reinforcement learning (RL). However, its original form has a significant limitation as it requires the zero-order term to be summable. In many important RL applications, this summable condition, however, cannot be met. This limitation motivates us to extend the Robbins-Siegmund theorem for almost supermart

Source: arXiv cs.LG — read the full report at the original publisher.

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