The paper presents a stability analysis for stochastic approximation algorithms with Markovian noise. The key contributions are:
Extending the Borkar-Meyn theorem for stability from the Martingale difference noise setting to the Markovian noise setting, with weaker assumptions than prior work.
Establishing stability under two sets of assumptions:
Demonstrating the wide applicability of the results, especially in off-policy reinforcement learning algorithms with linear function approximation and eligibility traces.
The analysis centers around the diminishing asymptotic rate of change of certain functions, which is implied by both the strong law of large numbers and the Lyapunov drift condition. This allows establishing the stability of the stochastic iterates without requiring the stronger assumptions needed in prior work.
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by Shuze Liu,Sh... at arxiv.org 04-30-2024
https://arxiv.org/pdf/2401.07844.pdfDeeper Inquiries