V-SHARE: Provable Convergence Guarantees for Advantage-based Algorithms

arXiv:2610.21448v1 Announce Type: cross Abstract: In reinforcement learning, advantage-based value-learning methods, unlike standard Q-learning, share information across actions by decomposing the action-value function into a state-dependent value component and action-specific advantages. While this mechanism has proven effective in both tabular and deep reinforcement learning, its theoretical understanding remains incomplete. We introduce V-SHARE, an advantage-based value-learning algorithm that combines cross-action value sharing with an importance-weighted Bellman-residual correction. To our knowledge, we provide the first complete theoretical characterization of an advantage-based algorithm, including both asymptotic convergence and non-asymptotic finite-sample guarantees. We identify a regime in which V-SHARE mitigates the rare-action bottleneck of asynchronous Q-learning and uncover a contraction--variance tradeoff between stronger deterministic contraction and increased importance-weighting noise. Motivated by this tradeoff, we develop decreasing residual-preconditioning schedules that combine faster early contraction with lower asymptotic noise. We further develop a two-timescale analysis that removes the single-timescale residual-weight threshold while preserving convergence guarantees. Experiments on discrete Markov decision processes (MDPs) and deep reinforcement-learning benchmarks corroborate our results.

Abstract:In reinforcement learning, advantage-based value-learning methods, unlike standard Q-learning, share information across actions by decomposing the action-value function into a state-dependent value component and action-specific advantages. While this mechanism has proven effective in both tabular and deep reinforcement learning, its theoretical understanding remains incomplete. We introduce V-SHARE, an advantage-based value-learning algorithm that combines cross-action value sharing with an importance-weighted Bellman-residual correction. To our knowledge, we provide the first complete theoretical characterization of an advantage-based algorithm, including both asymptotic convergence and non-asymptotic finite-sample guarantees. We identify a regime in which V-SHARE mitigates the rare-action bottleneck of asynchronous Q-learning and uncover a contraction--variance tradeoff between stronger deterministic contraction and increased importance-weighting noise. Motivated by this tradeoff, we develop decreasing residual-preconditioning schedules that combine faster early contraction with lower asymptotic noise. We further develop a two-timescale analysis that removes the single-timescale residual-weight threshold while preserving convergence guarantees. Experiments on discrete Markov decision processes (MDPs) and deep reinforcement-learning benchmarks corroborate our results.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2610.21448 [cs.LG]

(or arXiv:2610.21448v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.21448 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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V-SHARE: Provable Convergence Guarantees for Advantage-based Algorithms

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