The paper establishes a shrinking‑tube concentration bound for projected stochastic approximation driven by an adaptive Markov chain, guaranteeing that after a chosen time every iterate stays within a tolerance that tightens over time. The bound’s probability of any exit after that time decays polynomially, and a matching lower bound shows this exponent is optimal under finite second moments. Extensions to recursions with martingale‑difference noise and predictable bias reveal how noise scale and bias affect exit‑probability decay and tube shrinkage, with applications to inventory learning and numerical gradient accuracy.
arXiv:2608. 25551v1 Announce Type: new Abstract: Stochastic gradient descent (SGD) is typically analyzed at a deterministic horizon chosen before the algorithm is run, even though practical stopping decisions are made adaptively by inspecting the evolving trajectory.
arXiv:2607. 23030v1 Announce Type: new Abstract: Developing efficient function-approximation methods for policy evaluation is a fundamental challenge in risk-aware reinforcement learning.
arXiv:2405.08253v4 Announce Type: replace-cross Abstract: This paper develops a framework for learning in discounted infinite-horizon Markov decision processes (MDPs) with Borel state and action spac...
arXiv:2607. 17595v1 Announce Type: new Abstract: We establish mean-square and concentration bounds for stochastic approximation (SA) with arbitrary norm contractive mappings, under a multiplicative noise model where the noise may scale affinely with the norm of the iterates, and the iterates are potentially unbounded.
arXiv:2607. 15229v1 Announce Type: new Abstract: We develop data-driven algorithms for maintaining $N$ independent identical machines under a \textit{block replacement policy}, in which each machine is replaced upon failure and all machines are jointly replaced at regular intervals of length $k$.
arXiv:2606. 31769v1 Announce Type: new Abstract: We study policy optimization for online episodic tabular Markov decision processes with unknown transition kernels, aiming for best-of-both-worlds guarantees together with data-dependent regret bounds.
arXiv:2606. 02363v1 Announce Type: new Abstract: We study sequential decision-making in partially observable environments against strategic, adaptive opponents, modeled as partially observable Markov games (POMGs).
arXiv:2607. 08789v1 Announce Type: new Abstract: Bayesian and multiplicative-weights updates reweight experts, models, or actions from sequential feedback.
arXiv:2606. 14679v1 Announce Type: new Abstract: Online inventory optimization (OIO) is online convex optimization with physical memory: inventory carryover makes the feasible action set depend on the past.
arXiv:2609. 28263v1 Announce Type: new Abstract: The growth of large language model (LLM) inference and search services increases the scale of online linear programming problems, motivating computationally efficient algorithms.
arXiv:2602. 05799v2 Announce Type: replace-cross Abstract: We study non-stationary single-item, periodic-review inventory control problems in which the demand distribution is unknown and may change over time.
arXiv:2411. 01302v2 Announce Type: replace Abstract: We study the convergence of $q$-learning and related algorithms introduced by Jia and Zhou (J.