Establishes maximal concentration bounds for stochastic approximation under heavy-tailed Markovian noise, with tails ranging from sub-Gaussian to heavier than Weibull depending on step sizes and contractivity properties, plus a truncation argument for unbounded noise.
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A diameter criterion tied to a potential function certifies convergence of difference inclusions, enabling discrete proofs for first-order optimization methods with diminishing steps.
High-probability generalization bounds for D-SGD are derived at the optimal rate O(1/sqrt(mn) log(1/δ)) via pointwise uniform stability across convex and non-convex settings.
Derives contraction-based Q-value extensions for exponential utility and proves almost-sure convergence of two-timescale and one-timescale model-free algorithms in discounted MDPs.
The paper motivates stochastic optimization problems from statistical perspectives and describes offline and online approaches to solve expectation minimization problems.
citing papers explorer
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Concentration of General Stochastic Approximation Under Heavy-Tailed Markovian Noise
Establishes maximal concentration bounds for stochastic approximation under heavy-tailed Markovian noise, with tails ranging from sub-Gaussian to heavier than Weibull depending on step sizes and contractivity properties, plus a truncation argument for unbounded noise.
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Convergence of difference inclusions via a diameter criterion
A diameter criterion tied to a potential function certifies convergence of difference inclusions, enabling discrete proofs for first-order optimization methods with diminishing steps.
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Unveiling High-Probability Generalization in Decentralized SGD
High-probability generalization bounds for D-SGD are derived at the optimal rate O(1/sqrt(mn) log(1/δ)) via pointwise uniform stability across convex and non-convex settings.
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Reinforcement Learning for Exponential Utility: Algorithms and Convergence in Discounted MDPs
Derives contraction-based Q-value extensions for exponential utility and proves almost-sure convergence of two-timescale and one-timescale model-free algorithms in discounted MDPs.
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Stochastic Optimization and Data Science
The paper motivates stochastic optimization problems from statistical perspectives and describes offline and online approaches to solve expectation minimization problems.