The paper introduces a contraction framework for stochastic operators that incorporates bootstrapping, where a variable is updated using a frozen copy as a target that is refreshed every $K$ steps. By modeling the sampled update as a stochastic operator, the authors derive a finite‑time bound for i.i.d. samples that applies to any target‑update period and does not require gradient structure or uniformly bounded sampling error. The framework shows that the iterates converge geometrically in root mean square to a ball around the fixed point, with the error floor scaling with the step size, and it generalizes existing deterministic and stochastic‑gradient bounds.
arXiv:2505.01361v3 Announce Type: replace
Abstract: Temporal difference (TD) learning is a foundational algorithm in reinforcement learning (RL). For nearly forty years, TD learning has served as a w...
By Hwanwoo Kim, Panos Toulis, Eric Laber
arXiv:2506. 01052v3 Announce Type: replace Abstract: We investigate the finite-time convergence properties of Temporal Difference (TD) learning with linear function approximation, a cornerstone of reinforcement learning.
By Wei-Cheng Lee, Francesco Orabona
arXiv:2606. 05967v1 Announce Type: cross Abstract: In this paper, we study the finite-time behavior of the TD(0) temporal-difference method with linear function approximation (LFA).
By Ziad Kobeissi (L2S), \'Elo\"ise Berthier (U2IS)
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.
By Liviu Aolaritei, Lucas L\'evy, Francis Bach, Michael I. Jordan
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.
By Siddharth Chandak
In this paper, we study the finite-time behavior of the TD(0) temporal-difference method with linear function approximation (LFA). We consider on-policy independent and identically distributed (i.
arXiv:2504.18184v5 Announce Type: replace
Abstract: We consider a class of statistical inverse problems involving the estimation of a regression operator from a Polish space to a separable Hilbert sp...
By Jia-Qi Yang, Lei Shi
arXiv:2607. 13414v1 Announce Type: cross Abstract: Non-expansive two-time-scale stochastic approximation is governed by a slow stochastic Krasnoselskii--Mann fixed-point iteration rather than by contraction to a unique equilibrium.
By Dhruv Sarkar, Vaneet Aggarwal
arXiv:2609.39837v1 Announce Type: new
Abstract: Policy mirror descent (PMD) enjoys fast convergence in regularized Markov decision processes (MDPs), but existing guarantees often rely on exact or inc...
By Qipei Chen, Wenye Li, Yule Sun, Ke Wei
arXiv:2604. 06039v2 Announce Type: replace-cross Abstract: Value iteration-type methods have been extensively studied for computing a nearly optimal value function in reinforcement learning (RL).
By Zhichao Jia, Guanghui Lan
The paper introduces Batched SGD, a variant that groups online samples into epochs and performs a single update per epoch using a low‑variance gradient estimate. This batching approach allows a straightforward high‑probability analysis without restrictive assumptions or auxiliary sequences, yielding near‑optimal rates for both strongly convex and non‑convex objectives under standard smoothness and sub‑Gaussian noise conditions. The authors also extend the method to federated learning, providing the first high‑probability guarantees with logarithmic communication complexity, linear speedup in the number of agents, and robustness to data heterogeneity.
By Feng Zhu, Robert W. Heath Jr., Aritra Mitra