arXiv Machine Learning By Liviu Aolaritei, Lucas L\'evy, Francis Bach, Michael I. Jordan

Beyond Optimal Rates in Stochastic Optimization: Trajectory-Adaptive Stopping Rules

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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.

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arXiv Machine Learning
Jun 3

Data- and Variance-dependent Regret Bounds for Online Tabular MDPs

arXiv:2602. 01903v2 Announce Type: replace Abstract: This work studies online episodic tabular Markov decision processes (MDPs) with known transitions and develops best-of-both-worlds algorithms that achieve refined data-dependent regret bounds in the adversarial regime and variance-dependent regret bounds in the stochastic regime.

By Mingyi Li, Taira Tsuchiya, Kenji Yamanishi
arXiv Machine Learning
Aug 20

Fast Best-in-Class Regret for Contextual Bandits

The paper investigates stochastic contextual bandits in an agnostic setting, aiming to compete with the best policy in a given class without assuming realizability or specific loss/reward models. It introduces an algorithm that updates the policy each round by minimizing a pessimistic objective— a clipped inverse‑propensity estimate of the policy value plus a variance penalty— and proves the first fast regret rates relative to the best‑in‑class policy. By exploiting entropy assumptions on the policy class and a H"olderian error‑bound condition, the authors achieve fast best‑in‑class regret rates, including polylogarithmic rates in the parametric case, using a sequential self‑normalized maximal inequality for bounded martingale empirical processes to derive uniform variance‑adaptive confidence bounds and ensure pessimism under adaptive data collection.

By Samuel Girard, Aurelien Bibaut, Arthur Gretton, Nathan Kallus, Houssam Zenati
arXiv Machine Learning
Jul 7

Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses

arXiv:2406. 14340v2 Announce Type: replace-cross Abstract: The standard stochastic gradient descent (SGD) optimization method, as well as adaptive methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (particularly, in the situation of constant learning rates).

By Steffen Dereich, Arnulf Jentzen, Adrian Riekert