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arXiv · 2403.02873

A General Reduction for High-Probability Analysis with General Light-Tailed Distributions

Amit Attia·Tomer Koren
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Abstract

We describe a general reduction technique for analyzing learning algorithms that are subject to light-tailed (but not necessarily bounded) randomness, a scenario that is often the focus of theoretical analysis. We show that the analysis of such an algorithm can be reduced, in a black-box manner and with only a small loss in logarithmic factors, to an analysis of a simpler variant of the same algorithm that uses bounded random variables and is often easier to analyze. This approach simultaneously applies to any light-tailed randomization, including exponential, sub-Gaussian, and more general fast-decaying distributions, without needing to appeal to specialized concentration inequalities. Derivations of a generalized Azuma inequality, convergence bounds in stochastic optimization, and regret analysis in multi-armed bandits with general light-tailed randomization are provided to illustrate the technique.

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Amit Attia, Tomer Koren. 2025-05-20. A General Reduction for High-Probability Analysis with General Light-Tailed Distributions. https://arxiv.org/abs/2403.02873

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