Year: 2025
Type: preprint
Abstract: We develop a new framework for deriving time-uniform concentration bounds for the output of stochastic sequential algorithms satisfying certain recursive inequalities akin to those defining the almost-supermartingale processes introduced by \cite{robbins1971convergence}. Our approach is of wide applicability, and can be deployed in settings in which exponential supermartingale processes, required by prevailing methodologies for anytime-valid concentration inequalities, are not readily available. Our results can be viewed as quantitative versions of the classical Robbins-Siegmund Lemma. We demonstrate the effectiveness of our method by providing new and optimal time-uniform concentration bounds for Oja's algorithm for streaming PCA, stochastic gradient descent, and stochastic approximations.
Source: arXiv (Cornell University)
Authors: Pham, Tuan, Rinaldo, Alessandro, Sarkar, Purnamrita
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7106749720
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