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

arXiv · AI, language, vision and robotics · article · Aug 26, 2026 · UTC

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. This mismatch creates a fundamental certification problem: fixed-time guarantees do not generally remain valid at data-dependent stopping times, while deterministic horizons derived from worst-case bounds can be highly conservative. We address this problem for strongly convex stochastic optimization by constructing fully observable, trajectory-adaptive upper confidence sequences

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