STaR-Bets: Sequential Target-Recalculating Bets for Tighter Confidence Intervals

arXiv — cs.LGWednesday, November 12, 2025 at 5:00:00 AM
The introduction of STaR-Bets marks a significant advancement in the field of statistics, particularly in constructing confidence intervals for bounded random variables. Traditional methods, while effective, often fall short in providing optimal guarantees, especially in fixed horizon settings. STaR-Bets bridges this gap by employing a betting-based algorithm that not only computes confidence intervals but does so with empirical performance that surpasses existing competitors. This is crucial in contexts where sampling is expensive, as obtaining the tightest possible confidence intervals can lead to more reliable outcomes in scientific research and machine learning applications. The algorithm's ability to achieve optimal width under certain conditions represents a strict improvement over classical concentration inequalities, making it a valuable tool for researchers and practitioners alike.
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