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TOOL · arXiv cs.LG English(EN) · 8h

Multi-Armed Sequential Hypothesis Testing by Betting

Researchers have developed a novel approach to sequential hypothesis testing, extending the concept to scenarios involving multiple data sources or "arms." This method aims to efficiently identify deviations from a null hypothesis, even when multiple arms are non-null, by optimizing performance as if an oracle knew which arm provided the most evidence. The work introduces generalized log-optimality and expected rejection time optimality criteria, utilizing a modified upper-confidence-bound algorithm and deriving concentration inequalities for optimal wealth growth rates. AI
- Kelly
RESEARCH · arXiv stat.ML English(EN) · 1mo · [2 sources]

The optimal betting wealth growth rate

This paper characterizes the optimal rate of wealth growth in a Kelly betting game when betting against a null hypothesis but drawing data from an alternative. The authors prove this rate equals a specific limit involving Kullback-Leibler divergence, which is generally smaller than a more commonly used quantity. They also establish conditions under which these two quantities are equal and derive the optimal worst-case growth rate against composite alternatives. AI

IMPACT This paper provides theoretical insights into optimal growth rates in statistical testing, potentially informing future AI research in decision-making under uncertainty.
- arXiv
- Kelly
- Larsson