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.
RANK_REASON This is a research paper published on arXiv.
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