Learning to Bet for Horizon-Aware Anytime-Valid Testing
We develop horizon-aware anytime-valid tests and confidence sequences for bounded means under a strict deadline $N$. Using the betting/e-process framework, we cast horizon-aware betting as a finite-horizon optimal control problem with state space $(t, \log W_t)$, where $t$ is the time and $W_t$ is the test martingale value. We first show that in certain interior regions of the state space, policies that deviate significantly from Kelly betting are provably suboptimal, while Kelly betting reaches the threshold with high probability. We then identify sufficient conditions showing that outside this region, more aggressive betting than Kelly can be better if the bettor is behind schedule, and...
| Authors | Ege Onur Taga, Samet Oymak, Shubhanshu Shekhar |
|---|---|
| Primary category | stat.ME |
| Published | 20 March 2026 |
| Last updated at source | 2 June 2026 |
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