Multi-Armed Bernoulli Bandits via Minimax Single-Arm Stopping
We develop an index policy for finite-horizon Bernoulli multi-armed bandits from minimax solutions to single-arm bandit (SAB) problems. Each SAB problem involves choosing between an unknown Bernoulli arm and a known reward. We show that minimizing worst-case regret of SAB problems over all non-anticipative policies admits an exact semi-infinite linear programming formulation. The resulting stopping policies offer a natural way to compare arms: the higher the known reward against which a policy continues sampling, the more promising the unknown arm. We turn this intuition into indices based on cumulative continuation probabilities, with a monotone adjustment and a reward-shortfall cap. By ...
| Authors | Huikang Liu, Zhengchao Wang, Daniel Kuhn et al. |
|---|---|
| Primary category | cs.LG |
| Published | 19 September 2026 |
| Last updated at source | 19 September 2026 |
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