Research map / Bandits and online learning / Multi-armed bandits
Asymptotically Optimal Quantile Pure Exploration for Infinite-Armed Bandits
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use separate phases for estimating the target quantile and searching for an acceptable arm, rather than paying the high-confidence cost in both arm count and samples per arm | Infinite-armed pure exploration, fixed confidence · Infinite-armed Bernoulli bandits | expected sample complexity dependence on \delta: O(\log^2(1/\delta)) -> O\left(\frac{\log (1/\delta)\log (1/\eta)}{\eta\varepsilon^2}\right) | Helped |
| Use gradually moving rejection thresholds and sample-count increases by powers of 1+\varrho, with thresholds moving in Fisher-information distance | Infinite-armed pure exploration, fixed budget · Infinite-armed Bernoulli bandits | sample complexity as \delta\to 0: (c_{\alpha,\beta}^{-1}\pm o(1))\log(1/\delta)\log\log(1/\delta)^2 | Helped |
| Impose an almost-sure fixed budget instead of a sample budget bounded only in expectation | Infinite-armed pure exploration · Infinite-armed Bernoulli bandits | sample complexity dependence on \delta: (c_{\alpha,\beta}^{-1}\pm o(1))\log(1/\delta)\log\log(1/\delta)^2 | Hurt |
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