Research map / Bandits and online learning / Multi-armed bandits
Regret Bounds for Batched Bandits
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use adaptive batch sizes with arm elimination | Stochastic multi-armed bandit · Stochastic multi-armed bandit | expected regret: O \left ( \frac{ K \log(K) \log (KT) T^{1/B}} {\displaystyle\min_{i:\Delta_i>0} \Delta_i} \right ) -> 9 T^{1/B} \ln(2KTB | Helped |
| Use arm elimination with batches growing geometrically | Stochastic multi-armed bandit · Stochastic multi-armed bandit with B batches | expected regret: O\left(T^{1/B} \log(T)\sum_{i:\Delta_i>0}{\Delta_i}^{-1}\right) | Helped |
| Use arm elimination and approximate G-design action sets | Stochastic linear bandit with finite action set · Stochastic linear bandit, finite action set | expected regret: O\left( T^{1/B} \sqrt{d T \log (KT)}\right) | Helped |
| Discretize the infinite action set using a 1/T-net | Batched stochastic linear bandit · Stochastic linear bandit, infinite action set | expected regret: O\left( T^{1/B} \cdot d \sqrt{T \log T} \right) | Helped |
| Reduce batched adversarial bandits to adversarial bandits with delays | Non-adaptive batched adversarial multi-armed bandit · Adversarial multi-armed bandit, non-adaptive batches | expected regret: O\left(\sqrt{\left(K+\frac T B\right)T\log(K)}\right) | Helped |
| Use only O(log T) batches instead of fully sequential feedback | Stochastic multi-armed bandit · Stochastic multi-armed bandit | expected regret: O\Big(\log(T) \sum_{i:\Delta_i>0}{\Delta_i}^{-1}\Big) | No clear effect |
| Use only Ω(log T) batches instead of fully sequential feedback | Stochastic linear bandit · Stochastic linear bandit | expected regret: O(d\sqrt{T\log T}) | No clear effect |
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