Better Best of Both Worlds Bounds for Bandits with Switching CostsDownload PDF

Published: 31 Oct 2022, Last Modified: 12 Oct 2022NeurIPS 2022 AcceptReaders: Everyone
Keywords: Multi-Armed Bandits, Online Learning, Optimization, Decision Making
Abstract: We study best-of-both-worlds algorithms for bandits with switching cost, recently addressed by Rouyer et al., 2021. We introduce a surprisingly simple and effective algorithm that simultaneously achieves minimax optimal regret bound (up to logarithmic factors) of $\mathcal{O}(T^{2/3})$ in the oblivious adversarial setting and a bound of $\mathcal{O}(\min\{\log (T)/\Delta^2,T^{2/3}\})$ in the stochastically-constrained regime, both with (unit) switching costs, where $\Delta$ is the gap between the arms. In the stochastically constrained case, our bound improves over previous results due to Rouyer et al., 2021, that achieved regret of $\mathcal{O}(T^{1/3}/\Delta)$. We accompany our results with a lower bound showing that, in general, $\tilde{\mathcal{\Omega}}(\min\{1/\Delta^2,T^{2/3}\})$ switching cost regret is unavoidable in the stochastically-constrained case for algorithms with $\mathcal{O}(T^{2/3})$ worst-case switching cost regret.
TL;DR: We introduce an algorithm that improves previous results in the best-of-both-worlds algorithms for bandits with switching cost domain, accompanied by an adequate lower bound.
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