An Improved Relaxation for Oracle-Efficient Adversarial Contextual Bandits
NeurIPS(2023)
Abstract
We present an oracle-efficient relaxation for the adversarial contextual
bandits problem, where the contexts are sequentially drawn i.i.d from a known
distribution and the cost sequence is chosen by an online adversary. Our
algorithm has a regret bound of
$O(T^{\frac{2}{3}}(K\log(|\Pi|))^{\frac{1}{3}})$ and makes at most $O(K)$ calls
per round to an offline optimization oracle, where $K$ denotes the number of
actions, $T$ denotes the number of rounds and $\Pi$ denotes the set of
policies. This is the first result to improve the prior best bound of
$O((TK)^{\frac{2}{3}}(\log(|\Pi|))^{\frac{1}{3}})$ as obtained by Syrgkanis et
al. at NeurIPS 2016, and the first to match the original bound of Langford and
Zhang at NeurIPS 2007 which was obtained for the stochastic case.
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Key words
bandits,improved relaxation,oracle-efficient
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