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- W2893802500 abstract "In the classical contextual bandits problem, in each round $t$, a learner observes some context $c$, chooses some action $a$ to perform, and receives some reward $r_{a,t}(c)$. We consider the variant of this problem where in addition to receiving the reward $r_{a,t}(c)$, the learner also learns the values of $r_{a,t}(c')$ for all other contexts $c'$; i.e., the rewards that would have been achieved by performing that action under different contexts. This variant arises in several strategic settings, such as learning how to bid in non-truthful repeated auctions (in this setting the context is the decision maker's private valuation for each auction). We call this problem the contextual bandits problem with cross-learning. The best algorithms for the classical contextual bandits problem achieve $tilde{O}(sqrt{CKT})$ regret against all stationary policies, where $C$ is the number of contexts, $K$ the number of actions, and $T$ the number of rounds. We demonstrate algorithms for the contextual bandits problem with cross-learning that remove the dependence on $C$ and achieve regret $O(sqrt{KT})$ (when contexts are stochastic with known distribution), $tilde{O}(K^{1/3}T^{2/3})$ (when contexts are stochastic with unknown distribution), and $tilde{O}(sqrt{KT})$ (when contexts are adversarial but rewards are stochastic)." @default.
- W2893802500 created "2018-10-05" @default.
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- W2893802500 date "2018-09-25" @default.
- W2893802500 modified "2023-09-27" @default.
- W2893802500 title "Contextual Bandits with Cross-learning" @default.
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