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Spotlight
Dynamic Planning and Learning under Recovering Rewards
David Simchi-Levi · Zeyu Zheng · Feng Zhu

Wed Jul 21 05:20 PM -- 05:25 PM (PDT) @ None
Motivated by emerging applications such as live-streaming e-commerce, promotions and recommendations, we introduce a general class of multi-armed bandit problems that have the following two features: (i) the decision maker can pull and collect rewards from at most $K$ out of $N$ different arms in each time period; (ii) the expected reward of an arm immediately drops after it is pulled, and then non-parametrically recovers as the idle time increases. With the objective of maximizing expected cumulative rewards over $T$ time periods, we propose, construct and prove performance guarantees for a class of ``Purely Periodic Policies''. For the offline problem when all model parameters are known, our proposed policy obtains an approximation ratio that is at the order of $1-\mathcal O(1/\sqrt{K})$, which is asymptotically optimal when $K$ grows to infinity. For the online problem when the model parameters are unknown and need to be learned, we design an Upper Confidence Bound (UCB) based policy that approximately has $\widetilde{\mathcal O}(N\sqrt{T}) regret against the offline benchmark. Our framework and policy design may have the potential to be adapted into other offline planning and online learning applications with non-stationary and recovering rewards.

Author Information

David Simchi-Levi (MIT)
Zeyu Zheng (University of California, Berkeley)
Feng Zhu (Massachusetts Institute of Technology)

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