Sleeping Combinatorial Bandits

• URL: http://arxiv.org/abs/2106.01624v1
• Date: Thu, 3 Jun 2021 06:49:44 GMT
• Title: Sleeping Combinatorial Bandits
• Authors: Kumar Abhishek, Ganesh Ghalme, Sujit Gujar, Yadati Narahari
• Abstract summary: We adapt the well-known CUCB algorithm in the sleeping bandits setting and refer to it as CSUCB. We prove -- under mild conditions -- that the CSUCB algorithm achieves an $O(sqrtT log (T)$ instance-dependent regret guarantee. Our results are quite general and hold under general environments -- such as non-additive reward functions, volatile arm availability, a variable number of base-arms to be pulled -- arising in practical applications.
• Score: 15.004764451770441
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: In this paper, we study an interesting combination of sleeping and combinatorial stochastic bandits. In the mixed model studied here, at each discrete time instant, an arbitrary \emph{availability set} is generated from a fixed set of \emph{base} arms. An algorithm can select a subset of arms from the \emph{availability set} (sleeping bandits) and receive the corresponding reward along with semi-bandit feedback (combinatorial bandits). We adapt the well-known CUCB algorithm in the sleeping combinatorial bandits setting and refer to it as \CSUCB. We prove -- under mild smoothness conditions -- that the \CSUCB\ algorithm achieves an $O(\log (T))$ instance-dependent regret guarantee. We further prove that (i) when the range of the rewards is bounded, the regret guarantee of \CSUCB\ algorithm is $O(\sqrt{T \log (T)})$ and (ii) the instance-independent regret is $O(\sqrt[3]{T^2 \log(T)})$ in a general setting. Our results are quite general and hold under general environments -- such as non-additive reward functions, volatile arm availability, a variable number of base-arms to be pulled -- arising in practical applications. We validate the proven theoretical guarantees through experiments.

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