Regret Bounds for Stochastic Combinatorial Multi-Armed Bandits with Linear Space Complexity
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Many real-world problems face the dilemma of choosing best K out of N options at a given time instant. This setup can be modelled as combinatorial bandit which chooses K out of N arms at each time, with an aim to achieve an efficient tradeoff between exploration and exploitation. This is the first work for combinatorial bandit where the reward received can be a non-linear function of the chosen K arms. The direct use of multi-armed bandit requires choosing among N-choose-K options making the state space large. In this paper, we present a novel algorithm which is computationally efficient and the storage is linear in N. The proposed algorithm is a divide-and-conquer based strategy, that we call CMAB-SM. Further, the proposed algorithm achieves a regret bound of Õ(K^1/2N^1/3T^2/3) for a time horizon T, which is sub-linear in all parameters T, N, and K. The evaluation results on different reward functions and arm distribution functions show significantly improved performance as compared to standard multi-armed bandit approach with NK choices.
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