Practical Adversarial Combinatorial Bandit Algorithm via Compression of Decision Sets

We consider the adversarial combinatorial multi-armed bandit (CMAB) problem, whose decisionset can be exponentially large with respect to the number of given arms. To avoid dealing with suchlarge decision sets directly, we propose an algorithm performed on a zero-suppressed binary decisiondiagram (ZDD), which is a compressed representation of the decision set. The proposed algorithmachieves either O(T ) regret with high probability or O(√T ) expected regret as the any-timeguarantee, where T is the number of past rounds. Typically, our algorithm works efficiently forCMAB problems defined on networks. Experimental results show that our algorithm is applicableto various large adversarial CMAB instances including adaptive routing problems on real-worldnetworks.