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We consider the adversarial combinatorial multi-armed bandit (CMAB) problem,whose decision set can be exponentially large with respect to the number ofgiven arms. To avoid dealing with such large decision sets directly, we proposean algorithm performed on a zero-suppressed binary decision diagram (ZDD),which is a compressed representation of the decision set. The proposedalgorithm achieves either $O(T^{2/3})$ regret with high probability or$O(\sqrt{T})$ expected regret as the any-time guarantee, where $T$ is thenumber of past rounds. Typically, our algorithm works efficiently for CMABproblems defined on networks. Experimental results show that our algorithm isapplicable to various large adversarial CMAB instances including adaptiverouting problems on real-world networks.

Practical Adversarial Combinatorial Bandit Algorithm via Compression of Decision Sets