Efficient Pure Exploration for Combinatorial Bandits with Semi-Bandit Feedback
arXiv:2101.08534
Abstract
Combinatorial bandits with semi-bandit feedback generalize multi-armed bandits, where the agent chooses sets of arms and observes a noisy reward for each arm contained in the chosen set. The action set satisfies a given structure such as forming a base of a matroid or a path in a graph. We focus on the pure-exploration problem of identifying the best arm with fixed confidence, as well as a more general setting, where the structure of the answer set differs from the one of the action set. Using the recently popularized game framework, we interpret this problem as a sequential zero-sum game and develop a CombGame meta-algorithm whose instances are asymptotically optimal algorithms with finite time guarantees. In addition to comparing two families of learners to instantiate our meta-algorithm, the main contribution of our work is a specific oracle efficient instance for best-arm identification with combinatorial actions. Based on a projection-free online learning algorithm for convex polytopes, it is the first computationally efficient algorithm which is asymptotically optimal and has competitive empirical performance.
45 pages. 3 tables. Appendices: from A to I. Figures: 1(a), 1(b), 2(a), 2(b), 3(a), 3(b), 3(c), 4(a), 4(b), 5(a), 5(b), 5(c), 5(d), 6(a), 6(b). To be published in the 32nd International Conference on Algorithmic Learning Theory and the Proceedings of Machine Learning Research vol 132:1-45, 2021