Efficient Pure Exploration for Combinatorial Bandits with Semi-Bandit Feedback

• URL: http://arxiv.org/abs/2101.08534v1
• Date: Thu, 21 Jan 2021 10:35:09 GMT
• Title: Efficient Pure Exploration for Combinatorial Bandits with Semi-Bandit Feedback
• Authors: Marc Jourdan, Mojm\'ir Mutn\'y, Johannes Kirschner, Andreas Krause
• Abstract summary: Combinatorial bandits generalize multi-armed bandits, where the agent chooses sets of arms and observes a noisy reward for each arm contained in the chosen set. 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. Based on a projection-free online learning algorithm for finite polytopes, it is the first computationally efficient algorithm which is convexally optimal and has competitive empirical performance.
• Score: 51.21673420940346
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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