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Combinatorial Pure Exploration for Dueling Bandit
Wei Chen · Yihan Du · Longbo Huang · Haoyu Zhao

Tue Jul 14 07:00 AM -- 07:45 AM & Tue Jul 14 07:00 PM -- 07:45 PM (PDT) @ Virtual #None

In this paper, we study combinatorial pure exploration for dueling bandits (CPE-DB): we have multiple candidates for multiple positions as modeled by a bipartite graph, and in each round we sample a duel of two candidates on one position and observe who wins in the duel, with the goal of finding the best candidate-position matching with high probability after multiple rounds of samples. CPE-DB is an adaptation of the original combinatorial pure exploration for multi-armed bandit (CPE-MAB) problem to the dueling bandit setting. We consider both the Borda winner and the Condorcet winner cases. For Borda winner, we establish a reduction of the problem to the original CPE-MAB setting and design PAC and exact algorithms that achieve both the sample complexity similar to that in the CPE-MAB setting (which is nearly optimal for a subclass of problems) and polynomial running time per round. For Condorcet winner, we first design a fully polynomial time approximation scheme (FPTAS) for the offline problem of finding the Condorcet winner with known winning probabilities, and then use the FPTAS as an oracle to design a novel pure exploration algorithm CAR-Cond with sample complexity analysis. CAR-Cond is the first algorithm with polynomial running time per round for identifying the Condorcet winner in CPE-DB.

Author Information

Wei Chen (Microsoft)
Yihan Du (IIIS, Tsinghua University)
Longbo Huang (Tsinghua University)
Haoyu Zhao (Tsinghua University)

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