Fusing Reward and Dueling Feedback in Stochastic Bandits
This addresses a problem in multi-armed bandit optimization for researchers and practitioners, offering incremental improvements by integrating two feedback types.
This paper tackles the problem of combining absolute reward and relative dueling feedback in stochastic bandits, showing that an efficient algorithm can achieve regret based on the smaller of the two feedback types per arm, with the decomposition fusion algorithm matching the derived lower bound up to a constant.
This paper investigates the fusion of absolute (reward) and relative (dueling) feedback in stochastic bandits, where both feedback types are gathered in each decision round. We derive a regret lower bound, demonstrating that an efficient algorithm may incur only the smaller among the reward and dueling-based regret for each individual arm. We propose two fusion approaches: (1) a simple elimination fusion algorithm that leverages both feedback types to explore all arms and unifies collected information by sharing a common candidate arm set, and (2) a decomposition fusion algorithm that selects the more effective feedback to explore the corresponding arms and randomly assigns one feedback type for exploration and the other for exploitation in each round. The elimination fusion experiences a suboptimal multiplicative term of the number of arms in regret due to the intrinsic suboptimality of dueling elimination. In contrast, the decomposition fusion achieves regret matching the lower bound up to a constant under a common assumption. Extensive experiments confirm the efficacy of our algorithms and theoretical results.