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We study the Combinatorial Pure Exploration problem with Continuous andSeparable reward functions (CPE-CS) in the stochastic multi-armed banditsetting. In a CPE-CS instance, we are given several stochastic arms withunknown distributions, as well as a collection of possible decisions. Eachdecision has a reward according to the distributions of arms. The goal is toidentify the decision with the maximum reward, using as few arm samples aspossible. The problem generalizes the combinatorial pure exploration problemwith linear rewards, which has attracted significant attention in recent years.In this paper, we propose an adaptive learning algorithm for the CPE-CSproblem, and analyze its sample complexity. In particular, we introduce a newhardness measure called the consistent optimality hardness, and give both theupper and lower bounds of sample complexity. Moreover, we give examples todemonstrate that our solution has the capacity to deal with non-linear rewardfunctions.

Combinatorial Pure Exploration with Continuous and Separable Reward Functions and Its Applications (Extended Version)