Combinatorial Pure Exploration with Continuous and Separable Reward Functions and Its Applications (Extended Version)
This work addresses a generalization of combinatorial pure exploration with linear rewards, offering a solution for non-linear reward functions, which is incremental as it builds on existing bandit frameworks.
The paper tackles the Combinatorial Pure Exploration problem with Continuous and Separable reward functions (CPE-CS) in stochastic multi-armed bandits, proposing an adaptive learning algorithm and analyzing its sample complexity with upper and lower bounds based on a new hardness measure called consistent optimality hardness.
We study the Combinatorial Pure Exploration problem with Continuous and Separable reward functions (CPE-CS) in the stochastic multi-armed bandit setting. In a CPE-CS instance, we are given several stochastic arms with unknown distributions, as well as a collection of possible decisions. Each decision has a reward according to the distributions of arms. The goal is to identify the decision with the maximum reward, using as few arm samples as possible. The problem generalizes the combinatorial pure exploration problem with linear rewards, which has attracted significant attention in recent years. In this paper, we propose an adaptive learning algorithm for the CPE-CS problem, and analyze its sample complexity. In particular, we introduce a new hardness measure called the consistent optimality hardness, and give both the upper and lower bounds of sample complexity. Moreover, we give examples to demonstrate that our solution has the capacity to deal with non-linear reward functions.