Online Stochastic Optimization under Correlated Bandit Feedback

TL;DR

This paper introduces the HCT algorithm for online stochastic optimization in bandit settings with correlated rewards, achieving improved regret bounds, lower memory use, and weaker smoothness assumptions, with applications to reinforcement learning.

Contribution

The paper presents the high-confidence tree (HCT) algorithm, a novel approach that handles correlated rewards and improves upon existing methods in regret, memory, and smoothness requirements.

Findings

HCT achieves regret bounds matching state-of-the-art.

HCT effectively handles correlated reward processes.

Preliminary empirical results support HCT's applicability.

Abstract

In this paper we consider the problem of online stochastic optimization of a locally smooth function under bandit feedback. We introduce the high-confidence tree (HCT) algorithm, a novel any-time $\mathcal{X}$-armed bandit algorithm, and derive regret bounds matching the performance of existing state-of-the-art in terms of dependency on number of steps and smoothness factor. The main advantage of HCT is that it handles the challenging case of correlated rewards, whereas existing methods require that the reward-generating process of each arm is an identically and independent distributed (iid) random process. HCT also improves on the state-of-the-art in terms of its memory requirement as well as requiring a weaker smoothness assumption on the mean-reward function in compare to the previous anytime algorithms. Finally, we discuss how HCT can be applied to the problem of policy search in reinforcement learning and we report preliminary empirical results.