Online Stochastic Optimization under Correlated Bandit Feedback
This work addresses the challenge of correlated rewards in bandit optimization, which is a problem for researchers and practitioners in reinforcement learning and online decision-making, though it appears incremental as it builds on existing methods.
The paper tackles the problem of online stochastic optimization under correlated bandit feedback by introducing the high-confidence tree (HCT) algorithm, which achieves regret bounds matching state-of-the-art methods while handling correlated rewards and reducing memory requirements.
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.