Simple Modification of the Upper Confidence Bound Algorithm by Generalized Weighted Averages
This is an incremental improvement for reinforcement learning practitioners, offering a simple modification to balance exploration and exploitation in bandit algorithms.
The authors tackled the multi-armed bandit problem by proposing GWA-UCB1, a generalized UCB algorithm using weighted averages, which outperformed existing methods like G-UCB1, UCB1-Tuned, and Thompson sampling in most tested stochastic and survival settings.
The multi-armed bandit (MAB) problem is a classical problem that models sequential decision-making under uncertainty in reinforcement learning. In this study, we propose a new generalized upper confidence bound (UCB) algorithm (GWA-UCB1) by extending UCB1, which is a representative algorithm for MAB problems, using generalized weighted averages, and present an effective algorithm for various problem settings. GWA-UCB1 is a two-parameter generalization of the balance between exploration and exploitation in UCB1 and can be implemented with a simple modification of the UCB1 formula. Therefore, this algorithm can be easily applied to UCB-based reinforcement learning models. In preliminary experiments, we investigated the optimal parameters of a simple generalized UCB1 (G-UCB1), prepared for comparison and GWA-UCB1, in a stochastic MAB problem with two arms. Subsequently, we confirmed the performance of the algorithms with the investigated parameters on stochastic MAB problems when arm reward probabilities were sampled from uniform or normal distributions and on survival MAB problems assuming more realistic situations. GWA-UCB1 outperformed G-UCB1, UCB1-Tuned, and Thompson sampling in most problem settings and can be useful in many situations. The code is available at https://github.com/manome/python-mab.