Online mixed discrete and continuous optimization: Algorithms, regret analysis and applications

Lintao Ye, Ming Chi, Zhi-Wei Liu, Xiaoling Wang, Vijay Gupta

Abstract: We study an online mixed discrete and continuous optimization problem where a decision maker interacts with an unknown environment over T rounds. At each round, the decision maker needs to jointly choose a discrete action and a continuous action and receives a reward associated with the chosen actions. The decision maker seeks to maximize the accumulative reward after T rounds. We propose algorithms to solve the online mixed discrete and continuous optimization problem that yield regret sublinear in T. We apply our algorithms to solve some important applications in practice with regret guarantees. We validate our theoretical results with numerical experiments.