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

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.