Abstract: Using airlines as a backdrop, we study optimal overbooking policies with endogenous customer demand, when customers internalize their expected cost of being bumped. We first consider the traditional setting in which compensation for bumped passengers is fixed and booking limits are the airline's only form of control. We provide sufficient conditions under which demand endogeneity leads to lower overbooking limits in this case. We then consider the broader problem of joint control of ticket price, bumping compensation, and booking…

Abstract: Despite the great empirical success of deep reinforcement learning, its theoretical foundation is less well understood. In this work, we make the first attempt to theoretically understand the deep Q-network (DQN) algorithm from both algorithmic and statistical perspectives. Specifically, we focus on a slight simplification of DQN that fully captures its key features. Under mild assumptions, we establish the algorithmic and statistical rates of convergence for the action-value functions of the iterative policy sequence obtained by DQN. In particular,…