Reinforcement Learning with Non-Cumulative Objective
This work tackles the problem of applying reinforcement learning to domains like communications and networking where objectives are not naturally cumulative, offering a method to adapt existing algorithms for such cases.
The paper addresses the limitation of cumulative objectives in reinforcement learning by proposing a generalized Bellman update for non-cumulative objectives, such as bottleneck objectives, and demonstrates its effectiveness on control tasks and network routing problems with improved flow rates.
In reinforcement learning, the objective is almost always defined as a \emph{cumulative} function over the rewards along the process. However, there are many optimal control and reinforcement learning problems in various application fields, especially in communications and networking, where the objectives are not naturally expressed as summations of the rewards. In this paper, we recognize the prevalence of non-cumulative objectives in various problems, and propose a modification to existing algorithms for optimizing such objectives. Specifically, we dive into the fundamental building block for many optimal control and reinforcement learning algorithms: the Bellman optimality equation. To optimize a non-cumulative objective, we replace the original summation operation in the Bellman update rule with a generalized operation corresponding to the objective. Furthermore, we provide sufficient conditions on the form of the generalized operation as well as assumptions on the Markov decision process under which the globally optimal convergence of the generalized Bellman updates can be guaranteed. We demonstrate the idea experimentally with the bottleneck objective, i.e., the objectives determined by the minimum reward along the process, on classical optimal control and reinforcement learning tasks, as well as on two network routing problems on maximizing the flow rates.