Distributed Value Functions

Many interesting problems, such as power grids, network switches, and tra c ow, that are candidates for solving with reinforcement learning (RL), also have properties that make distributed solutions desirable. We propose an algorithm for distributed reinforcement learning based on distributing the representation of the value function across nodes. Each node in the system only has the ability to sense state locally, choose actions locally, and receive reward locally (the goal of the system is to maximize the sum of the rewards over all nodes and over all time). However each node is allowed to give its neighbors the current estimate of its value function for the states it passes through. We present a value function learning rule, using that information, that allows each node to learn a value function that is an estimate of a weighted sum of future rewards for all the nodes in the network. With this representation, each node can choose actions to improve the performance of the overall system. We demonstrate our algorithm on the distributed control of a simulated power grid. We compare it against other methods including: use of a global reward signal, nodes that act locally with no communication, and nodes that share rewards (but not value function) information with each other. Our results show that the distributed value function algorithm outperforms the others, and we conclude with an analysis of what problems are best suited for distributed value functions and the new research directions opened up by this work.