Decentralized Cooperative Reinforcement Learning with Hierarchical Information Structure

Multi-agent reinforcement learning (MARL) problems are challenging due to information asymmetry. To overcome this challenge, existing methods often require high level of coordination or communication between the agents. We consider two-agent multi-armed bandits (MABs) and Markov decision processes (MDPs) with a hierarchical information structure arising in applications, which we exploit to propose simpler and more efficient algorithms that require no coordination or communication. In the structure, in each step the ``leader" chooses her action first, and then the ``follower" decides his action after observing the leader's action. The two agents observe the same reward (and the same state transition in the MDP setting) that depends on their joint action. For the bandit setting, we propose a hierarchical bandit algorithm that achieves a near-optimal gap-independent regret of $\widetilde{\mathcal{O}}(\sqrt{ABT})$ and a near-optimal gap-dependent regret of $\mathcal{O}(\log(T))$, where $A$ and $B$ are the numbers of actions of the leader and the follower, respectively, and $T$ is the number of steps. We further extend to the case of multiple followers and the case with a deep hierarchy, where we both obtain near-optimal regret bounds. For the MDP setting, we obtain $\widetilde{\mathcal{O}}(\sqrt{H^7S^2ABT})$ regret, where $H$ is the number of steps per episode, $S$ is the number of states, $T$ is the number of episodes. This matches the existing lower bound in terms of $A, B$, and $T$.

Common Information based Approximate State Representations in Multi-Agent Reinforcement Learning

Due to information asymmetry, finding optimal policies for Decentralized Partially Observable Markov Decision Processes (Dec-POMDPs) is hard with the complexity growing doubly exponentially in the horizon length. The challenge increases greatly in the multi-agent reinforcement learning (MARL) setting where the transition probabilities, observation kernel, and reward function are unknown. Here, we develop a general compression framework with approximate common and private state representations, based on which decentralized policies can be constructed. We derive the optimality gap of executing dynamic programming (DP) with the approximate states in terms of the approximation error parameters and the remaining time steps. When the compression is exact (no error), the resulting DP is equivalent to the one in existing work. Our general framework generalizes a number of methods proposed in the literature. The results shed light on designing practically useful deep-MARL network structures under the "centralized learning distributed execution" scheme.