Scalable Policy Optimization for Networked Multi-Agent Reinforcement Learning with Continuous State-Action Spaces

We develop the Continuous Distributed Coupled Policy Gradient (CDCPG) algorithm for cooperative reinforcement learning in networked Markov decision processes with continuous state and action spaces. Each agent maintains a local actor over a bounded graph neighborhood, and a localized least-squares temporal-difference critic evaluates a truncated action-value function through a spectral random-feature representation of the local transition kernel. The analysis makes four contributions. First, the truncated action-value function is constructed as a conditional expectation over the neighborhood, yielding a well-posed localized Bellman theory that removes the continuation-kernel mismatch of naive truncation arguments. Second, we expose a dimensional obstruction to temporal-difference stability for normalized random features and prove an unconditional excitation bound that reduces stability to a symmetric persistence-of-excitation condition, monitorable through an online matrix-concentration certificate. Third, under exponential spatial decay of agent interactions, the excitation condition, and smoothness of the objective, CDCPG drives an averaged per-agent stationarity measure to within any excess $ε$ of an explicitly characterized approximation floor using $\widetilde{\mathcal{O}}(ε^{-2})$ shared-oracle samples, and the excess dependence matches the smooth nonconvex first-order rate; per-agent computation and communication are governed by the neighborhood size rather than the network size. Fourth, an adaptive-locality rule selects the radius that balances truncation and graph-decay residuals against the target accuracy. Experiments on a networked linear-quadratic benchmark corroborate the locality and feature-dimension predictions.