UCLA

Multi-agent systems have attracted attention in applications such as satellite networks and autonomous traffic. However, as the number of agents grows, the joint state, observation, and action spaces expand. This growth can lead to higher computational complexity, communication overhead, and unstable optimization. Scalability therefore asks whether agents can operate without their online burden growing with the total system size. We study scalability in estimation and decision-making, focusing on these two problems under uncertainty. In estimation, uncertainty appears through unknown inputs, unmeasured signals that nonetheless enter the dynamics. In decision-making, uncertainty arises from changing population distributions and common noise. Based on how agents are modeled and interact, we consider two regimes: the networked regime and the population regime. We primarily study estimation in the networked regime and decision-making in the population regime. In the networked regime, agents are finite and identifiable, and communicate over a time-varying graph. In the population regime, agents are numerous and interchangeable, each responding to the population distribution rather than to individuals. In the networked regime, we develop recursive filters that jointly estimate the state and unknown input. By decoupling the unknown-input and state-estimation steps, the filters remain unbiased and prevent model mismatch from contaminating the state estimate. Prior knowledge of the unknown input is further incorporated to reduce estimation variance, and its effect on estimator rank conditions is analyzed. These filters are then decentralized for heterogeneous networks with time-varying topology, where agents exchange only local estimates while approaching full-information accuracy. Because sensing and planning are coupled, we also study sensor coverage, whose placement admits a submodular approximation bound governed by a curvature constant. We prove that this curvature is inflated by the discretization itself and derive the explicit law by which it grows as the grid is refined. In the population regime, we formulate the problem as a mean-field game and develop a Master Online Mirror Descent algorithm that learns a single policy network conditioned on the population distribution and common-noise history. Through iterative learning and a specialized regularizer, the policy converges stably toward Nash equilibria across different initial distributions and common-noise realizations. On benchmarks, it reduces exploitability faster than existing deep reinforcement learning methods, allowing each agent to make decisions independently even as the population approaches the infinite limit, while still driving the overall system toward equilibrium.