arXiv subjects

Chaoying Pei

Publications and source records attributed to Chaoying Pei.

4 recordsLinked to original sources

arXiv2026

An Occupation-Measure and Frank-Wolfe Framework for Heterogeneous Mean-Field Control

Heterogeneous mean-field control (MFC) problems involve multiple interacting populations with distinct dynamics, control constraints, and interaction patterns, making both analysis and computation substantially more difficult than in the homogeneous setting. In particular, existing formulations do not readily yield scalable solution methods that preserve population-level structure. To address this, we develop a heterogeneous occupation-measure mean-field control (OM-MFC) framework that lifts the problem to a population-level optimization over measures subject to dynamical constraints that are linear in the measures. We show that the resulting optimization problem is convex under a positive-semidefinite matrix-valued kernel condition, which captures coupled interactions across populations. Based on this formulation, we derive a Frank-Wolfe (FW) method whose linear minimization subproblem decomposes into independent population-wise optimal control problems, enabling parallel computation without requiring an a priori discretization of the measure space. Numerical examples on UAV coordination and search-and-rescue scenarios illustrate that the proposed framework captures symmetric coordination, asymmetric yielding, and directional interaction effects within a unified and computationally tractable trajectory-optimization framework.

math.OC↗

arXiv2026

Convexifying Mean-Field Control: An Occupation-Measure and Frank-Wolfe Approach

Large-scale robotic swarms motivate the use of mean-field control (MFC). Classical partial differential equation (PDE)-based formulations provide a principled framework but can become computationally challenging in higher dimensions, whereas machine learning achieves scalability at the cost of approximation and guarantees. In this work, we establish an optimization-based framework that lifts the MFC problem into the space of occupation measures, resulting in a convex relaxation formulated as an optimization over measures. The resulting problem is solved using a Frank-Wolfe (FW) algorithm in the measure space, with each iteration reduced to a tractable optimal control problem. This approach retains the O(1/k) convergence rate of FW, avoids discretization of the state space, and naturally incorporates interaction and safety constraints. Numerical experiments demonstrate agreement with analytic and PDE-based baselines in two dimensions and show that the method scales to three-dimensional environments with multiple obstacles, where standard grid-based PDE solvers become impractical. A full 3D instance with ten obstacles is solved in minutes on a standard workstation, underscoring the practicality and scalability of the proposed framework.

math.OC↗

arXiv2026

Occupation-Measure Mean-Field Control: Optimization over Measures and Frank-Wolfe Methods

Coordinating large populations of autonomous agents, such as UAV swarms or satellite constellations, poses significant computational challenges for traditional multi-agent control methods. This paper introduces a new optimization framework for large-population control, termed occupation-measure mean-field control (OM-MFC). The framework models the evolution of agent populations directly in the space of occupation measures and casts large-population control as an infinite-dimensional optimization problem over measures, which becomes convex under a positive-semidefiniteness condition on the interaction kernel. A Frank--Wolfe (FW) algorithm and its fully-corrective variant (FCFW) are developed to solve the resulting problem efficiently, where each iteration reduces to a classical optimal control subproblem. Theoretical results establish convexity, existence of optimal solutions, and convergence guarantees of the proposed algorithms. Owing to its measure-based formulation, the framework naturally accommodates systems with very large numbers of agents. Numerical experiments on UAV swarm coordination and satellite constellation control demonstrate the scalability and effectiveness of the proposed approach in high-dimensional and constrained environments.

math.OC↗

arXiv2024

Towards an Adaptable and Generalizable Optimization Engine in Decision and Control: A Meta Reinforcement Learning Approach

Sampling-based model predictive control (MPC) has found significant success in optimal control problems with non-smooth system dynamics and cost function. Many machine learning-based works proposed to improve MPC by a) learning or fine-tuning the dynamics/ cost function, or b) learning to optimize for the update of the MPC controllers. For the latter, imitation learning-based optimizers are trained to update the MPC controller by mimicking the expert demonstrations, which, however, are expensive or even unavailable. More significantly, many sequential decision-making problems are in non-stationary environments, requiring that an optimizer should be adaptable and generalizable to update the MPC controller for solving different tasks. To address those issues, we propose to learn an optimizer based on meta-reinforcement learning (RL) to update the controllers. This optimizer does not need expert demonstration and can enable fast adaptation (e.g., few-shots) when it is deployed in unseen control tasks. Experimental results validate the effectiveness of the learned optimizer regarding fast adaptation.

cs.LG↗