AI RESEARCH
Maximum Principle of Optimal Probability Density Control
arXiv CS.LG
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ArXi:2505.18362v3 Announce Type: replace-cross We develop a general theoretical framework for optimal probability density control on standard measure spaces, aimed at addressing large-scale multi-agent control problems. In particular, we establish a maximum principle (MP) for control problems posed on infinite-dimensional spaces of probability distributions and control vector fields. We further derive the Hamilton--Jacobi--Bellman equation for the associated value functional defined on the space of probability distributions.