Related papers: Maximum Principle of Optimal Probability Density C…
We consider the problem of controlling the group behavior of a large number of dynamic systems that are constantly interacting with each other. These systems are assumed to have identical dynamics (e.g., birds flock, robot swarm) and their…
The paper presents an approach to studying optimal control problems in the space of nonnegative measures with dynamics given by a nonlocal balance law. This approach relies on transforming the balance law into a continuity equation in the…
We study optimal control problems for interacting branching diffusion processes, a class of measure-valued dynamics capturing both spatial motion and branching mechanisms. From the perspective of the dynamic programming principle, we…
We study discrete-time finite-horizon optimal control problems in probability spaces, whereby the state of the system is a probability measure. We show that, in many instances, the solution of dynamic programming in probability spaces…
The paper addresses an optimal ensemble control problem for nonlocal continuity equations on the space of probability measures. We admit the general nonlinear cost functional, and an option to directly control the nonlocal terms of the…
Within the framework of viscosity solution, we study the relationship between the maximum principle (MP) in [9] and the dynamic programming principle (DPP) in [10] for a fully coupled forward-backward stochastic controlled system (FBSCS)…
In this work, we investigate a stochastic control framework for global optimization over both Euclidean spaces and the Wasserstein space of probability measures, where the objective function may be non-convex and/or non-differentiable. In…
We derive a framework to compute optimal controls for problems with states in the space of probability measures. Since many optimal control problems constrained by a system of ordinary differential equations (ODE) modelling interacting…
In this paper, the optimal consensus problem for general nonlinear multi-agent systems is studied, where both leaderless and leader-follower cases are considered in a unified framework. The key idea is to convert consensus problems into…
We study a multiscale stochastic optimal control problem subject to state constraints on the slow variable. To address this class of problems, we develop a rigorous theoretical framework based on singular perturbation analysis, tailored to…
We consider fully nonlinear Hamilton-Jacobi-Bellman equations associated to diffusion control problems involving a finite set-valued (or switching) control and possibly a continuum-valued control. We construct a lower complexity…
The numerical realization of the dynamic programming principle for continuous-time optimal control leads to nonlinear Hamilton-Jacobi-Bellman equations which require the minimization of a nonlinear mapping over the set of admissible…
We introduce the concept of {\it mean-field optimal control} which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional…
In this paper, we aim to solve the high dimensional stochastic optimal control problem from the view of the stochastic maximum principle via deep learning. By introducing the extended Hamiltonian system which is essentially an FBSDE with a…
We explore the approximation of feedback control of integro-differential equations containing a fractional Laplacian term. To obtain feedback control for the state variable of this nonlocal equation we use the Hamilton--Jacobi--Bellman…
Optimal control of diffusion processes is intimately connected to the problem of solving certain Hamilton-Jacobi-Bellman equations. Building on recent machine learning inspired approaches towards high-dimensional PDEs, we investigate the…
Maximum entropy reinforcement learning (RL) methods have been successfully applied to a range of challenging sequential decision-making and control tasks. However, most of existing techniques are designed for discrete-time systems. As a…
Stochastic optimal control control problems with merely measurable coefficients are not well understood. In this manuscript, we consider fully non-linear stochastic optimal control problems in infinite horizon with measurable coefficients…
We consider a general class of stochastic optimal control problems, where the state process lives in a real separable Hilbert space and is driven by a cylindrical Brownian motion and a Poisson random measure; no special structure is imposed…
The aim of this work is to develop a deep learning method for solving high-dimensional stochastic control problems based on the Hamilton--Jacobi--Bellman (HJB) equation and physics-informed learning. Our approach is to parameterize the…