Related papers: Disordered high-dimensional optimal control
An optimal control problem with a time-parameter is considered. The functional to be optimized includes the maximum over time-horizon reached by a function of the state variable, and so an $L^\infty$-term. In addition to the classical…
This article is concerned with an optimal control problem derived by mean-field forward-backward stochastic differential equation with noisy observation, where the drift coefficients of the state equation and the observation equation are…
Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…
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…
This paper presents an application of mean field control to dynamic production optimization. Both noncooperative and cooperative solutions are considered. We first introduce a market of a large number of agents (firms) with sticky prices…
We study the convergence problem of mean-field control theory in the presence of state constraints and non-degenerate idiosyncratic noise. Our main result is the convergence of the value functions associated to stochastic control problems…
This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…
The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with…
We discuss and compare two methods of investigations for the asymptotic regime of stochastic differential games with a finite number of players as the number of players tends to the infinity. These two methods differ in the order in which…
The optimal control of epidemic-like stochastic processes is important both historically and for emerging applications today, where it can be especially important to include time-varying parameters that impact viral epidemic-like…
In this paper, we consider the problem of multi-objective optimal control of a dynamical system with additive and multiplicative noises with given second moments and arbitrary probability distributions. The objectives are given by quadratic…
We study a specific class of finite-horizon mean field optimal stopping problems by means of the dynamic programming approach. In particular, we consider problems where the state process is not affected by the stopping time. Such problems…
In this paper, we study the optimal control of a discrete-time stochastic differential equation (SDE) of mean-field type, where the coefficients can depend on both a function of the law and the state of the process. We establish a new…
This paper is concerned with a discrete-time mean-field stochastic linear-quadratic optimal control problem arose from financial application. Through matrix dynamical optimization method, a group of linear feedback controls is investigated.…
In this paper, we are concerned with a stochastic optimal control problem of mean-field type under partial observation, where the state equation is governed by the controlled nonlinear mean-field stochastic differential equation, moreover…
This article proposes an improved trajectory optimization approach for stochastic optimal control of dynamical systems affected by measurement noise by combining optimal control with maximum likelihood techniques to improve the reduction of…
Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an…
Recent work linking deep neural networks and dynamical systems opened up new avenues to analyze deep learning. In particular, it is observed that new insights can be obtained by recasting deep learning as an optimal control problem on…
In this paper we present a dynamic programing approach to stochastic optimal control problems with dynamic, time-consistent risk constraints. Constrained stochastic optimal control problems, which naturally arise when one has to consider…
This article is concerned with stochastic control problems for backward doubly stochastic differential equations of mean-field type, where the coefficient functions depend on the joint distribution of the state process and the control…