相关论文: Lipschitzian Estimates in Discrete-Time Constraine…

We study optimal control problems governed by abstract infinite dimensional stochastic differential equations using the dynamic programming approach. In the first part, we prove Lipschitz continuity, semiconcavity and semiconvexity of the…

We investigate conditions of optimality for an infinite horizon control problem and consider their correspondence with the value function. Assuming Lipschitz continuity of the value function, we prove that sensitivity relations plus the…

We study the optimal value function for control problems on Banach spaces that involve both continuous and discrete control decisions. For problems involving semilinear dynamics subject to mixed control inequality constraints, one can show…

In the last decades, control problems with infinite horizons and discount factors have become increasingly central not only for economics but also for applications in artificial intelligence and machine learning. The strong links between…

We study a family of optimal control problems in which one aims at minimizing a cost that mixes a quadratic control penalization and the variance of the system, both for finitely many agents and for the mean-field dynamics as their number…

We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…

This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…

We study a finite horizon optimal control problem for the continuity equation under a weighted integral state constraint on the mass outside a fixed set. The model is cast in a Hilbert framework for densities. On a suitable invariant…

The present paper considers a stochastic optimal control problem, in which the cost function is defined through a backward stochastic differential equation with infinite horizon driven by G-Brownian motion. Then we study the regularities of…

We study a stochastic control problem on a bounded domain, which arises from a continuous-time optimal management model. Via the corresponding Hamilton-Jacobi-Bellman equation the value function is shown to be jointly continuous and to…

We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…

We study the optimal control of discrete time mean filed dynamical systems under partial observations. We express the global law of the filtered process as a controlled system with its own dynamics. Following a dynamic programming approach,…

In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…

In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze the optimal control via the value function. Due to the non-smoothness of the $L^0$ cost…

In this paper we consider discrete time stochastic optimal control problems over infinite and finite time horizons. We show that for a large class of such problems the Taylor polynomials of the solutions to the associated Dynamic…

This paper examines stochastic optimal control problems in which the state is perfectly known, but the controller's measure of time is a stochastic process derived from a strictly increasing L\'evy process. We provide dynamic programming…

This paper addresses the problem of stochastic optimization with decision-dependent uncertainty, a class of problems where the probability distribution of the uncertain parameters is influenced by the decision-maker's actions. While recent…

We present a dynamic programming-based solution to a stochastic optimal control problem up to a hitting time for a discrete-time Markov control process. Firstly, we determine an optimal control policy to steer the process toward a compact…

We introduce a continuous policy-value iteration algorithm where the approximations of the value function of a stochastic control problem and the optimal control are simultaneously updated through Langevin-type dynamics. This framework…

We analyze an optimal stopping problem with a constraint on the expected cost. When the reward function and cost function are Lipschitz continuous in state variable, we show that the value of such an optimal stopping problem is a continuous…