Related papers: Dynamic programming equation for the mean field op…
We consider a broad class of dynamic programming (DP) problems that involve a partially linear structure and some positivity properties in their system equation and cost function. We address deterministic and stochastic problems, possibly…
In this paper, we first establish the dynamic programming principle for stochastic optimal control problems defined on compact Riemannian manifolds without boundary. Subsequently, we derive the associated Hamilton-Jacobi-Bellman (HJB)…
Sampling from high-dimensional Gibbs measures poses a challenge when the energy landscape consists of multiple metastable states. Enhanced-sampling methods mitigate this difficulty by introducing adaptive biasing potentials to facilitate…
This paper is devoted to a class of finite horizon deterministic mean field games with Grushin type dynamics, state constraints and nonlocal coupling. First, we consider the optimal control problem that each agent aims to solve when the…
We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an…
We consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem with reward function depending on the density of the state processes of agents still present in the game.…
Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade (Lasry and Lions, Japanese journal of mathematics, 2007). In this…
This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…
We are interested in the study of stochastic games for which each player faces an optimal stopping problem. In our setting, the players may interact through the criterion to optimise as well as through their dynamics. After briefly…
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 study the convergence problem for mean field control, also known as optimal control of McKean-Vlasov dynamics. We assume that the data is smooth but not convex, and thus the limiting value function $\mathcal{U} :[0,T] \times…
In this paper, we consider the classic stochastic (dynamic) knapsack problem, a fundamental mathematical model in revenue management, with general time-varying random demand. Our main goal is to study the optimal policies, which can be…
Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…
Some approaches to solving challenging dynamic programming problems, such as Q-learning, begin by transforming the Bellman equation into an alternative functional equation, in order to open up a new line of attack. Our paper studies this…
Using the tools of the Markov Decision Processes, we justify the dynamic programming approach to the optimal impulse control of deterministic dynamical systems. We prove the equivalence of the integral and differential forms of the…
This study addresses primal-dual dynamics for a stochastic programming problem for capacity network design. It is proven that consensus can be achieved on the \textit{here and now} variables which represent the capacity of the network. The…
We consider dynamic programming problems with a large time horizon, and give sufficient conditions for the existence of the uniform value. As a consequence, we obtain an existence result when the state space is precompact, payoffs are…
We study an optimal control problem of McKean--Vlasov branching diffusion processes, in which the interaction term is determined by the marginal measure induced by all alive particles in the system. Accordingly, the value function is…
We consider interacting agent systems with a large number of stochastic agents (or particles) influenced by a fixed number of external stochastic lead agents. Such examples arise, for example in models of opinion dynamics, where a small…
This paper focuses on a mean-field optimal stopping problem with non-Markov dynamics and common noise, inspired by Talbi, Touzi, and Zhang \cite{TalbiTouziZhang1,TalbiTouziZhang3}. The goal is to establish the limit theory and demonstrate…