Related papers: Dynamic programming equation for the mean field op…
We study the optimal control of path-dependent McKean-Vlasov equations valued in Hilbert spaces motivated by non Markovian mean-field models driven by stochastic PDEs. We first establish the well-posedness of the state equation, and then we…
We describe an abstract control-theoretic framework in which the validity of the dynamic programming principle can be established in continuous time by a verification of a small number of structural properties. As an application we treat…
In this paper we present the Warm-starting Dynamic Thresholding algorithm, developed using dynamic programming, for a variant of the standard online selection problem. The problem allows job positions to be either free or already occupied…
In this paper, we study a regularised relaxed optimal control problem and, in particular, we are concerned with the case where the control variable is of large dimension. We introduce a system of mean-field Langevin equations, the invariant…
Liquid droplet dynamics are widely used in biological and engineering applications, which contain complex interfacial instabilities and pattern formation such as droplet merging, splitting, and transport. This paper studies a class of mean…
We propose a new method called the N-particle underdamped Langevin algorithm for optimizing a special class of non-linear functionals defined over the space of probability measures. Examples of problems with this formulation include…
In this paper we are interested in a new type of {\it mean-field}, non-Markovian stochastic control problems with partial observations. More precisely, we assume that the coefficients of the controlled dynamics depend not only on the paths…
We consider challenging dynamic programming models where the associated Bellman equation, and the value and policy iteration algorithms commonly exhibit complex and even pathological behavior. Our analysis is based on the new notion of…
We provide an alternative approach to the existence of solutions to dynamic programming equations arising in the discrete game-theoretic interpretations for various nonlinear partial differential equations including the infinity Laplacian,…
This research considers the ranking and selection with input uncertainty. The objective is to maximize the posterior probability of correctly selecting the best alternative under a fixed simulation budget, where each alternative is measured…
We study a combined optimal control/stopping problem under a nonlinear expectation ${\cal E}^f$ induced by a BSDE with jumps, in a Markovian framework. The terminal reward function is only supposed to be Borelian. The value function $u$…
For sequential stochastic control problems with standard Borel measurement and control action spaces, we introduce a general (universally applicable) dynamic programming formulation, establish its well-posedness, and provide new existence…
We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with respect to the control variable. Particular instances of the problem considered here are mean…
The planning domain has experienced increased interest in the formal synthesis of decision-making policies. This formal synthesis typically entails finding a policy which satisfies formal specifications in the form of some well-defined…
We explore the dynamics of active elements performing persistent random motion with fluctuating active speed and in the presence of translational noise in a $d$-dimensional harmonic trap, modeling active speed generation through an…
We consider mean field social optimization in nonlinear diffusion models. By dynamic programming with a representative agent employing cooperative optimizer selection, we derive a new Hamilton--Jacobi--Bellman (HJB) equation to be called…
We study stochastic optimal control problems for (possibly degenerate) McKean-Vlasov controlled diffusions and obtain discrete-time as well as finite interacting particle approximations. (i) Under mild assumptions, we first prove the…
We present a novel simulation-free framework for training continuous-time diffusion processes over very general objective functions. Existing methods typically involve either prescribing the optimal diffusion process -- which only works for…
In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed…
In the nonlinear diffusion framework, stochastic processes of McKean-Vlasov type play an important role. In some cases they correspond to processes attracted by their own probability distribution: the so-called self-stabilizing processes.…