Related papers: On a Class of Singular Stochastic Control Problems…
We study continuous-time reinforcement learning (RL) for stochastic control in which system dynamics are governed by jump-diffusion processes. We formulate an entropy-regularized exploratory control problem with stochastic policies to…
We study zero-sum stochastic games between a singular controller and a stopper when the (state-dependent) diffusion matrix of the underlying controlled diffusion process is degenerate. In particular, we show the existence of a value for the…
We study a stochastic optimal control problem for jump-diffusion systems whose drift coefficient is piecewise Lipschitz continuous and exhibits threshold-induced discontinuities. Such dynamics naturally arise in applications with…
We propose a novel reformulation of the stochastic optimal control problem as an approximate inference problem, demonstrating, that such a interpretation leads to new practical methods for the original problem. In particular we characterise…
Optimal control problems are inherently hard to solve as the optimization must be performed simultaneously with updating the underlying system. Starting from an initial guess, Howard's policy improvement algorithm separates the step of…
This paper studies a class of continuous-time scalar-state stochastic Linear-Quadratic (LQ) optimal control problem with the linear control constraints. Applying the state separation theorem induced from its special structure, we develop…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
In this paper, we consider an inverse space-dependent source problem for a time-fractional diffusion equation. To deal with the ill-posedness of the problem, we transform the problem into an optimal control problem with total variational…
In this paper, we study a class of multi-dimensional reflected backward stochastic differential equations when the noise is driven by a Brownian motion and an independent Poisson point process, and when the solution is forced to stay in a…
This paper studies indefinite stochastic linear-quadratic (LQ) optimal control for jump-diffusion systems with random coefficients. We construct an algebraic inverse flow from the zero-control base system, extract the semimartingale kernel…
Recent advancements in diffusion models and diffusion bridges primarily focus on finite-dimensional spaces, yet many real-world problems necessitate operations in infinite-dimensional function spaces for more natural and interpretable…
We consider a class of stochastic control problems which has been widely used in optimal foraging theory. The state processes have two distinct dynamics, characterized by two pairs of drift and diffusion coefficients, depending on whether…
Interaction of a domain wall with boundaries of a system is studied for a class of stochastic driven particle models. Reflection maps are introduced for the description of this process. We show that, generically, a domain wall reflects…
In this work, we focus on the alignment problem of diffusion models with a continuous reward function, which represents specific objectives for downstream tasks, such as increasing darkness or improving the aesthetics of images. The central…
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 study a reflected Markov-modulated Brownian motion with a two sided reflection in which the drift, diffusion coefficient and the two boundaries are (jointly) modulated by a finite state space irreducible continuous time…
Classical reverse diffusion is generated by changing the drift at fixed noise. We show that the quantum version of this principle obeys an exact law with a sharp phase boundary. For Gaussian pure-loss dynamics, the canonical model of…
This paper is concerned with the distributed control and stabilization problems for linear discrete-time large scale systems with imposed constraints. The main contributions of this paper are: Firstly, by using the maximum principle…
We revisit an absolutely-continuous version of the stochastic control problem driven by a L\'evy process. A strategy must be absolutely continuous with respect to the Lebesgue measure and the running cost function is assumed to be convex.…
We consider a class of stochastic impulse control problems of general stochastic processes i.e. not necessarily Markovian. Under fairly general conditions we establish existence of an optimal impulse control. We also prove existence of…