Related papers: Stochastic Optimal Control for Diffusion Bridges i…
We study high-dimensional stochastic optimal control problems in which many agents cooperate to minimize a convex cost functional. We consider both the full-information problem, in which each agent observes the states of all other agents,…
Adversarial diffusion and diffusion-inversion methods have advanced unpaired image-to-image translation, but each faces key limitations. Adversarial approaches require target-domain adversarial loss during training, which can limit…
We take a new look at the relation between the optimal transport problem and the Schr\"{o}dinger bridge problem from the stochastic control perspective. We show that the connections are richer and deeper than described in existing…
The maximum principle for optimal control problems of fully coupled forward-backward doubly stochastic differential equations (FBDSDEs in short) in the global form is obtained, under the assumptions that the diffusion coefficients do not…
We solve explicitly a two-dimensional singular control problem of finite fuel type for infinite time horizon. The problem stems from the optimal liquidation of an asset position in a financial market with multiplicative and transient price…
Distributionally robust optimal control (DROC) is gaining interest. This study presents a reformulation method for discrete DROC (DDROC) problems to design optimal control policies under a worst-case distributional uncertainty. The…
Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…
Approximate methods to solve stochastic optimal control (SOC) problems have received significant interest from researchers in the past decade. Probabilistic inference approaches to SOC have been developed to solve nonlinear quadratic…
In 1931/32, Schroedinger studied a hot gas Gedankenexperiment, an instance of large deviations of the empirical distribution and an early example of the so-called maximum entropy inference method. This so-called Schroedinger bridge problem…
This work proposes a method for solving linear stochastic optimal control (SOC) problems using sum of squares and semidefinite programming. Previous work had used polynomial optimization to approximate the value function, requiring a high…
One important property of DIstribution Correction Estimation (DICE) methods is that the solution is the optimal stationary distribution ratio between the optimized and data collection policy. In this work, we show that DICE-based methods…
Over the last few years, sampling-based stochastic optimal control (SOC) frameworks have shown impressive performances in reinforcement learning (RL) with applications in robotics. However, such approaches require a large amount of samples…
Utility-based power allocation in wireless ad-hoc networks is inherently nonconvex because of the global coupling induced by the co-channel interference. To tackle this challenge, we first show that the globally optimal point lies on the…
This work introduces a stochastic model predictive control scheme for dynamic chance constraints. We consider linear discrete-time systems affected by unbounded additive stochastic disturbance. To synthesize an optimal controller, we solve…
We consider the task of generating discrete-time realisations of a nonlinear multivariate diffusion process satisfying an It\^o stochastic differential equation conditional on an observation taken at a fixed future time-point. Such…
Recent studies have extended the use of the stochastic Hamilton-Jacobi-Bellman (HJB) equation to include complex variables for deriving quantum mechanical equations. However, these studies often assume that it is valid to apply the HJB…
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…
Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…
This paper aims to conduct a comprehensive theoretical analysis of current diffusion models. We introduce a novel generative learning methodology utilizing the Schr{\"o}dinger bridge diffusion model in latent space as the framework for…
Diffusion and flow-driven instability, or transport-driven instability, is one of the central mechanisms to generate inhomogeneous gradient of concentrations in spatially distributed chemical systems. However, verifying the transport-driven…