Related papers: Generative Modelling with Tensor Train approximati…

We propose a framework for discrete scientific data compression based on the tensor-train (TT) decomposition. Our approach is tailored to handle unstructured output data from discrete element method (DEM) simulations, demonstrating its…

Presented is a method for efficient computation of the Hamilton-Jacobi (HJ) equation for time-optimal control problems using the generalized Hopf formula. Typically, numerical methods to solve the HJ equation rely on a discrete grid of the…

This work reformulates language generation as a stochastic optimal control problem, providing a unified theoretical perspective to analyze autoregressive and diffusion models and explain their limitations (Efficiency-Fidelity Paradox,…

Real-world physical systems, like composite materials and porous media, exhibit complex heterogeneities and multiscale nature, posing significant computational challenges. Computational homogenization is useful for predicting macroscopic…

Nonlinear filtering with correlated noise leads to a Duncan-Mortensen-Zakai (DMZ) equation in the form of a stochastic partial differential equation (SPDE). Unlike the independent noise case, the presence of correlation prevents the…

We propose a neural network approach that yields approximate solutions for high-dimensional optimal control problems and demonstrate its effectiveness using examples from multi-agent path finding. Our approach yields controls in a feedback…

We propose a novel data-driven neural network (NN) optimization framework for solving an optimal stochastic control problem under stochastic constraints. Customized activation functions for the output layers of the NN are applied, which…

In reinforcement learning (RL), the long-term behavior of decision-making policies is evaluated based on their average returns. Distributional RL has emerged, presenting techniques for learning return distributions, which provide additional…

We address the problem of computing a control for a time-dependent nonlinear system to reach a target set in a minimal time. To solve this minimal time control problem, we introduce a hierarchy of linear semi-infinite programs, the values…

This paper develops a comparison theorem for viscosity solutions of a new class of Hamilton-Jacobi-Bellman (HJB) equations, which is used to solve the separated problem governed by the K-S equation in the Wasserstein space. A distinctive…

Stochastic optimal control problems for Hamiltonian dynamics on graphs have wide-ranging applications in mechanics and quantum field theory, particularly in systems with graph-based structures. In this paper, we establish the existence and…

This paper presents a mathematical formulation to perform temporal parallelisation of continuous-time optimal control problems, which can be solved via the Hamilton--Jacobi--Bellman (HJB) equation. We divide the time interval of the control…

In this note, we study a class of indefinite stochastic McKean-Vlasov linear-quadratic (LQ in short) control problem under the control taking nonnegative values. In contrast to the conventional issue, both the classical dynamic programming…

The ergodic control problem for a non-degenerate controlled diffusion controlled through its drift is considered under a uniform stability condition that ensures the well-posedness of the associated Hamilton-Jacobi-Bellman (HJB) equation. A…

This paper addresses the model-free nonlinear optimal problem with generalized cost functional, and a data-based reinforcement learning technique is developed. It is known that the nonlinear optimal control problem relies on the solution of…

The interplay between stochastic processes and optimal control has been extensively explored in the literature. With the recent surge in the use of diffusion models, stochastic processes have increasingly been applied to sample generation.…

Consider the problem of predicting the next symbol given a sample path of length n, whose joint distribution belongs to a distribution class that may have long-term memory. The goal is to compete with the conditional predictor that knows…

We develop a new method HTBB for the multidimensional black-box approximation and gradient-free optimization, which is based on the low-rank hierarchical Tucker decomposition with the use of the MaxVol indices selection procedure. Numerical…

Tensor train (TT) decomposition, a powerful tool for analyzing multidimensional data, exhibits superior performance in many machine learning tasks. However, existing methods for TT decomposition either suffer from noise overfitting, or…

This paper introduces a new type of second order stochastic backward Hamilton-Jacobi-Bellman (HJB) equations for optimal stochastic control problems with a currently observable but non-predicable parameter process, in addition to the…