相关论文: Adaptive low-rank approximation and denoised Monte…

We develop a Monte-Carlo based numerical method for solving discrete-time stochastic optimal control problems with inventory. These are optimal control problems in which the control affects only a deterministically evolving inventory…

Large Language Models (LLMs) are highly resource-intensive to fine-tune due to their enormous size. While low-rank adaptation is a prominent parameter-efficient fine-tuning approach, it suffers from sensitivity to hyperparameter choices,…

Uncertainty quantification based on stochastic spectral methods suffers from the curse of dimensionality. This issue was mitigated recently by low-rank tensor methods. However, there exist two fundamental challenges in low-rank tensor-based…

We derive and analyze numerical methods for underdamped (kinetic) Langevin dynamics in a domain with elastic reflection at the boundary. First-order approximations are based on an Euler-type scheme incorporating collision-handling at the…

We made a comparative analysis of numerical methods for multidimensional optimization. The main parameter is a number of computations of the test function to reach necessary accuracy, as it is computationally "slow". For complex functions,…

We solve a regularized weighted low-rank approximation problem by a stochastic gradient descent on a manifold. To guarantee the convergence of our stochastic gradient descent, we establish a convergence theorem on manifolds for…

Many physical and mathematical models involve random fields in their input data. Examples are ordinary differential equations, partial differential equations and integro--differential equations with uncertainties in the coefficient…

We propose a numerical integrator for determining low-rank approximations to solutions of large-scale matrix differential equations. The considered differential equations are semilinear and stiff. Our method consists of first splitting the…

This paper proposes an effective low-rank alternating direction doubling algorithm (R-ADDA) for computing numerical low-rank solutions to large-scale sparse continuous-time algebraic Riccati matrix equations. The method is based on the…

Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard…

In this paper we propose several adaptive gradient methods for stochastic optimization. Unlike AdaGrad-type of methods, our algorithms are based on Armijo-type line search and they simultaneously adapt to the unknown Lipschitz constant of…

We construct an efficient classical analogue of the quantum matrix inversion algorithm (HHL) for low-rank matrices. Inspired by recent work of Tang, assuming length-square sampling access to input data, we implement the pseudoinverse of a…

We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…

We consider a class of finite time horizon nonlinear stochastic optimal control problem, where the control acts additively on the dynamics and the control cost is quadratic. This framework is flexible and has found applications in many…

Langevin Monte Carlo (LMC) is a popular Bayesian sampling method. For the log-concave distribution function, the method converges exponentially fast, up to a controllable discretization error. However, the method requires the evaluation of…

We consider the problem of computing tractable approximations of time-dependent d x d large positive semi-definite (PSD) matrices defined as solutions of a matrix differential equation. We propose to use "low-rank plus diagonal" PSD…

The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…

Science and engineering problems subject to uncertainty are frequently both computationally expensive and feature nonsmooth parameter dependence, making standard Monte Carlo too slow, and excluding efficient use of accelerated uncertainty…

Hamiltonian Monte Carlo and underdamped Langevin Monte Carlo are state-of-the-art methods for taking samples from high-dimensional distributions with a differentiable density function. To generate samples, they numerically integrate…

In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…