相关论文: Bringing regularized optimal transport to lightspe…

We consider finite Markov decision processes (MDPs) with convex constraints and known dynamics. In principle, this problem is amenable to off-the-shelf convex optimization solvers, but typically this approach suffers from poor scalability.…

In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…

Optimal transport is a framework that facilitates the most efficient allocation of a limited amount of resources. However, the most efficient allocation scheme does not necessarily preserve the most fairness. In this paper, we establish a…

This paper considers constrained linear dynamic games with quadratic objective functions, which can be cast as affine variational inequalities. By leveraging the problem structure, we apply the Douglas-Rachford splitting, which generates a…

The Douglas Rachford algorithm is an algorithm that converges to a minimizer of a sum of two convex functions. The algorithm consists in fixed point iterations involving computations of the proximity operators of the two functions…

Three-dimensional neutron transport calculations using the Method of Characteristics (MOC) are highly regarded for their exceptional computational efficiency, precision, and stability. Nevertheless, when dealing with extensive-scale…

In this article, we propose and study a stochastic and relaxed preconditioned Douglas--Rachford splitting method to solve saddle-point problems that have separable dual variables. We prove the almost sure convergence of the iteration…

In this paper, we investigate the behavior of the family of graph-based splitting algorithms specialized to the problem of finding a point in the intersection of linear subspaces. The algorithms in this family, which encompasses several…

Distributionally robust optimization has been shown to offer a principled way to regularize learning models. In this paper, we find that Tikhonov regularization is distributionally robust in an optimal transport sense (i.e., if an adversary…

Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…

We present efficient implementations of atom reconfiguration algorithms for both CPUs and GPUs, along with a batching routine to merge displacement operations for parallel execution. Leveraging graph-theoretic methods, our approach derives…

Splitting and projection-type algorithms have been applied to many optimization problems due to their simplicity and efficiency, but the application of these algorithms to optimal control is less common. In this paper we utilize the…

Modeling data sharing in GPU programs is a challenging task because of the massive parallelism and complex data sharing patterns provided by GPU architectures. Better GPU caching efficiency can be achieved through careful task scheduling…

Recent works demonstrate the advantages of hardware rasterization for 3D Gaussian Splatting (3DGS) in forward-pass rendering through fast GPU-optimized graphics and fixed memory footprint. However, extending these benefits to backward-pass…

First-order optimization methods, such as stochastic gradient descent (SGD) and its variants, are widely used in machine learning applications due to their simplicity and low per-iteration costs. However, they often require larger numbers…

Many practical applications require solving an optimization over large and high-dimensional data sets, which makes these problems hard to solve and prohibitively time consuming. In this paper, we propose a parallel distributed algorithm…

Entropic regularized optimal transport (OT) via the Sinkhorn algorithm has become a fundamental tool in machine learning, yet existing implementations either suffer from numerical instability for small regularization parameters or incur…

Optimal transport problems pose many challenges when considering their numerical treatment. We investigate the solution of a PDE-constrained optimisation problem subject to a particular transport equation arising from the modelling of image…

Operator splitting schemes are a class of powerful algorithms that solve complicated monotone inclusion and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which all simple pieces of the…

Whilst optimal transport (OT) is increasingly being recognized as a powerful and flexible approach for dealing with fairness issues, current OT fairness methods are confined to the use of discrete OT. In this paper, we leverage recent…