Related papers: Distributed Randomized Gradient-Free Mirror Descen…
Mirror Descent (MD) is a scalable first-order method widely used in large-scale optimization, with applications in image processing, policy optimization, and neural network training. This paper generalizes MD to optimization on Riemannian…
Distributed Optimization is an increasingly important subject area with the rise of multi-agent control and optimization. We consider a decentralized stochastic optimization problem where the agents on a graph aim to asynchronously optimize…
While there is an extensive body of research analyzing policy gradient methods for discounted cumulative-reward MDPs, prior work on policy gradient methods for average-reward MDPs has been limited, with most existing results restricted to…
Decentralized stochastic optimization has emerged as a fundamental paradigm for large-scale machine learning. However, practical implementations often rely on biased gradient estimators arising from communication compression or inexact…
We present Re-weighted Gradient Descent (RGD), a novel optimization technique that improves the performance of deep neural networks through dynamic sample re-weighting. Leveraging insights from distributionally robust optimization (DRO)…
This paper considers a distributed stochastic strongly convex optimization, where agents connected over a network aim to cooperatively minimize the average of all agents' local cost functions. Due to the stochasticity of gradient estimation…
We develop and analyse an approach to optimize functions $l\colon \mathbb{R}^d \rightarrow \mathbb{R}$ not assumed to be convex, differentiable or even continuous. The algorithm belongs to the class of model-based search methods. The idea…
This paper addresses a distributed convex optimization problem with a class of coupled constraints, which arise in a multi-agent system composed of multiple communities modeled by cliques. First, we propose a fully distributed…
We consider a generic decentralized constrained optimization problem over static, directed communication networks, where each agent has exclusive access to only one convex, differentiable, local objective term and one convex constraint set.…
In this paper, we propose a method of distributed stochastic gradient descent (SGD), with low communication load and computational complexity, and still fast convergence. To reduce the communication load, at each iteration of the algorithm,…
We propose a novel adaptive, accelerated algorithm for the stochastic constrained convex optimization setting. Our method, which is inspired by the Mirror-Prox method, \emph{simultaneously} achieves the optimal rates for smooth/non-smooth…
We propose a novel Bregman descent algorithm for minimizing a convex function that is expressed as the sum of a differentiable part (defined over an open set) and a possibly nonsmooth term. The approach, referred to as the Variable Bregman…
We study an explicit mirror-descent method for finite-horizon deterministic optimal control problems. The method is motivated by Pontryagin's maximum principle: at each iteration, one solves the state and adjoint equations and updates the…
$L_0$-smoothness, which has been pivotal to advancing decentralized optimization theory, is often fairly restrictive for modern tasks like deep learning. The recent advent of relaxed $(L_0,L_1)$-smoothness condition enables improved…
We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…
We consider the problem of simultaneously learning to linearly combine a very large number of kernels and learn a good predictor based on the learnt kernel. When the number of kernels $d$ to be combined is very large, multiple kernel…
Based on the idea of randomized coordinate descent of $\alpha$-averaged operators, a randomized primal-dual optimization algorithm is introduced, where a random subset of coordinates is updated at each iteration. The algorithm builds upon a…
Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…
We consider the problem of minimizing a non-convex function over a smooth manifold $\mathcal{M}$. We propose a novel algorithm, the Orthogonal Directions Constrained Gradient Method (ODCGM) which only requires computing a projection onto a…
Consider $n$ agents connected over a network collaborating to minimize the average of their local cost functions combined with a common nonsmooth function. This paper introduces a unified algorithmic framework for solving such a problem…