相关论文: Data-Driven Mirror Descent with Input-Convex Neura…

Learning-to-optimize (L2O) is an emerging research area in large-scale optimization with applications in data science. Recently, researchers have proposed a novel L2O framework called learned mirror descent (LMD), based on the classical…

Learning-to-optimize is an emerging framework that leverages training data to speed up the solution of certain optimization problems. One such approach is based on the classical mirror descent algorithm, where the mirror map is modelled…

Optimisers are an essential component for training machine learning models, and their design influences learning speed and generalisation. Several studies have attempted to learn more effective gradient-descent optimisers via solving a…

This paper presents a comprehensive convergence analysis for the mirror descent (MD) method, a widely used algorithm in convex optimization. The key feature of this algorithm is that it provides a generalization of classical gradient-based…

This paper is concerned with convergence analysis for the mirror descent (MD) method, a well-known algorithm in convex optimization. An analysis framework via integral quadratic constraints (IQCs) is constructed to analyze the convergence…

We propose an input convex neural network (ICNN)-based self-supervised learning framework to solve continuous constrained optimization problems. By integrating the augmented Lagrangian method (ALM) with the constraint correction mechanism,…

A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…

Many problems in machine learning can be formulated as optimizing a convex functional over a vector space of measures. This paper studies the convergence of the mirror descent algorithm in this infinite-dimensional setting. Defining Bregman…

Constrained competitive optimization involves multiple agents trying to minimize conflicting objectives, subject to constraints. This is a highly expressive modeling language that subsumes most of modern machine learning. In this work we…

Recently, adversarial imitation learning has shown a scalable reward acquisition method for inverse reinforcement learning (IRL) problems. However, estimated reward signals often become uncertain and fail to train a reliable statistical…

This paper explores a new framework for reinforcement learning based on online convex optimization, in particular mirror descent and related algorithms. Mirror descent can be viewed as an enhanced gradient method, particularly suited to…

Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the…

Policy optimization, which finds the desired policy by maximizing value functions via optimization techniques, lies at the heart of reinforcement learning (RL). In addition to value maximization, other practical considerations arise as…

Most modern learning problems are highly overparameterized, meaning that there are many more parameters than the number of training data points, and as a result, the training loss may have infinitely many global minima (parameter vectors…

In this paper, we propose Distributed Mirror Descent (DMD) algorithm for constrained convex optimization problems on a (strongly-)connected multi-agent network. We assume that each agent has a private objective function and a constraint…

Value iteration-type methods have been extensively studied for computing a nearly optimal value function in reinforcement learning (RL). Under a generative sampling model, these methods can achieve sharper sample complexity than policy…

Learning to optimize is an approach that leverages training data to accelerate the solution of optimization problems. Many approaches use unrolling to parametrize the update step and learn optimal parameters. Although L2O has shown…

Inspired by the remarkable success of large neural networks, there has been significant interest in understanding the generalization performance of over-parameterized models. Substantial efforts have been invested in characterizing how…

This paper seeks to address how to solve non-smooth convex and strongly convex optimization problems with functional constraints. The introduced Mirror Descent (MD) method with adaptive stepsizes is shown to have a better convergence rate…

Mirror Descent (MD) is a well-known method of solving non-smooth convex optimization problems. This paper analyzes the stochastic variant of MD with adaptive stepsizes. Its convergence on average is shown to be faster than with the fixed…