相关论文: Boosting Data-Driven Mirror Descent with Randomiza…

Smoothness is crucial for attaining fast rates in first-order optimization. However, many optimization problems in modern machine learning involve non-smooth objectives. Recent studies relax the smoothness assumption by allowing the…

Despite perfectly interpolating the training data, deep neural networks (DNNs) can often generalize fairly well, in part due to the "implicit regularization" induced by the learning algorithm. Nonetheless, various forms of regularization,…

Learning to Optimize (L2O) stands at the intersection of traditional optimization and machine learning, utilizing the capabilities of machine learning to enhance conventional optimization techniques. As real-world optimization problems…

Mirror descent is an elegant optimization technique that leverages a dual space of parametric models to perform gradient descent. While originally developed for convex optimization, it has increasingly been applied in the field of machine…

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…

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…

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…

In recent years, attention has been focused on the relationship between black-box optimiza- tion problem and reinforcement learning problem. In this research, we propose the Mirror Descent Search (MDS) algorithm which is applicable both for…

In this paper, we examine the convergence of mirror descent in a class of stochastic optimization problems that are not necessarily convex (or even quasi-convex), and which we call variationally coherent. Since the standard technique of…

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…

Stochastic mirror descent (SMD) is a fairly new family of algorithms that has recently found a wide range of applications in optimization, machine learning, and control. It can be considered a generalization of the classical stochastic…

The mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed…

Learning to optimize (L2O) has recently emerged as a promising approach to solving optimization problems by exploiting the strong prediction power of neural networks and offering lower runtime complexity than conventional solvers. While L2O…

Relative smoothness - a notion introduced by Birnbaum et al. (2011) and rediscovered by Bauschke et al. (2016) and Lu et al. (2016) - generalizes the standard notion of smoothness typically used in the analysis of gradient type methods. In…

Online learning algorithms are fast, memory-efficient, easy to implement, and applicable to many prediction problems, including classification, regression, and ranking. Several online algorithms were proposed in the past few decades, some…

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…

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…

High-velocity streams of high-dimensional data pose significant "big data" analysis challenges across a range of applications and settings. Online learning and online convex programming play a significant role in the rapid recovery of…

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…

This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…