相关论文: Variational Principles for Mirror Descent and Mirr…

Mirror descent is a well established tool for solving convex optimization problems with convex constraints. This article introduces continuous-time mirror descent dynamics for approximating optimal Markov controls for stochastic control…

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…

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 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…

The goal is to modify the known method of mirror descent (MD), proposed by A.S. Nemirovsky and D.B. Yudin in 1979. The paper shows the idea of a new, so-called inertial MD method with the example of a deterministic optimization problem in…

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…

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…

The logarithmic divergence is an extension of the Bregman divergence motivated by optimal transport and a generalized convex duality, and satisfies many remarkable properties. Using the geometry induced by the logarithmic divergence, we…

We discuss a special form of gradient descent that in the literature has become known as the so-called linearised Bregman iteration. The idea is to replace the classical (squared) two norm metric in the gradient descent setting with a…

Inspired by the recent paper (L. Ying, Mirror descent algorithms for minimizing interacting free energy, Journal of Scientific Computing, 84 (2020), pp. 1-14),we explore the relationship between the mirror descent and the variable metric…

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…

We propose primal-dual stochastic mirror descent for the convex optimization problems with functional constraints. We obtain the rate of convergence in terms of probability of large deviations.

Recent work by Woodworth et al. (2020) shows that the optimization dynamics of gradient descent for overparameterized problems can be viewed as low-dimensional dual dynamics induced by a mirror map, explaining the implicit regularization…

Nonconvex-nonconcave saddle-point optimization in machine learning has triggered lots of research for studying non-monotone variational inequalities (VI). In this work, we introduce two mirror frameworks, called mirror extragradient method…

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…

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…

Recently there were proposed some innovative convex optimization concepts, namely, relative smoothness [1] and relative strong convexity [2,3]. These approaches have significantly expanded the class of applicability of gradient-type methods…

This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…

In this paper, we consider the problem of phase retrieval, which consists of recovering an $n$-dimensional real vector from the magnitude of its $m$ linear measurements. We propose a mirror descent (or Bregman gradient descent) algorithm…

In this paper, we consider the online proximal mirror descent for solving the time-varying composite optimization problems. For various applications, the algorithm naturally involves the errors in the gradient and proximal operator. We…