Related papers: Efficient Online Mirror Descent Stochastic Approxi…
In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex and convex optimization, with a focus on addressing constrained optimization, high-dimensional setting and saddle-point avoiding. To handle…
This paper investigates group distributionally robust optimization (GDRO) with the goal of learning a model that performs well over $m$ different distributions. First, we formulate GDRO as a stochastic convex-concave saddle-point problem,…
We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in the primal variable, we develop the first stochastic restart scheme for this…
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…
Stochastic compositional minimax problems are prevalent in machine learning, yet there are only limited established on the convergence of this class of problems. In this paper, we propose a formal definition of the stochastic compositional…
This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The…
In this paper, we consider the problem of stochastic optimization, where the objective function is in terms of the expectation of a (possibly non-convex) cost function that is parametrized by a random variable. While the convergence speed…
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.
Saddle points provide a hierarchical view of the energy landscape, revealing transition pathways and interconnected basins of attraction, and offering insight into the global structure, metastability, and possible collective mechanisms of…
This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…
We consider an online two-stage stochastic optimization with long-term constraints over a finite horizon of $T$ periods. At each period, we take the first-stage action, observe a model parameter realization and then take the second-stage…
Markov Decision Processes (MDPs) have been used to formulate many decision-making problems in science and engineering. The objective is to synthesize the best decision (action selection) policies to maximize expected rewards (minimize…
This paper considers the problem of minimizing an expectation function over a closed convex set, coupled with a {\color{black} functional or expectation} constraint on either decision variables or problem parameters. We first present a new…
In the paper, we propose a class of efficient adaptive bilevel methods based on mirror descent for nonconvex bilevel optimization, where its upper-level problem is nonconvex possibly with nonsmooth regularization, and its lower-level…
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 success of deep neural networks hinges on our ability to accurately and efficiently optimize high-dimensional, non-convex functions. In this paper, we empirically investigate the loss functions of state-of-the-art networks, and how…
We propose some adaptive mirror descent dethods for convex programming problems with delta-subgradients and prove some theoretical results.
In this paper, we derive a randomized version of the Mirror-Prox method for solving some structured matrix saddle-point problems, such as the maximal eigenvalue minimization problem. Deterministic first-order schemes, such as Nesterov's…
In this paper we consider online mirror descent (OMD) algorithms, a class of scalable online learning algorithms exploiting data geometric structures through mirror maps. Necessary and sufficient conditions are presented in terms of the…
We consider a two-stage stochastic optimization problem, in which a long-term optimization variable is coupled with a set of short-term optimization variables in both objective and constraint functions. Despite that two-stage stochastic…