Related papers: Projection-Free Methods for Solving Nonconvex-Conc…
In this paper, we explore a broad class of constrained saddle point problems with a bilevel structure, wherein the upper-level objective function is nonconvex-concave and smooth over compact and convex constraint sets, subject to a strongly…
This paper addresses constrained smooth saddle-point problems in settings where projection onto the feasible sets is computationally expensive. We bridge the gap between projection-based and projection-free optimization by introducing a…
The Frank-Wolfe algorithm is a classic method for constrained optimization problems. It has recently been popular in many machine learning applications because its projection-free property leads to more efficient iterations. In this paper,…
We propose a primal-dual smoothing framework for finding a near-stationary point of a class of non-smooth non-convex optimization problems with max-structure. We analyze the primal and dual gradient complexities of the framework via two…
Stochastic nonconvex-concave min-max saddle point problems appear in many machine learning and control problems including distributionally robust optimization, generative adversarial networks, and adversarial learning. In this paper, we…
We propose and analyze a general framework called nonlinear preconditioned primal-dual with projection for solving nonconvex-nonconcave and non-smooth saddle-point problems. The framework consists of two steps. The first is a nonlinear…
This paper investigates projection-free algorithms for stochastic constrained multi-level optimization. In this context, the objective function is a nested composition of several smooth functions, and the decision set is closed and convex.…
Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…
We propose a projection-free conditional gradient-type algorithm for smooth stochastic multi-level composition optimization, where the objective function is a nested composition of $T$ functions and the constraint set is a closed convex…
In the paper, we generalize the approach Gasnikov et. al, 2017, which allows to solve (stochastic) convex optimization problems with an inexact gradient-free oracle, to the convex-concave saddle-point problem. The proposed approach works,…
Using convex combination and linesearch techniques, we introduce a novel primal-dual algorithm for solving structured convex-concave saddle point problems with a generic smooth nonbilinear coupling term. Our adaptive linesearch strategy…
We consider (stochastic) convex-concave saddle point (SP) problems with high-dimensional decision variables, arising in various applications including machine learning problems. To contend with the challenges in computing full gradients, we…
We develop an inexact primal-dual first-order smoothing framework to solve a class of non-bilinear saddle point problems with primal strong convexity. Compared with existing methods, our framework yields a significant improvement over the…
Recently, saddle point problems have received much attention due to their powerful modeling capability for a lot of problems from diverse domains. Applications of these problems occur in many applied areas, such as robust optimization,…
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…
This paper develops projection-free algorithms for online convex optimization with stochastic constraints. We design an online primal-dual projection-free framework that can take any projection-free algorithms developed for online convex…
We study projection-free methods for functional constrained optimization with convex or smooth nonconvex objectives. Such problems arise in applications such as portfolio optimization and radiation therapy planning, where risk-aware…
When faced with multiple minima of an "inner-level" convex optimization problem, the convex bilevel optimization problem selects an optimal solution which also minimizes an auxiliary "outer-level" convex objective of interest. Bilevel…
In this paper, we provide a sub-gradient based algorithm to solve general constrained convex optimization without taking projections onto the domain set. The well studied Frank-Wolfe type algorithms also avoid projections. However, they are…
In this paper, we propose a novel primal-dual inexact gradient projection method for nonlinear optimization problems with convex-set constraint. This method only needs inexact computation of the projections onto the convex set for each…