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Recent applications that arise in machine learning have surged significant interest in solving min-max saddle point games. This problem has been extensively studied in the convex-concave regime for which a global equilibrium solution can be…
Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…
Smooth convex minimization over the unit trace-norm ball is an important optimization problem in machine learning, signal processing, statistics and other fields, that underlies many tasks in which one wishes to recover a low-rank matrix…
This study develops a fixed-time convergent saddle point dynamical system for solving min-max problems under a relaxation of standard convexity-concavity assumption. In particular, it is shown that by leveraging the dynamical systems…
Randomly initialized first-order optimization algorithms are the method of choice for solving many high-dimensional nonconvex problems in machine learning, yet general theoretical guarantees cannot rule out convergence to critical points of…
Zeroth-order optimization, which does not use derivative information, is one of the significant research areas in the field of mathematical optimization and machine learning. Although various studies have explored zeroth-order algorithms,…
First-order methods for minimization and saddle point (min-max) problems are widely used for solving large-scale problems, in particular arising in machine learning. The majority of works obtain favorable complexity guarantees of such…
In this paper, we investigate a class of nonconvex and nonsmooth fractional programming problems, where the numerator composed of two parts: a convex, nonsmooth function and a differentiable, nonconvex function, and the denominator consists…
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 presents an efficient gradient projection-based method for structural topological optimization problems characterized by a nonlinear objective function which is minimized over a feasible region defined by bilateral bounds and a…
This paper proposes a new algorithm -- the \underline{S}ingle-timescale Do\underline{u}ble-momentum \underline{St}ochastic \underline{A}pprox\underline{i}matio\underline{n} (SUSTAIN) -- for tackling stochastic unconstrained bilevel…
The analysis of projection-free first order methods is often complicated by the presence of different kinds of "good" and "bad" steps. In this article, we propose a unifying framework for projection-free methods, aiming to simplify the…
Smooth minimax optimization problems play a central role in a wide range of applications, including machine learning, game theory, and operations research. However, existing algorithmic frameworks vary significantly depending on the problem…
In this paper, we focus on solving a class of constrained non-convex non-concave saddle point problems in a decentralized manner by a group of nodes in a network. Specifically, we assume that each node has access to a summand of a global…
Convergence to a saddle point for convex-concave functions has been studied for decades, while recent years has seen a surge of interest in non-convex (zero-sum) smooth games, motivated by their recent wide applications. It remains an…
Bilevel reinforcement learning (RL), which features intertwined two-level problems, has attracted growing interest recently. The inherent non-convexity of the lower-level RL problem is, however, to be an impediment to developing bilevel…
The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…
Gradient-based first-order convex optimization algorithms find widespread applicability in a variety of domains, including machine learning tasks. Motivated by the recent advances in fixed-time stability theory of continuous-time dynamical…
Constrained optimization with multiple functional inequality constraints has significant applications in machine learning. This paper examines a crucial subset of such problems where both the objective and constraint functions are weakly…
In this paper, we consider bilevel optimization problem where the lower-level has coupled constraints, i.e. the constraints depend both on the upper- and lower-level variables. In particular, we consider two settings for the lower-level…