Related papers: Escaping saddle points in zeroth-order optimizatio…

Many problems in machine learning and game theory can be formulated as saddle-point problems, for which various first-order methods have been developed and proven efficient in practice. Under the general convex-concave assumption, most…

In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…

Satisfaction of the strict saddle property has become a standard assumption in non-convex optimization, and it ensures that many first-order optimization algorithms will almost always escape saddle points. However, functions exist in…

Value iteration is a fixed point iteration technique utilized to obtain the optimal value function and policy in a discounted reward Markov Decision Process (MDP). Here, a contraction operator is constructed and applied repeatedly to arrive…

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 black-box smooth optimization problems, where the objective and constraint functions are not explicitly known but can be queried. The main goal of this work is to generate a sequence of feasible points converging…

In this paper, we propose two new solution schemes to solve the stochastic strongly monotone variational inequality problems: the stochastic extra-point solution scheme and the stochastic extra-momentum solution scheme. The first one is a…

We consider stochastic unconstrained bilevel optimization problems when only the first-order gradient oracles are available. While numerous optimization methods have been proposed for tackling bilevel problems, existing methods either tend…

This paper proposes and analyzes an iterative minimization formulation for search- ing index-1 saddle points of an energy function. This formulation differs from other eigenvector-following methods by constructing a new objective function…

This paper is devoted to the design of efficient primal-dual algorithm (PDA) for solving convex optimization problems with known saddle-point structure. We present a new PDA with larger acceptable range of parameters and correction, which…

This paper studies the complexity of finding approximate stationary points for the smooth nonconvex-strongly-concave (NC-SC) saddle point problem: $\min_x\max_yf(x,y)$. Under the standard first-order smoothness conditions where $f$ is…

Motivated by TRACE algorithm [Curtis et al. 2017], we propose a trust region algorithm for finding second order stationary points of a linearly constrained non-convex optimization problem. We show the convergence of the proposed algorithm…

Reinforcement learning (RL) often has a hierarchical structure, where an upper-level (UL) learner selects model parameters and a lower-level (LL) decision-making process responds, naturally leading to a bilevel optimization problem. Most…

We consider stochastic strongly-convex-strongly-concave (SCSC) saddle point (SP) problems which frequently arise in applications ranging from distributionally robust learning to game theory and fairness in machine learning. We focus on the…

We consider the problem of finding an approximate second-order stationary point of a constrained non-convex optimization problem. We first show that, unlike the gradient descent method for unconstrained optimization, the vanilla projected…

We propose an approach to saddle point optimization relying only on oracles that solve minimization problems approximately. We analyze its convergence property on a strongly convex--concave problem and show its linear convergence toward the…

Second-order optimization methods offer notable advantages in training deep neural networks by utilizing curvature information to achieve faster convergence. However, traditional second-order techniques are computationally prohibitive,…

This paper introduces a novel Homogeneous Second-order Descent Ascent (HSDA) algorithm for nonconvex-strongly concave minimax optimization problems. At each iteration, HSDA uniquely computes a search direction by solving a homogenized…

Safe derivative-free optimization under unknown constraints is a fundamental challenge in modern learning and control. Existing zeroth-order (ZO) methods typically still assume access to a first-order oracle of the constraint functions or…

First order policy optimization has been widely used in reinforcement learning. It guarantees to find the optimal policy for the state-feedback linear quadratic regulator (LQR). However, the performance of policy optimization remains…