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In this work we investigate stochastic non-convex optimization problems where the objective is an expectation over smooth loss functions, and the goal is to find an approximate stationary point. The most popular approach to handling such…
In this work and its accompanying Part II [1], we develop an accelerated algorithmic framework, DAMA (Decentralized Accelerated Minimax Approach), for nonconvex Polyak-Lojasiewicz minimax optimization over decentralized multi-agent…
Decentralized stochastic optimization has emerged as a fundamental paradigm for large-scale machine learning. However, practical implementations often rely on biased gradient estimators arising from communication compression or inexact…
This paper proposes a provably convergent multiblock ADMM for nonconvex optimization with nonlinear dynamics constraints, overcoming the divergence issue in classical extensions. We consider a class of optimization problems that arise from…
Variance reduction has emerged in recent years as a strong competitor to stochastic gradient descent in non-convex problems, providing the first algorithms to improve upon the converge rate of stochastic gradient descent for finding…
We present a coupled system of ODEs which, when discretized with a constant time step/learning rate, recovers Nesterov's accelerated gradient descent algorithm. The same ODEs, when discretized with a decreasing learning rate, leads to novel…
The Energy Conserving Descent (ECD) algorithm was recently proposed (De Luca & Silverstein, 2022) as a global non-convex optimization method. Unlike gradient descent, appropriately configured ECD dynamics escape strict local minima and…
Performance analysis of first-order algorithms with inexact oracles has gained recent attention due to various emerging applications in which obtaining exact gradients is impossible or computationally expensive. Previous research has…
We study novel robust zero-order algorithms with acceleration for the solution of real-time optimization problems. In particular, we propose a family of extremum seeking dynamics that can be universally modeled as singularly perturbed…
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…
In this paper we demonstrate a novel alternating direction method of multipliers (ADMM) algorithm for the solution of the hybrid vehicle energy management problem considering both power split and engine on/off decisions. The solution of a…
Training deep neural networks is challenging. To accelerate training and enhance performance, we propose PadamP, a novel optimization algorithm. PadamP is derived by applying the adaptive estimation of the p-th power of the second-order…
We propose in this paper a new minimization algorithm based on a slightly modified version of the scalar auxiliary variable (SAV) approach coupled with a relaxation step and an adaptive strategy. It enjoys several distinct advantages over…
In this paper we study a second order dynamical system with variable coefficients in connection to the minimization problem of a smooth nonconvex function. The convergence of the trajectories generated by the dynamical system to a critical…
We propose an unconstrained optimization method based on the well-known primal-dual hybrid gradient (PDHG) algorithm. We first formulate the optimality condition of the unconstrained optimization problem as a saddle point problem. We then…
In this paper, a general stochastic optimization procedure is studied, unifying several variants of the stochastic gradient descent such as, among others, the stochastic heavy ball method, the Stochastic Nesterov Accelerated Gradient…
In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then,…
Currently, widely used first-order deep learning optimizers include non-adaptive learning rate optimizers and adaptive learning rate optimizers. The former is represented by SGDM (Stochastic Gradient Descent with Momentum), while the latter…
Gradient-based minimax optimal algorithms have greatly promoted the development of continuous optimization and machine learning. One seminal work due to Yurii Nesterov [Nes83a] established $\tilde{\mathcal{O}}(\sqrt{L/\mu})$ gradient…
Many important machine learning applications involve regularized nonconvex bi-level optimization. However, the existing gradient-based bi-level optimization algorithms cannot handle nonconvex or nonsmooth regularizers, and they suffer from…