Related papers: Gradient- and Newton-Based Unit Vector Extremum Se…
Reinforcement learning for control over continuous spaces typically uses high-entropy stochastic policies, such as Gaussian distributions, for local exploration and estimating policy gradient to optimize performance. Many robotic control…
Gradient-based iterative optimization methods are the workhorse of modern machine learning. They crucially rely on careful tuning of parameters like learning rate and momentum. However, one typically sets them using heuristic approaches…
The problem of steering a particular class of $n$-dimensional continuous-time dynamical systems towards the minima of a function without gradient information is considered. We propose an hybrid controller, implementing a discrete-time…
Stochastic gradient algorithms have been the main focus of large-scale learning problems and they led to important successes in machine learning. The convergence of SGD depends on the careful choice of learning rate and the amount of the…
In this paper, we present the discrete-time unbiased extremum seeking (ES) algorithm for n-dimensional (nD) static quadratic maps in the presence of unknown time-varying measurement delays bounded by known constants which can be large. The…
This paper discusses the design of an extremum seeking controller that relies on a monitoring function for a class of SISO uncertain nonlinear systems characterized by arbitrary and uncertain relative degree. Our demonstration illustrates…
The Stochastic Gradient Descent method (SGD) and its stochastic variants have become methods of choice for solving finite-sum optimization problems arising from machine learning and data science thanks to their ability to handle large-scale…
The topics of source seeking and Newton-based extremum seeking have flourished, independently, but never combined. We present the first Newton-based source seeking algorithm. The algorithm employs forward velocity tuning, as in the very…
In this paper, we propose a unified convergence analysis for a class of generic shuffling-type gradient methods for solving finite-sum optimization problems. Our analysis works with any sampling without replacement strategy and covers many…
In this work, we consider smooth unconstrained optimization problems and we deal with the class of gradient methods with momentum, i.e., descent algorithms where the search direction is defined as a linear combination of the current…
This article aims to provide an accessible, tutorial-style introduction to hybrid extremum-seeking systems, which are model-free, feedback-optimization controllers that incorporate hybrid dynamics, meaning both continuous-time and…
We study trade-offs between convergence rate and robustness to gradient errors in the context of first-order methods. Our focus is on generalized momentum methods (GMMs)--a broad class that includes Nesterov's accelerated gradient,…
Gradient descent and stochastic gradient descent are central to modern machine learning, yet their behavior under large step sizes remains theoretically unclear. Recent work suggests that acceleration often arises near the edge of…
Vector extrapolation methods are widely used in large-scale simulation studies, and numerous extrapolation-based acceleration techniques have been developed to enhance the convergence of linear and nonlinear fixed-point iterative methods.…
Extremum seeking control (ESC) are optimization algorithms in continuous time, with model-based ESCs using true derivative information of the cost function and model-free ESCs utilizing perturbation-based estimates instead. Stability…
Stochastically controlled stochastic gradient (SCSG) methods have been proved to converge efficiently to first-order stationary points which, however, can be saddle points in nonconvex optimization. It has been observed that a stochastic…
Extremum seeking (ES) optimization approach has been very popular due to its non-model based analysis and implementation. This approach has been mostly used with gradient based search algorithms. Since least squares (LS) algorithms are…
We propose and analyze a new stochastic gradient method, which we call Stochastic Unbiased Curvature-aided Gradient (SUCAG), for finite sum optimization problems. SUCAG constitutes an unbiased total gradient tracking technique that uses…
Stochastic gradient descent (\textsc{Sgd}) methods are the most powerful optimization tools in training machine learning and deep learning models. Moreover, acceleration (a.k.a. momentum) methods and diagonal scaling (a.k.a. adaptive…
Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research. In this paper, we extend previous work on the \textbf{Quadratic Gradient (QG)} and rigorously…