Related papers: A probabilistic incremental proximal gradient meth…
We investigate a family of approximate multi-step proximal point methods, framed as implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…
We introduce a novel policy learning method that integrates analytical gradients from differentiable environments with the Proximal Policy Optimization (PPO) algorithm. To incorporate analytical gradients into the PPO framework, we…
We propose the superiorization of incremental algorithms for tomographic image reconstruction. The resulting methods follow a better path in its way to finding the optimal solution for the maximum likelihood problem in the sense that they…
We consider solving a convex, possibly stochastic optimization problem over a randomly time-varying multi-agent network. Each agent has access to some local objective function, and it only has unbiased estimates of the gradients of the…
Model training algorithms which observe a small portion of the training set in each computational step are ubiquitous in practical machine learning, and include both stochastic and online optimization methods. In the vast majority of cases,…
We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the…
The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…
The particle-based, rapid incremental smoother (PARIS) is a sequential Monte Carlo technique allowing for efficient online approximation of expectations of additive functionals under Feynman--Kac path distributions. Under weak assumptions,…
This paper aims to investigate the distributed stochastic optimization problems on compact embedded submanifolds (in the Euclidean space) for multi-agent network systems. To address the manifold structure, we propose a distributed…
In this paper, we consider a class of continuous-time, continuous-space stochastic optimal control problems. Building upon recent advances in Markov chain approximation methods and sampling-based algorithms for deterministic path planning,…
During the last decade, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs) have been shown to work well in practice and to possess theoretical guarantees such as probabilistic…
Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the…
The Bayesian conjugate gradient method offers probabilistic solutions to linear systems but suffers from poor calibration, limiting its utility in uncertainty quantification tasks. Recent approaches leveraging postiterations to construct…
Online optimization has gained increasing interest due to its capability of tracking real-world streaming data. Although online optimization methods have been widely studied in the setting of frequentist statistics, few works have…
Building upon recent works on linesearch-free adaptive proximal gradient methods, this paper proposes adaPG$^{q,r}$, a framework that unifies and extends existing results by providing larger stepsize policies and improved lower bounds.…
This paper explores numerical methods for solving a convex differentiable semi-infinite program. We introduce a primal-dual gradient method which performs three updates iteratively: a momentum gradient ascend step to update the constraint…
We introduce Kalman Gradient Descent, a stochastic optimization algorithm that uses Kalman filtering to adaptively reduce gradient variance in stochastic gradient descent by filtering the gradient estimates. We present both a theoretical…
Hyperparameter optimization in machine learning is often achieved using naive techniques that only lead to an approximate set of hyperparameters. Although techniques such as Bayesian optimization perform an intelligent search on a given…
Previous works in prompt engineering for large language models have introduced different gradient-free probability-based prompt selection methods that aim to choose the optimal prompt among the candidates for a given task but have failed to…
This paper is concerned with sequential filtering based stochastic optimization (FSO) approaches that leverage a probabilistic perspective to implement the incremental proximity method (IPM). The present FSO methods are derived based on the…