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Classical trust region methods were designed to solve problems in which function and gradient information are exact. This paper considers the case when there are bounded errors (or noise) in the above computations and proposes a simple…

Optimization and Control · Mathematics 2022-01-05 Shigeng Sun , Jorge Nocedal

In this paper, we study a few challenging theoretical and numerical issues on the well known trust region policy optimization for deep reinforcement learning. The goal is to find a policy that maximizes the total expected reward when the…

Optimization and Control · Mathematics 2019-11-27 Mingming Zhao , Yongfeng Li , Zaiwen Wen

In this paper, we study stochastic non-convex optimization with non-convex random functions. Recent studies on non-convex optimization revolve around establishing second-order convergence, i.e., converging to a nearly second-order optimal…

Optimization and Control · Mathematics 2017-11-02 Mingrui Liu , Tianbao Yang

We develop a trust-region method for minimizing the sum of a smooth term $f$ and a nonsmooth term $h$), both of which can be nonconvex. Each iteration of our method minimizes a possibly nonconvex model of $f + h$ in a trust region. The…

Optimization and Control · Mathematics 2021-08-04 Aleksandr Y. Aravkin , Robert Baraldi , Dominique Orban

We propose a novel algorithm, TR-SVR, for solving unconstrained stochastic optimization problems. This method builds on the trust-region framework, which effectively balances local and global exploration in optimization tasks. TR-SVR…

Optimization and Control · Mathematics 2024-12-03 Xinshou Zheng

We develop a stochastic trust-region algorithm for minimizing the sum of a possibly nonconvex Lipschitz-smooth function that can only be evaluated stochastically and a nonsmooth, deterministic, convex function. This algorithm, which we call…

Optimization and Control · Mathematics 2025-10-06 Robert J. Baraldi , Aurya Javeed , Drew P. Kouri , Katya Scheinberg

Due to the rapid growth of data and computational resources, distributed optimization has become an active research area in recent years. While first-order methods seem to dominate the field, second-order methods are nevertheless attractive…

Machine Learning · Computer Science 2018-06-21 Celestine Dünner , Aurelien Lucchi , Matilde Gargiani , An Bian , Thomas Hofmann , Martin Jaggi

We present an adaptive trust-region method for unconstrained optimization that allows inexact solutions to the trust-region subproblems. Our method is a simple variant of the classical trust-region method of \citet{sorensen1982newton}. The…

Optimization and Control · Mathematics 2025-08-27 Fadi Hamad , Oliver Hinder

Concise complexity analyses are presented for simple trust region algorithms for solving unconstrained optimization problems. In contrast to a traditional trust region algorithm, the algorithms considered in this paper require certain…

Optimization and Control · Mathematics 2018-02-23 Frank E. Curtis , Zachary Lubberts , Daniel P. Robinson

Worst-case complexity guarantees for nonconvex optimization algorithms have been a topic of growing interest. Multiple frameworks that achieve the best known complexity bounds among a broad class of first- and second-order strategies have…

Optimization and Control · Mathematics 2020-11-23 Frank E. Curtis , Daniel P. Robinson , Clément Royer , Stephen J. Wright

In recent years, random subspace methods have been actively studied for large-dimensional nonconvex problems. Recent subspace methods have improved theoretical guarantees such as iteration complexity and local convergence rate while…

Optimization and Control · Mathematics 2025-03-25 Rei Higuchi , Pierre-Louis Poirion , Akiko Takeda

We present a stochastic trust-region model-based framework in which its radius is related to the probabilistic models. Especially, we propose a specific algorithm, termed STRME, in which the trust-region radius depends linearly on the…

Optimization and Control · Mathematics 2022-09-30 Xiaoyu Wang , Ya-xiang Yuan

We introduce deterministic perturbation schemes for the recently proposed random directions stochastic approximation (RDSA) [17], and propose new first-order and second-order algorithms. In the latter case, these are the first second-order…

Optimization and Control · Mathematics 2019-03-29 Prashanth L A , Shalabh Bhatnagar , Nirav Bhavsar , Michael Fu , Steven I. Marcus

Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in…

Multiagent Systems · Computer Science 2020-04-01 Stefan Vlaski , Ali H. Sayed

We present a finite-time analysis of two smoothed functional stochastic approximation algorithms for simulation-based optimization. The first is a two time-scale gradient-based method, while the second is a three time-scale Newton-based…

Machine Learning · Computer Science 2026-04-01 Kaustubh Kartikey , Shalabh Bhatnagar

In this paper we present a novel quasi-Newton algorithm for use in stochastic optimisation. Quasi-Newton methods have had an enormous impact on deterministic optimisation problems because they afford rapid convergence and computationally…

Systems and Control · Electrical Eng. & Systems 2019-09-04 Adrian Wills , Thomas Schön

We present a new accelerated stochastic second-order method that is robust to both gradient and Hessian inexactness, which occurs typically in machine learning. We establish theoretical lower bounds and prove that our algorithm achieves…

Optimization and Control · Mathematics 2024-05-28 Artem Agafonov , Dmitry Kamzolov , Alexander Gasnikov , Ali Kavis , Kimon Antonakopoulos , Volkan Cevher , Martin Takáč

In this paper, we propose several new stochastic second-order algorithms for policy optimization that only require gradient and Hessian-vector product in each iteration, making them computationally efficient and comparable to policy…

Optimization and Control · Mathematics 2023-01-31 Jinsong Liu , Chenghan Xie , Qi Deng , Dongdong Ge , Yinyu Ye

Nowadays stochastic approximation methods are one of the major research direction to deal with the large-scale machine learning problems. From stochastic first order methods, now the focus is shifting to stochastic second order methods due…

Machine Learning · Computer Science 2019-12-30 Vinod Kumar Chauhan , Anuj Sharma , Kalpana Dahiya

Stochastic variational inference allows for fast posterior inference in complex Bayesian models. However, the algorithm is prone to local optima which can make the quality of the posterior approximation sensitive to the choice of…

Machine Learning · Statistics 2015-05-29 Lucas Theis , Matthew D. Hoffman