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This paper focus on the convergence of stochastic approximation with Nesterov momentum. Nesterov acceleration has proven effective in machine learning for its ability to reduce computational complexity. The issue of delayed information in…

Optimization and Control · Mathematics 2024-06-11 Zhang Ming-Kun

In this paper, we are interested in optimal decisions in a partially observable Markov universe. Our viewpoint departs from the dynamic programming viewpoint: we are directly approximating an optimal strategic tree depending on the…

General Mathematics · Mathematics 2007-05-23 Frederic Dambreville

We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…

Optimization and Control · Mathematics 2021-05-18 Jonathan Lacotte , Yifei Wang , Mert Pilanci

Continuous-time Markov decision processes are an important class of models in a wide range of applications, ranging from cyber-physical systems to synthetic biology. A central problem is how to devise a policy to control the system in order…

Systems and Control · Computer Science 2016-06-01 Ezio Bartocci , Luca Bortolussi , Tomǎš Brázdil , Dimitrios Milios , Guido Sanguinetti

Update formulas for the Hessian approximations in quasi-Newton methods such as BFGS can be derived as analytical solutions to certain nearest-matrix problems. In this article, we propose a similar idea for deriving new limited memory…

Optimization and Control · Mathematics 2024-03-06 Erik Berglund , Mikael Johansson

Recently, there has been a surge of interest in designing variants of the classical Newton-CG in which the Hessian of a (strongly) convex function is replaced by suitable approximations. This is mainly motivated by large-scale finite-sum…

Optimization and Control · Mathematics 2022-06-14 Yang Liu , Fred Roosta

We consider minimizing a smooth and strongly convex objective function using a stochastic Newton method. At each iteration, the algorithm is given an oracle access to a stochastic estimate of the Hessian matrix. The oracle model includes…

Optimization and Control · Mathematics 2022-11-29 Sen Na , Michał Dereziński , Michael W. Mahoney

Quasi-Newton methods employ an update rule that gradually improves the Hessian approximation using the already available gradient evaluations. We propose higher-order secant updates which generalize this idea to higher-order derivatives,…

Optimization and Control · Mathematics 2024-03-07 Karl Welzel , Raphael A. Hauser

We present a modification of the Hybrid Monte Carlo algorithm for tackling the critical slowing down of generating Markov chains of lattice gauge configurations towards the continuum limit. We propose a new method to exchange information…

High Energy Physics - Lattice · Physics 2019-04-24 Xiao-Yong Jin , James C. Osborn

In the context of Markov decision processes running in continuous time, one of the most intriguing challenges is the efficient approximation of finite horizon reachability objectives. A multitude of sophisticated model checking algorithms…

Systems and Control · Computer Science 2015-08-03 Yuliya Butkova , Hassan Hatefi , Holger Hermanns , Jan Krcal

In Markov games, playing against non-stationary opponents with learning ability is still challenging for reinforcement learning (RL) agents, because the opponents can evolve their policies concurrently. This increases the complexity of the…

Artificial Intelligence · Computer Science 2020-05-27 Hao Chen , Chang Wang , Jian Huang , Jianxing Gong

We study reinforcement learning methods with linear function approximation under non-Markov state and cost processes. We first consider the policy evaluation method and show that the algorithm converges under suitable ergodicity conditions…

Machine Learning · Computer Science 2026-01-05 Ali Devran Kara

We investigate the problem of best policy identification in discounted linear Markov Decision Processes in the fixed confidence setting under a generative model. We first derive an instance-specific lower bound on the expected number of…

Machine Learning · Computer Science 2022-08-12 Jerome Taupin , Yassir Jedra , Alexandre Proutiere

We present metrics for measuring the similarity of states in a finite Markov decision process (MDP). The formulation of our metrics is based on the notion of bisimulation for MDPs, with an aim towards solving discounted infinite horizon…

Artificial Intelligence · Computer Science 2012-07-19 Norman Ferns , Prakash Panangaden , Doina Precup

Markov decision processes (MDPs) are a popular model for performance analysis and optimization of stochastic systems. The parameters of stochastic behavior of MDPs are estimates from empirical observations of a system; their values are not…

Artificial Intelligence · Computer Science 2017-10-26 Dimitri Scheftelowitsch , Peter Buchholz , Vahid Hashemi , Holger Hermanns

Markov Decision Processes (MDPs) have been used to formulate many decision-making problems in science and engineering. The objective is to synthesize the best decision (action selection) policies to maximize expected rewards (or minimize…

Optimization and Control · Mathematics 2015-07-07 Mahmoud El Chamie , Behcet Acikmese

Semi-Markov processes are Markovian processes in which the firing time of the transitions is modelled by probabilistic distributions over positive reals interpreted as the probability of firing a transition at a certain moment in time. In…

Formal Languages and Automata Theory · Computer Science 2017-12-04 Mathias Ruggaard Pedersen , Nathanaël Fijalkow , Giorgio Bacci , Kim Guldstrand Larsen , Radu Mardare

Markov decision processes (MDPs) provide a fundamental model for sequential decision making under process uncertainty. A classical synthesis task is to compute for a given MDP a winning policy that achieves a desired specification. However,…

Logic in Computer Science · Computer Science 2024-07-18 Roman Andriushchenko , Milan Češka , Sebastian Junges , Filip Macák

We introduce a new framework for analyzing (Quasi-}Newton type methods applied to non-smooth optimization problems. The source of randomness comes from the evaluation of the (approximation) of the Hessian. We derive, using a variant of…

Optimization and Control · Mathematics 2025-03-05 Titus Pinta

Many machine learning models depend on solving a large scale optimization problem. Recently, sub-sampled Newton methods have emerged to attract much attention for optimization due to their efficiency at each iteration, rectified a weakness…

Optimization and Control · Mathematics 2016-09-06 Haishan Ye , Luo Luo , Zhihua Zhang