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Motivated by collaborative reinforcement learning (RL) and optimization with time-correlated data, we study a generic federated stochastic approximation problem involving $M$ agents, where each agent is characterized by an agent-specific…

Machine Learning · Computer Science 2025-04-17 Feng Zhu , Aritra Mitra , Robert W. Heath

In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems. This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems. Specifically in this…

Optimization and Control · Mathematics 2013-03-19 Mihaly Petreczky , Rafael Wisniewski , John Leth

We propose a novel framework for analyzing convergence rates of stochastic optimization algorithms with adaptive step sizes. This framework is based on analyzing properties of an underlying generic stochastic process, in particular by…

Optimization and Control · Mathematics 2018-10-23 Jose Blanchet , Coralia Cartis , Matt Menickelly , Katya Scheinberg

This paper provides a non-asymptotic analysis of linear stochastic approximation (LSA) algorithms with fixed stepsize. This family of methods arises in many machine learning tasks and is used to obtain approximate solutions of a linear…

Machine Learning · Statistics 2021-06-03 Alain Durmus , Eric Moulines , Alexey Naumov , Sergey Samsonov , Kevin Scaman , Hoi-To Wai

Temporal difference (TD) learning is a cornerstone reinforcement learning (RL) method for policy evaluation, where the goal is to estimate the value function of a Markov decision process under a fixed policy. While a substantial body of…

Machine Learning · Computer Science 2026-02-02 Donghwan Lee , Do Wan Kim

We study time-uniform statistical inference for parameters in stochastic approximation (SA), which encompasses a bunch of applications in optimization and machine learning. To that end, we analyze the almost-sure convergence rates of the…

Machine Learning · Statistics 2024-10-22 Chuhan Xie , Kaicheng Jin , Jiadong Liang , Zhihua Zhang

Using a martingale concentration inequality, concentration bounds `from time $n_0$ on' are derived for stochastic approximation algorithms with contractive maps and both martingale difference and Markov noises. These are applied to…

Machine Learning · Computer Science 2022-06-14 Siddharth Chandak , Vivek S. Borkar , Parth Dodhia

In this paper, we establish the almost sure convergence of two-timescale stochastic gradient descent algorithms in continuous time under general noise and stability conditions, extending well known results in discrete time. We analyse…

Optimization and Control · Mathematics 2021-10-01 Louis Sharrock , Nikolas Kantas

This paper studies the performative prediction problem where a learner aims to minimize the expected loss with a decision-dependent data distribution. Such setting is motivated when outcomes can be affected by the prediction model, e.g., in…

Optimization and Control · Mathematics 2024-05-24 Haitong Liu , Qiang Li , Hoi-To Wai

We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…

Machine Learning · Statistics 2025-09-30 Reza Sadeghi Hafshejani , Mohamad Kazem Shirani Fradonbeh

Prediction via deterministic continuous-time models will always be subject to model error, for example due to unexplainable phenomena, uncertainties in any data driving the model, or discretisation/resolution issues. In this paper, we build…

Dynamical Systems · Mathematics 2025-06-30 Liam Blake , John Maclean , Sanjeeva Balasuriya

The law of the iterated logarithm (LIL) for the time-homogeneous Markov process with a unique invariant measure characterizes the almost sure maximum possible fluctuation of time averages around the ergodic limit. Whether a numerical…

Numerical Analysis · Mathematics 2025-11-10 Chuchu Chen , Xinyu Chen , Jialin Hong

A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space and a stochastic trigonometric method for the temporal…

Numerical Analysis · Mathematics 2015-11-26 Rikard Anton , David Cohen , Stig Larsson , Xiaojie Wang

We prove a bound on the finite sample error of sequential Monte Carlo (SMC) on static spaces using the $L_2$ distance between interpolating distributions and the mixing times of Markov kernels. This result is unique in that it is the first…

Computation · Statistics 2025-08-26 Joe Marion , Joseph Mathews , Scott C. Schmidler

We present adaptive sequential SAA (sample average approximation) algorithms to solve large-scale two-stage stochastic linear programs. The iterative algorithm framework we propose is organized into \emph{outer} and \emph{inner} iterations…

Optimization and Control · Mathematics 2020-12-08 Raghu Pasupathy , Yongjia Song

We propose a two-point flux approximation finite-volume scheme for a stochastic non-linear parabolic equation with a multiplicative noise. The time discretization is implicit except for the stochastic noise term in order to be compatible…

Numerical Analysis · Mathematics 2023-03-24 Caroline Bauzet , Flore Nabet , Kerstin Schmitz , Aleksandra Zimmermann

We study one-sided and $\alpha$-correct sequential hypothesis testing for data generated by an ergodic Markov chain. The null hypothesis is that the unknown transition matrix belongs to a prescribed set $P$ of stochastic matrices, and the…

Statistics Theory · Mathematics 2026-02-20 Alhad Sethi , Kavali Sofia Sagar , Shubhada Agrawal , Debabrota Basu , P. N. Karthik

In 2013, Lu and Ren \cite {luren} considered anticipated backward stochastic differential equations driven by finite state, continuous time Markov chain noise and established the existence and uniqueness of the solutions of these equations…

Probability · Mathematics 2015-05-14 Zhe Yang , Robert J. Elliott

We consider spatially extended conductance based neuronal models with noise described by a stochastic reaction diffusion equation with additive noise coupled to a control variable with multiplicative noise but no diffusion. We only assume a…

Probability · Mathematics 2020-01-16 Martin Sauer , Wilhelm Stannat

This paper is concerned with developing and analyzing two novel implicit temporal discretization methods for the stochastic semilinear wave equations with multiplicative noise. The proposed methods are natural extensions of well-known…

Numerical Analysis · Mathematics 2024-08-26 Xiaobing Feng , Yukun Li , Liet Vo