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We study accuracy of bootstrap procedures for estimation of quantiles of a smooth function of a sum of independent sub-Gaussian random vectors. We establish higher-order approximation bounds with error terms depending on a sample size and a…

Statistics Theory · Mathematics 2020-09-21 Mayya Zhilova

This paper proposes an identification algorithm for Single Input Single Output (SISO) Linear Time-Invariant (LTI) systems. In the noise-free setting, where the first $T$ Markov parameters can be precisely estimated, all Markov parameters…

Optimization and Control · Mathematics 2023-04-12 Jiayun Li , Yilin Mo

The paper suggests a generalization of the Sign-Perturbed Sums (SPS) finite sample system identification method for the identification of closed-loop observable stochastic linear systems in state-space form. The solution builds on the…

Systems and Control · Electrical Eng. & Systems 2024-06-11 Szabolcs Szentpéteri , Balázs Csanád Csáji

In this paper we study the asymptotic behavior of a stochastic approximation scheme on two timescales with set-valued drift functions and in the presence of non-additive iterate-dependent Markov noise. It is shown that the recursion on each…

Systems and Control · Computer Science 2016-11-21 Vinayaka Yaji , Shalabh Bhatnagar

We derive new and improved non-asymptotic deviation inequalities for the sample average approximation (SAA) of an optimization problem. Our results give strong error probability bounds that are "sub-Gaussian"~even when the randomness of the…

Optimization and Control · Mathematics 2022-03-28 Roberto I. Oliveira , Philip Thompson

his study presents a novel technique to estimate the computational complexity of sequential decoding using the Berry-Esseen theorem. Unlike the theoretical bounds determined by the conventional central limit theorem argument, which often…

Information Theory · Computer Science 2007-08-20 Po-Ning Chen , Yunghsiang S. Han , Carlos R. P. Hartmann , Hong-Bin Wu

In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without…

Machine Learning · Computer Science 2019-03-22 Anastasios Tsiamis , George J. Pappas

The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…

Probability · Mathematics 2020-01-03 Marina Riabiz , Tohid Ardeshiri , Ioannis Kontoyiannis , Simon Godsill

We investigate the statistical properties of Temporal Difference (TD) learning with Polyak-Ruppert averaging, arguably one of the most widely used algorithms in reinforcement learning, for the task of estimating the parameters of the…

Machine Learning · Statistics 2026-02-25 Weichen Wu , Gen Li , Yuting Wei , Alessandro Rinaldo

We consider the problem of estimating the asymptotic variance of a function defined on a Markov chain, an important step for statistical inference of the stationary mean. We design a novel recursive estimator that requires $O(1)$…

Statistics Theory · Mathematics 2024-09-24 Shubhada Agrawal , Prashanth L. A. , Siva Theja Maguluri

Traditionally, stochastic approximation schemes for SVIs have relied on strong monotonicity and Lipschitzian properties of the underlying map. In contrast, we consider monotone stochastic variational inequality (SVI) problems where the…

Optimization and Control · Mathematics 2016-01-06 Farzad Yousefian , Angelia Nedić , Uday V. Shanbhag

This paper studies the control-oriented identification problem of set-valued moving average systems with uniform persistent excitations and observation noises. A stochastic approximation-based (SA-based) algorithm without projections or…

Systems and Control · Electrical Eng. & Systems 2025-03-25 Jieming Ke , Ying Wang , Yanlong Zhao , Ji-Feng Zhang

We study parameter inference in simulation-based stochastic models where the analytical form of the likelihood is unknown. The main difficulty is that score evaluation as a ratio of noisy Monte Carlo estimators induces bias and instability,…

Machine Learning · Statistics 2025-10-31 Zehao Li , Zhouchen Lin , Yijie Peng

We consider maximum likelihood estimation for both causal and noncausal autoregressive time series processes with non-Gaussian $\alpha$-stable noise. A nondegenerate limiting distribution is given for maximum likelihood estimators of the…

Statistics Theory · Mathematics 2009-08-14 Beth Andrews , Matthew Calder , Richard A. Davis

The tuning of stochastic gradient algorithms (SGAs) for optimization and sampling is often based on heuristics and trial-and-error rather than generalizable theory. We address this theory--practice gap by characterizing the large-sample…

Computation · Statistics 2023-07-21 Jeffrey Negrea , Jun Yang , Haoyue Feng , Daniel M. Roy , Jonathan H. Huggins

Stochastic approximation (SA) is a powerful and scalable computational method for iteratively estimating the solution of optimization problems in the presence of randomness, particularly well-suited for large-scale and streaming data…

Statistics Theory · Mathematics 2023-10-03 Meimei Liu , Zuofeng Shang , Yun Yang

We present a probabilistic model for stochastic iterative algorithms with the use case of optimization algorithms in mind. Based on this model, we present PAC-Bayesian generalization bounds for functions that are defined on the trajectory…

Machine Learning · Computer Science 2024-08-22 Michael Sucker , Peter Ochs

Many machine learning and optimization algorithms can be cast as instances of stochastic approximation (SA). The convergence rate of these algorithms is known to be slow, with the optimal mean squared error (MSE) of order $O(n^{-1})$. In…

Optimization and Control · Mathematics 2024-09-13 Caio Kalil Lauand , Sean Meyn

This paper compiles several aspects of the dynamics of stochastic approximation algorithms with Markov iterate-dependent noise when the iterates are not known to be stable beforehand. We achieve the same by extending the lock-in probability…

Dynamical Systems · Mathematics 2019-02-22 Prasenjit Karmakar , Shalabh Bhatnagar

SARSA is an on-policy algorithm to learn a Markov decision process policy in reinforcement learning. We investigate the SARSA algorithm with linear function approximation under the non-i.i.d.\ data, where a single sample trajectory is…

Machine Learning · Computer Science 2019-11-20 Shaofeng Zou , Tengyu Xu , Yingbin Liang