相关论文: General Feasibility Bounds for Sample Average Appr…

This paper is concerned with a class of stochastic optimization problems defined on a Banach space with almost sure conic-type constraints. For this class of problems, we investigate the consistency of optimal values and solutions…

We derive an objective function that can be optimized to give an estimator of the Vapnik- Chervonenkis dimension for model selection in regression problems. We verify our estimator is consistent. Then, we verify it performs well compared to…

Recent advances have significantly improved our understanding of the sample complexity of learning in average-reward Markov decision processes (AMDPs) under the generative model. However, much less is known about the constrained…

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…

We consider the solution of finite-sum minimization problems, such as those appearing in nonlinear least-squares or general empirical risk minimization problems. We are motivated by problems in which the summand functions are…

One of the main theoretical challenges in learning dynamical systems from data is providing upper bounds on the generalization error, that is, the difference between the expected prediction error and the empirical prediction error measured…

We study the unconstrained minimization of a smooth and strongly convex population loss function under a stochastic oracle that introduces both additive and multiplicative noise; this is a canonical and widely-studied setting that arises…

This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The…

We study the problem of minimizing the average of a very large number of smooth functions, which is of key importance in training supervised learning models. One of the most celebrated methods in this context is the SAGA algorithm. Despite…

Trajectory optimization under uncertainty underpins a wide range of applications in robotics. However, existing methods are limited in terms of reasoning about sources of epistemic and aleatoric uncertainty, space and time correlations,…

In this dissertation, I derive a new method to estimate the Vapnik-Chervonenkis Dimension (VCD) for the class of linear functions. This method is inspired by the technique developed by Vapnik et al. Vapnik et al. (1994). My contribution…

This monograph deals with adaptive supervised classification, using tools borrowed from statistical mechanics and information theory, stemming from the PACBayesian approach pioneered by David McAllester and applied to a conception of…

Motivated by applications in reinforcement learning (RL), we study a nonlinear stochastic approximation (SA) algorithm under Markovian noise, and establish its finite-sample convergence bounds under various stepsizes. Specifically, we show…

In this paper, we study the almost sure boundedness and the convergence of the stochastic approximation (SA) algorithm. At present, most available convergence proofs are based on the ODE method, and the almost sure boundedness of the…

Vapnik--Chervonenkis' theorem is a seminal result in machine learning. It establishes sufficient conditions for empirical probabilities to converge to theoretical probabilities, uniformly over families of events. It also provides an…

We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds…

This paper studies linear stochastic approximation (SA) algorithms and their application to multi-agent systems in engineering and sociology. As main contribution, we provide necessary and sufficient conditions for convergence of linear SA…

Many machine learning and optimization algorithms are built upon the framework of stochastic approximation (SA), for which the selection of step-size (or learning rate) $\{\alpha_n\}$ is crucial for success. An essential condition for…

We analyze a family of supervised learning algorithms based on sample compression schemes that are stable, in the sense that removing points from the training set which were not selected for the compression set does not alter the resulting…

Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…