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We present two approaches for linear prediction of long-memory time series. The first approach consists in truncating the Wiener-Kolmogorov predictor by restricting the observations to the last $k$ terms, which are the only available values…
In this work, we consider the deterministic optimization using random projections as a statistical estimation problem, where the squared distance between the predictions from the estimator and the true solution is the error metric. In…
We investigate stochastic averaging theory for locally Lipschitz discrete-time nonlinear systems with stochastic perturbation and its applications to convergence analysis of discrete-time stochastic extremum seeking algorithms. Firstly, by…
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…
The paper is focused on the nonlinear stability analysis of stochastic $\theta$-methods. In particular, we consider nonlinear stochastic differential equations such that the mean-square deviation between two solutions exponentially decays,…
We study the consistency of stochastic dynamic programs under converging probability distributions and other approximations. Utilizing results on the epi-convergence of expectation functions with varying measures and integrands, and the…
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…
This paper studies the performative prediction problem which optimizes a stochastic loss function with data distribution that depends on the decision variable. We consider a setting where the agent(s) provides samples adapted to the…
When there are infinitely many scenarios, the current studies of two-stage stochastic programming problems rely on the relatively complete recourse assumption. However, such assumption can be unrealistic for many real-world problems. This…
Regularly varying stochastic processes model extreme dependence between process values at different locations and/or time points. For such processes we propose a two-step parameter estimation of the extremogram, when some part of the domain…
Stochastic Approximation (SA) is a widely used algorithmic approach in various fields, including optimization and reinforcement learning (RL). Among RL algorithms, Q-learning is particularly popular due to its empirical success. In this…
We consider the optimization of a smooth and strongly convex objective using constant step-size stochastic gradient descent (SGD) and study its properties through the prism of Markov chains. We show that, for unbiased gradient estimates…
We consider bilevel linear problems, where some parameters are stochastic, and the leader has to decide in a here-and-now fashion, while the follower has complete information. In this setting, the leader's outcome can be modeled by a random…
A common approach in forecasting problems is to estimate a least-squares regression (or other statistical learning models) from past data, which is then applied to predict future outcomes. An underlying assumption is that the same…
Recent extensive numerical experiments in high scale machine learning have allowed to uncover a quite counterintuitive phase transition, as a function of the ratio between the sample size and the number of parameters in the model. As the…
Finite-precision floating point arithmetic unavoidably introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be…
The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently a stationary stochastic process (time…
We propose a method to compute an approximation of the moments of a discrete-time stochastic polynomial system. We use the Carleman linearization technique to transform this finite-dimensional polynomial system into an infinite-dimensional…
We study the approximability of general convex sets in $\mathbb{R}^n$ by intersections of halfspaces, where the approximation quality is measured with respect to the standard Gaussian distribution $N(0,I_n)$ and the complexity of an…
Stochastic alternating algorithms for bi-objective optimization are considered when optimizing two conflicting functions for which optimization steps have to be applied separately for each function. Such algorithms consist of applying a…