Related papers: Stochastic fixed-point iterations for nonexpansive…
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…
We study a decentralized variant of stochastic approximation, a data-driven approach for finding the root of an operator under noisy measurements. A network of agents, each with its own operator and data observations, cooperatively find the…
The asymptotic behavior of stochastic gradient algorithms is studied. Relying on results from differential geometry (Lojasiewicz gradient inequality), the single limit-point convergence of the algorithm iterates is demonstrated and…
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…
We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. Focusing on a stochastic query model that provides noisy evaluations of the operator, we analyze a variance-reduced stochastic…
We present a theoretical framework for characterizing incremental stability of nonlinear stochastic systems perturbed by compound Poisson shot noise and finite-measure L\'{e}vy noise. For each noise type, we compare trajectories of the…
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…
We study the problem of efficiently computing the derivative of the fixed-point of a parametric nondifferentiable contraction map. This problem has wide applications in machine learning, including hyperparameter optimization, meta-learning…
In this paper, we introduce new implicit and explicit iterative schemes which converge strongly to a unique solution of variational inequality problems for strongly accretive operators over a common fixed point set of finite family of…
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…
We study the singular values and Lyapunov exponents of non-stationary random matrix products subject to small, absolutely continuous, additive noise. Consider a fixed sequence of matrices of bounded norm. Independently perturb the matrices…
We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis…
Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…
Large-scale nonsmooth optimization problems arise in many real-world applications, but obtaining exact function and subgradient values for these problems may be computationally expensive or even infeasible. In many practical settings, only…
Motivated by the maneuvering target tracking with sensors such as radar and sonar, this paper considers the joint and recursive estimation of the dynamic state and the time-varying process noise covariance in nonlinear state space models.…
We introduce novel convergence results for asynchronous iterations that appear in the analysis of parallel and distributed optimization algorithms. The results are simple to apply and give explicit estimates for how the degree of asynchrony…
Motivated by the widespread use of temporal-difference (TD-) and Q-learning algorithms in reinforcement learning, this paper studies a class of biased stochastic approximation (SA) procedures under a mild "ergodic-like" assumption on the…
Motivated by global warming issues, we consider a time se- ries that consists of a nondecreasing trend observed with station- ary fluctuations, nonparametric estimation of the trend under monotonicity assumption is considered. The rescaled…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…
We study stochastic approximation procedures for approximately solving a $d$-dimensional linear fixed point equation based on observing a trajectory of length $n$ from an ergodic Markov chain. We first exhibit a non-asymptotic bound of the…