arXiv research

Improved stochastic Halpern iteration for fixed-point approximation in normed spaces.

The paper relaxes assumptions for analyzing stochastic optimization algorithms.

Optimizes solving complex min-max problems with stochastic and nonconvex elements.

New algorithms solve monotone inclusions and convex-concave minimax problems.

VR-GHAL method solves stochastic fixed-point equations with high probability.

Two accelerated extragradient methods converge at $O(1/k)$ rate for co-hypomonotone inclusions.

Survey on extragradient methods for solving nonlinear equations and inclusions.

New model-free RL algorithm tackles robust average-reward problems with finite sample complexity analysis.

New analysis of stochastic approximation with non-expansive mappings.

Derives error bounds for stochastic iterative algorithms using Stein's method.

Improved SEG method converges to Nash equilibrium in bilinear games.

In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic subspace ascent. A common feature of these methods is that in their update rule a cert…

Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic programming algorithms for solving Markov decision problems. These recursive stochastic a…

New algorithm minimizes worst-case regret in uncertain, time-varying dynamics.

New method speeds up distributed linear regression.

In the paper, we study the stochastic alternating direction method of multipliers (ADMM) for the nonconvex optimizations, and propose three classes of the nonconvex stochastic ADMM with variance reduction, based on different reduced variance stochastic gradients. Specifically, the first class called the nonconvex stoch…

New method solves constrained stochastic optimization problems efficiently.

This paper studies the problem of distributed stochastic optimization in an adversarial setting where, out of the $m$ machines which allegedly compute stochastic gradients every iteration, an $α$-fraction are Byzantine, and can behave arbitrarily and adversarially. Our main result is a variant of stochastic gradient de…

Paper provides tail bounds for stochastic mirror descent in heavy-tailed noise.

Developed an efficient iterative algorithm for SVI model.

The paper analyzes convergence rates for SGD and SHB methods.

In this paper, we propose a stochastic Primal-Dual Hybrid Gradient (PDHG) approach for solving a wide spectrum of regularized stochastic minimization problems, where the regularization term is composite with a linear function. It has been recognized that solving this kind of problem is challenging since the closed-form…

Paper improves a method for fast global and local convergence in optimization.

Predicts the number of polynomial additions in Buchberger's algorithm using machine learning.

Principal component analysis (PCA) is one of the most powerful tools in machine learning. The simplest method for PCA, the power iteration, requires $\mathcal O(1/Δ)$ full-data passes to recover the principal component of a matrix with eigen-gap $Δ$. Lanczos, a significantly more complex method, achieves an accelerated…

Optimizes convergence rate of stochastic proximal algorithms for composite convex problems.

In this paper, we prove some convergence results of a special case of optimistic policy iteration algorithm for stochastic shortest path problem. We consider both Monte Carlo and $TD(λ)$ methods for the policy evaluation step under the condition that the termination state will eventually be reached almost surely.

Adaptive SAA solves large-scale stochastic linear programs efficiently.

We develop methods for parameter estimation in settings with large-scale data sets, where traditional methods are no longer tenable. Our methods rely on stochastic approximations, which are computationally efficient as they maintain one iterate as a parameter estimate, and successively update that iterate based on a si…

We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs numerically requires the approximation of nested conditional expectations, i.e., it…

SIGMA model improves graph matching across various applications.

This paper provides a framework to analyze stochastic gradient algorithms in a mean squared error (MSE) sense using the asymptotic normality result of the stochastic gradient descent (SGD) iterates. We perform this analysis by taking the asymptotic normality result and applying it to the finite iteration case. Specific…

In this paper, we propose a new adaptive stochastic gradient Langevin dynamics (ASGLD) algorithmic framework and its two specialized versions, namely adaptive stochastic gradient (ASG) and adaptive gradient Langevin dynamics(AGLD), for non-convex optimization problems. All proposed algorithms can escape from saddle poi…

Optimizes CM for stochastic convex optimization with progressive precision.

Develops minibatch stochastic proximal gradient for large-scale learning models.

The paper analyzes generalization of noisy iterative algorithms using communication theory.

In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these metho…

Unified framework for solving fixed-point equations in deterministic and stochastic settings.

Unified analysis of stochastic iterative algorithms using Lyapunov functions.

We describe stochastic Newton and stochastic quasi-Newton approaches to efficiently solve large linear least-squares problems where the very large data sets present a significant computational burden (e.g., the size may exceed computer memory or data are collected in real-time). In our proposed framework, stochasticity…

Paper develops bounds for stochastic approximation with averaging.

Method solves complex optimization problems with high probability bounds.

A new method speeds up option pricing under Heston's stochastic volatility model.

A new hybrid algorithm reduces stochastic gradient evaluations for nonconvex optimization.

We propose and analyze a variant of the classic Polyak-Ruppert averaging scheme, broadly used in stochastic gradient methods. Rather than a uniform average of the iterates, we consider a weighted average, with weights decaying in a geometric fashion. In the context of linear least squares regression, we show that this …

We describe and analyze a simple algorithm for principal component analysis and singular value decomposition, VR-PCA, which uses computationally cheap stochastic iterations, yet converges exponentially fast to the optimal solution. In contrast, existing algorithms suffer either from slow convergence, or computationally…

Recurrent iterated function systems (RIFSs) are improvements of iterated function systems (IFSs) using elements of the theory of Marcovian stochastic processes which can produce more natural looking images. We construct new RIFSs consisting substantially of a vertical contraction factor function and nonlinear transform…

This work's purpose is to understand the dynamics of some social systems whose properties can be captured by certain iterated function systems. To achieve this intension, we start from the theory of iterated function systems, and then we study two specific economic models on random utility function and optimal stochast…