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We consider the problem of computing reachability probabilities: given a Markov chain, an initial state of the Markov chain, and a set of goal states of the Markov chain, what is the probability of reaching any of the goal states from the…

Normalizing flows learn a diffeomorphic mapping between the target and base distribution, while the Jacobian determinant of that mapping forms another real-valued function. In this paper, we show that the Jacobian determinant mapping is…

Accounting for the uncertainty in the predictions of modern neural networks is a challenging and important task in many domains. Existing algorithms for uncertainty estimation require modifying the model architecture and training procedure…

Decentralized stochastic optimization methods have gained a lot of attention recently, mainly because of their cheap per iteration cost, data locality, and their communication-efficiency. In this paper we introduce a unified convergence…

Motivated by problems arising in decentralized control problems and non-cooperative Nash games, we consider a class of strongly monotone Cartesian variational inequality (VI) problems, where the mappings either contain expectations or their…

We propose an online learning algorithm for a class of machine learning models under a separable stochastic approximation framework. The essence of our idea lies in the observation that certain parameters in the models are easier to…

The paper considers distributed stochastic optimization over randomly switching networks, where agents collaboratively minimize the average of all agents' local expectation-valued convex cost functions. Due to the stochasticity in gradient…

Motivated by the increasing availability of high-performance parallel computing, we design a distributed parallel algorithm for linearly-coupled block-structured nonconvex constrained optimization problems. Our algorithm performs…

This work blends the inexact Newton method with iterative combined approximations (ICA) for solving topology optimization problems under the assumption of geometric nonlinearity. The density-based problem formulation is solved using a…

Part I of this paper considered optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network…

In this paper, we present a detailed convergence analysis of a recently developed approximate Newton-type fully distributed optimization method for smooth, strongly convex local loss functions, called Network-GIANT, which has been…

This paper presents a stochastic approximation proximal subgradient (SAPS) method for stochastic convex-concave minimax optimization. By accessing unbiased and variance bounded approximate subgradients, we show that this algorithm exhibits…

In this paper, we analyze the recently proposed stochastic primal-dual hybrid gradient (SPDHG) algorithm and provide new theoretical results. In particular, we prove almost sure convergence of the iterates to a solution with convexity and…

Natural gradient descent has proven effective at mitigating the effects of pathological curvature in neural network optimization, but little is known theoretically about its convergence properties, especially for \emph{nonlinear} networks.…

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…

The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high…

Several classical adaptive optimization algorithms, such as line search and trust region methods, have been recently extended to stochastic settings where function values, gradients, and Hessians in some cases, are estimated via stochastic…

We study approximation algorithms for the following three string measures that are widely used in practice: edit distance (ED), longest common subsequence (LCS), and longest increasing sequence (LIS). All three problems can be solved…

The problem of posterior inference is central to Bayesian statistics and a wealth of Markov Chain Monte Carlo (MCMC) methods have been proposed to obtain asymptotically correct samples from the posterior. As datasets in applications grow…

A trivializing map is a field transformation whose Jacobian determinant exactly cancels the interaction terms in the action, providing a representation of the theory in terms of a deterministic transformation of a distribution from which…