arXiv research

Transforms offline algorithms to online with low regret in random order model.

Improved matrix approximation using randomized algorithms.

Quantum algorithms reduce clustering input size, achieving near-linear approximation.

Stochastic approximation algorithms show exponential progress bounds.

Four algorithms improve sparse tensor BR1Approx with theoretical guarantees.

We develop an efficient algorithm for low-rank approximation with improved approximation guarantees.

Efficiently reduces tensor ranks using mean-field approximation.

Efficient algorithms for online learning with changing action sets, achieving no-approximate-regret guarantees.

Efficiently private clustering algorithms with tight approximation ratios.

Boosting Nyström improves accuracy of matrix approximations.

New algorithms improve approximation of matrix norms, with applications in statistics and machine learning.

Paper develops efficient RL algorithm for general value function approximation.

Sparse optimization refers to an optimization problem involving the zero-norm in objective or constraints. In this paper, nonconvex approximation approaches for sparse optimization have been studied with a unifying point of view in DC (Difference of Convex functions) programming framework. Considering a common DC appro…

One-pass algorithm finds small subset for $\ell_p$ subspace approximation with additive error.

Approximate dynamic programming algorithms, such as approximate value iteration, have been successfully applied to many complex reinforcement learning tasks, and a better approximate dynamic programming algorithm is expected to further extend the applicability of reinforcement learning to various tasks. In this paper w…

New algorithms for approximating stochastic processes efficiently.

In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within classical algorithms for low-rank approximation in order to exploit the possible sp…

We propose a hierarchy for approximate inference based on the Dobrushin, Lanford, Ruelle (DLR) equations. This hierarchy includes existing algorithms, such as belief propagation, and also motivates novel algorithms such as factorized neighbors (FN) algorithms and variants of mean field (MF) algorithms. In particular, w…

Paper presents a randomized algorithm for SPCA with high probability approximation.

Paper analyzes normal approximation for two-timescale stochastic algorithms, revealing interaction between fast and slow timescales.

This thesis disentangles Gauss-Newton and variational approximations in Bayesian deep learning.

Study Whittle index learning algorithms for restless bandits with constant stepsizes.

New algorithm finds near-optimal policies efficiently in zero-sum games.

Novel algorithm for Markov decision processes using rank-one approximation.

New MCMC algorithm reduces subset selection passes to 2 for optimal $k$-dimensional subspace approximation.

Paper proves large deviation principle for stochastic approximations.

Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential equations into the theoretical framework of diffusion approximation, extending the …

Efficient algorithm approximates discrete random variables with minimal Kolmogorov distance.

Algorithm finds Nash equilibria in complex games with function approximation.

We propose practical algorithms for entrywise $\ell_p$-norm low-rank approximation, for $p = 1$ or $p = \infty$. The proposed framework, which is non-convex and gradient-based, is easy to implement and typically attains better approximations, faster, than state of the art. From a theoretical standpoint, we show that th…

Simulation-based inference methods can produce unreliable posterior approximations.

Accelerated RPCholesky speeds up kernel matrix approximations.

RPCholesky approximates kernel matrices with few evaluations.

The paper gives a systematic study of the approximate versions of three greedy-type algorithms that are widely used in convex optimization. By approximate version we mean the one where some of evaluations are made with an error. Importance of such versions of greedy-type algorithms in convex optimization and in approxi…

New algorithm FLUTE achieves uniform-PAC convergence in RL with linear approx.

A practical algorithm improves approximate OT distances using quantization.

We study the optimal design problems where the goal is to choose a set of linear measurements to obtain the most accurate estimate of an unknown vector in $d$ dimensions. We study the $A$-optimal design variant where the objective is to minimize the average variance of the error in the maximum likelihood estimate of th…

$Q$-learning with function approximation is one of the most popular methods in reinforcement learning. Though the idea of using function approximation was proposed at least 60 years ago, even in the simplest setup, i.e, approximating $Q$-functions with linear functions, it is still an open problem on how to design a pr…

Paper introduces a new multi-kernel algorithm for better gradient approximation.

This paper is a follow up to the previous author's paper on convex optimization. In that paper we began the process of adjusting greedy-type algorithms from nonlinear approximation for finding sparse solutions of convex optimization problems. We modified there three the most popular in nonlinear approximation in Banach…

We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method can be used to approximate any posterior distribution, provided that it is given i…

Meta-algorithm selects optimal model complexity in RL with function approximation.

Approximate probabilistic inference algorithms are central to many fields. Examples include sequential Monte Carlo inference in robotics, variational inference in machine learning, and Markov chain Monte Carlo inference in statistics. A key problem faced by practitioners is measuring the accuracy of an approximate infe…

New MARL algorithms resolve the curse of multiagency with function approximation.

We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data. We employ a set of standard basis functions, e.g., polynomials, to approximate the governing equation with high accuracy. Upon recasting the problem into a function approximation problem, we …

Paper improves tensor approximation for streaming data.

Collaborative filtering (CF) is a popular technique in today's recommender systems, and matrix approximation-based CF methods have achieved great success in both rating prediction and top-N recommendation tasks. However, real-world user-item rating matrices are typically sparse, incomplete and noisy, which introduce ch…

Improved approximation for socially fair clustering with $\ell_p$-objective.