arXiv research

Develops an online method for solving constrained optimization problems with debiasing techniques.

Optimizes stochastic linear bandits with efficient, asymptotically optimal algorithm.

Asymptotically optimal algorithm for contextual linear bandits.

Optimizes identifying top-k items from comparisons with minimal comparisons.

Paper analyzes and compares ELF algorithms for federated learning.

Paper proposes a novel metric learning algorithm using Riemannian optimization.

New method solves constrained stochastic optimization problems efficiently.

A framework for transformer attention layers derived from SVR.

A new algorithm tackles bilevel optimization with multiple inner minima.

We consider empirical risk minimization of linear predictors with convex loss functions. Such problems can be reformulated as convex-concave saddle point problems, and thus are well suitable for primal-dual first-order algorithms. However, primal-dual algorithms often require explicit strongly convex regularization in …

We study primal-dual type stochastic optimization algorithms with non-uniform sampling. Our main theoretical contribution in this paper is to present a convergence analysis of Stochastic Primal Dual Coordinate (SPDC) Method with arbitrary sampling. Based on this theoretical framework, we propose Optimality Violation-ba…

PDCA algorithm learns policies for RL with constraints using a primal-dual approach.

We provide theoretical complexity analysis for new algorithms to compute the optimal transport (OT) distance between two discrete probability distributions, and demonstrate their favorable practical performance over state-of-art primal-dual algorithms and their capability in solving other problems in large-scale, such …

This work develops confidence intervals for off-policy evaluation.

This paper considers asymptotically hyperbolic manifolds with a finite boundary intersecting the usual infinite boundary -- cornered asymptotically hyperbolic manifolds -- and proves a theorem of Cartan-Hadamard type near infinity for the normal exponential map on the finite boundary. As a main application, a normal fo…

New algorithm speeds up large-scale statistical inference.

New method accelerates convergence for entropy-regularized reinforcement learning problems.

PURE-CD algorithm proves complexity bounds for convex-concave problems.

New algorithm achieves sublinear regret in CMDPs without error cancellations.

New algorithm samples constrained distributions efficiently.

Accelerates machine learning algorithms for sparse data.

Quantized Stochastic Primal-Dual Methods for Distributed Optimization

In this paper, we propose a new primal-dual algorithm for minimizing $f(x) + g(x) + h(Ax)$, where $f$, $g$, and $h$ are proper lower semi-continuous convex functions, $f$ is differentiable with a Lipschitz continuous gradient, and $A$ is a bounded linear operator. The proposed algorithm has some famous primal-dual algo…

We consider a skew ruled surface $Φ$ in the Euclidean space $E^{3}$ and relative normalizations of it, so that the relative normals at each point lie in the corresponding asymptotic plane of $Φ$. We call such relative normalizations and the resulting relative images of $Φ$ \emph{asymptotic}. We determine all ruled surf…

We study a stochastic and distributed algorithm for nonconvex problems whose objective consists of a sum of $N$ nonconvex $L_i/N$-smooth functions, plus a nonsmooth regularizer. The proposed NonconvEx primal-dual SpliTTing (NESTT) algorithm splits the problem into $N$ subproblems, and utilizes an augmented Lagrangian b…

We consider the convex-concave saddle point problem $\min_{x}\max_{y} f(x)+y^\top A x-g(y)$ where $f$ is smooth and convex and $g$ is smooth and strongly convex. We prove that if the coupling matrix $A$ has full column rank, the vanilla primal-dual gradient method can achieve linear convergence even if $f$ is not stron…

Paper proposes a debiased estimator for adaptive linear regression.

Binarization of digital documents is the task of classifying each pixel in an image of the document as belonging to the background (parchment/paper) or foreground (text/ink). Historical documents are often subjected to degradations, that make the task challenging. In the current work a deep neural network architecture …

Local asymptotic minimax risk bounds in a locally asymptotically mixture of normal family of distributions have been investigated under asymmetric loss functions and the asymptotic distribution of the optimal estimator that attains the bound has been obtained.

PAPAL algorithm finds mixed Nash equilibria in continuous games.

Paper explores weighted averaging schemes for SGD, achieving asymptotic normality and optimality.

The paper proves asymptotic normality for multinomial logistic regression on null covariates.

In this paper, we introduce a primal-dual algorithm for solving (martingale) optimal transportation problems, with cost functions satisfying the twist condition, close to the one that has been used recently for training generative adversarial networks. As some additional applications, we consider anomaly detection and …

We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our main analysis technique provides a fresh perspective on Nesterov's excessive gap te…

New methods solve saddle point problems without line search.

Drago optimizes DRO problems with faster convergence.

Paper proves robust M-estimators' coordinates' normality in high dimensions.

Operational risk models commonly employ maximum likelihood estimation (MLE) to fit loss data to heavy-tailed distributions. Yet several desirable properties of MLE (e.g. asymptotic normality) are generally valid only for large sample-sizes, a situation rarely encountered in operational risk. In this paper, we study how…

Efficient algorithm solves best subset selection problem.

Normal distributions ensure asymptotic variance reduction in moment matching Monte Carlo.

Proves mass-capacity inequalities for critical area-normalized capacitors, improving Schwarzschild metric uniqueness.

Improved first-order algorithm for entropy regularized OT with faster convergence.

Unified algorithm solves convex optimization problems with optimal rates.

A framework for modular training of robust generative models.

Defines mass for non-smooth hyperbolic spaces using a modified flow.

Kernel smoothing on unknown manifolds with bounds and asymptotic normality.

Develops methods for reliable inference on batched bandit data.

We propose a doubly stochastic primal-dual coordinate optimization algorithm for empirical risk minimization, which can be formulated as a bilinear saddle-point problem. In each iteration, our method randomly samples a block of coordinates of the primal and dual solutions to update. The linear convergence of our method…