arXiv research

Efficient algorithm converges to Nash equilibrium in bilinear problems with bandit feedback.

New methods solve saddle point problems without line search.

In this paper we consider solving saddle point problems using two variants of Gradient Descent-Ascent algorithms, Extra-gradient (EG) and Optimistic Gradient Descent Ascent (OGDA) methods. We show that both of these algorithms admit a unified analysis as approximations of the classical proximal point method for solving…

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…

Improved convergence rates for saddle-point optimization algorithms.

New ODE models show saddle-point optimization methods converge differently, with last-iterate convergence for OGDA.

Owing to their connection with generative adversarial networks (GANs), saddle-point problems have recently attracted considerable interest in machine learning and beyond. By necessity, most theoretical guarantees revolve around convex-concave (or even linear) problems; however, making theoretical inroads towards effici…

We study the online saddle point problem, an online learning problem where at each iteration a pair of actions need to be chosen without knowledge of the current and future (convex-concave) payoff functions. The objective is to minimize the gap between the cumulative payoffs and the saddle point value of the aggregate …

New methods solve min-max problems on manifolds using Riemannian Hamiltonians.

New methods reduce communication in distributed training for variational inequalities.

We develop efficient algorithms to train $\ell_1$-regularized linear classifiers with large dimensionality $d$ of the feature space, number of classes $k$, and sample size $n$. Our focus is on a special class of losses that includes, in particular, the multiclass hinge and logistic losses. Our approach combines several…

Paper analyzes algorithms for nonstationary saddle-point optimization problems.

Study introduces statistical mechanics for min-max problems.

New method solves saddle-point problems faster than existing methods.

New algorithm reduces regret in graphical bilinear bandits.

Last iterate of Extragradient algorithm converges slower than averaged iterates in saddle point problems.

FeDualEx tackles saddle point optimization in federated learning with composite objectives.

Gradient-based optimization methods are the most popular choice for finding local optima for classical minimization and saddle point problems. Here, we highlight a systemic issue of gradient dynamics that arise for saddle point problems, namely the presence of undesired stable stationary points that are no local optima…

New algorithm solves saddle point problems in Banach spaces.

A new method helps escape saddle points in non-convex optimization.

Algorithm identifies correct hypothesis from alternatives in bandit problems.

New algorithm reduces regret in sequential decision-making problems.

Identifies bilinear systems from a single trajectory with optimal sample complexity.

Equivalence of convex optimization, saddle-point problems, and variational inequalities is a well-established concept. The variational inequality (VI) is a static problem which is studied under dynamical settings using a framework called the projected dynamical system, whose stationary points coincide with the static s…

Decentralized method solves saddle point problems with theoretical guarantees.

Optimal privacy-preserving algorithm for solving saddle point problems.

In this article, we study the convergence of Mirror Descent (MD) and Optimistic Mirror Descent (OMD) for saddle point problems satisfying the notion of coherence as proposed in Mertikopoulos et al. We prove convergence of OMD with exact gradients for coherent saddle point problems, and show that monotone convergence on…

We consider saddle point problems which objective functions are the average of $n$ strongly convex-concave individual components. Recently, researchers exploit variance reduction methods to solve such problems and achieve linear-convergence guarantees. However, these methods have a slow convergence when the condition n…

A distributed optimization method solves saddle point problems with strong concavity and convexity.

We reformulate LIPs as min-max problems for easier solution.

Algorithm identifies bilinear dynamical systems from noisy data.

We are interested in approximation of a multivariate function $f(x_1,\dots,x_d)$ by linear combinations of products $u^1(x_1)\cdots u^d(x_d)$ of univariate functions $u^i(x_i)$, $i=1,\dots,d$. In the case $d=2$ it is a classical problem of bilinear approximation. In the case of approximation in the $L_2$ space the bili…

We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible parallel optimization for large-scale problems. Our method shares the efficiency an…

This paper extends Newton's method to distributed learning, avoiding saddle points and handling Byzantine workers.

We extend the Frank-Wolfe (FW) optimization algorithm to solve constrained smooth convex-concave saddle point (SP) problems. Remarkably, the method only requires access to linear minimization oracles. Leveraging recent advances in FW optimization, we provide the first proof of convergence of a FW-type saddle point solv…

We consider the problem of computing optimal policies in average-reward Markov decision processes. This classical problem can be formulated as a linear program directly amenable to saddle-point optimization methods, albeit with a number of variables that is linear in the number of states. To address this issue, recent …

Study learns linear system dynamics from noisy bilinear data.

Non-bilinear observations make optimal control harder, showing non-convex costs and non-affine optimal controllers.

Houdini finds high-dimensional saddle points under few constraints.

GenFlow optimizes faster, avoiding saddle points in fixed time.

We consider a generic convex-concave saddle point problem with separable structure, a form that covers a wide-ranged machine learning applications. Under this problem structure, we follow the framework of primal-dual updates for saddle point problems, and incorporate stochastic block coordinate descent with adaptive st…

BiN normalizes financial time-series for better forecasting.

Nonconvex optimization problems such as the ones in training deep neural networks suffer from a phenomenon called saddle point proliferation. This means that there are a vast number of high error saddle points present in the loss function. Second order methods have been tremendously successful and widely adopted in the…

Unified framework for solving MDPs with stochastic mirror descent.

New method stabilizes saddle-point optimization with unbounded gradients.

We consider the problem of finding local minimizers in non-convex and non-smooth optimization. Under the assumption of strict saddle points, positive results have been derived for first-order methods. We present the first known results for the non-smooth case, which requires different analysis and a different algorithm…

A generalized optimistic method for saddle point problems with improved complexity.

New method simplifies optimization landscapes by transforming saddle points.