相关论文: HessianFR: An Efficient Hessian-based Follow-the-R…

In this paper, we study stochastic non-convex optimization with non-convex random functions. Recent studies on non-convex optimization revolve around establishing second-order convergence, i.e., converging to a nearly second-order optimal…

We provide the first theoretical analysis on the convergence rate of the asynchronous stochastic variance reduced gradient (SVRG) descent algorithm on non-convex optimization. Recent studies have shown that the asynchronous stochastic…

Best rank-one approximation is one of the most fundamental tasks in tensor computation. In order to fully exploit modern multi-core parallel computers, it is necessary to develop decoupling algorithms for computing the best rank-one…

Training generative adversarial networks (GANs) is known to be difficult, especially for financial time series. This paper first analyzes the well-posedness problem in GANs minimax games and the convexity issue in GANs objective functions.…

We introduce a new algorithm for the numerical computation of Nash equilibria of competitive two-player games. Our method is a natural generalization of gradient descent to the two-player setting where the update is given by the Nash…

Counterfactual Regret Minimization (CFR) and its variants are widely recognized as effective algorithms for solving extensive-form imperfect information games. Recently, many improvements have been focused on enhancing the convergence speed…

Stochastic variance-reduced gradient (SVRG) algorithms have been shown to work favorably in solving large-scale learning problems. Despite the remarkable success, the stochastic gradient complexity of SVRG-type algorithms usually scales…

A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…

In this paper, we study Newton-conjugate gradient (Newton-CG) methods for minimizing a nonconvex function $f$ whose Hessian is $(H_f,\nu)$-H\"older continuous with modulus $H_f>0$ and exponent $\nu\in(0,1]$. Recently proposed Newton-CG…

We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms,…

This paper studies minimax optimization problems defined over infinite-dimensional function classes of overparameterized two-layer neural networks. In particular, we consider the minimax optimization problem stemming from estimating linear…

Using quasi-Newton methods in stochastic optimization is not a trivial task given the difficulty of extracting curvature information from the noisy gradients. Moreover, pre-conditioning noisy gradient observations tend to amplify the noise.…

We develop provably efficient reinforcement learning algorithms for two-player zero-sum finite-horizon Markov games with simultaneous moves. To incorporate function approximation, we consider a family of Markov games where the reward…

This report investigates the fitting of the Hessian or its inverse for stochastic optimizations using a Hessian fitting criterion derived from the preconditioned stochastic gradient descent (PSGD) method. This criterion is closely related…

We propose a new first-order optimization algorithm -- AcceleratedGradient-OptimisticGradient (AG-OG) Descent Ascent -- for separable convex-concave minimax optimization. The main idea of our algorithm is to carefully leverage the structure…

Data-driven modeling increasingly requires to find a Nash equilibrium in multi-player games, e.g. when training GANs. In this paper, we analyse a new extra-gradient method for Nash equilibrium finding, that performs gradient extrapolations…

Recent work has established an empirically successful framework for adapting learning rates for stochastic gradient descent (SGD). This effectively removes all needs for tuning, while automatically reducing learning rates over time on…

Bilevel optimization has arisen as a powerful tool in modern machine learning. However, due to the nested structure of bilevel optimization, even gradient-based methods require second-order derivative approximations via Jacobian- or/and…

We study stochastic Nash equilibrium problems with expected valued cost functions whose pseudogradient satisfies restricted monotonicity properties which hold only with respect to the solution. We propose a forward-backward algorithm and…

We study online optimization methods for zero-sum games, a fundamental problem in adversarial learning in machine learning, economics, and many other domains. Traditional methods approximate Nash equilibria (NE) using either regret-based…