Owing to their connection with generative adversarial networks (GANs), saddle-point
problems have recently attracted considerable interest in machine learning and beyond. By …

The gradient noise (GN) in the stochastic gradient descent (SGD) algorithm is often
considered to be Gaussian in the large data regime by assuming that the classical central …

In game-theoretic learning, several agents are simultaneously following their individual
interests, so the environment is non-stationary from each player's perspective. In this context …

We introduce a general framework for competitive gradient-based learning that
encompasses a wide breadth of multiagent learning algorithms, and analyze the limiting …

This paper deals with a natural stochastic optimization procedure derived from the so-called
Heavy-ball method differential equation, which was introduced by Polyak in the 1960s with …

We consider the problem of sampling from constrained distributions, which has posed
significant challenges to both non-asymptotic analysis and algorithmic design. We propose …

One of the most widely used optimization methods for large-scale machine learning
problems is distributed asynchronous stochastic gradient descent (DASGD). However, a key …

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 …

Lipschitz continuity is a central requirement for achieving the optimal O (1/T) rate of
convergence in monotone, deterministic variational inequalities (a setting that includes …

We study a class of evolutionary game dynamics defined by balancing a gain determined by
the game's payoffs against a cost of motion that captures the difficulty with which the …