Related papers: Omega: Optimistic EMA Gradients
Smooth minimax optimization problems play a central role in a wide range of applications, including machine learning, game theory, and operations research. However, existing algorithmic frameworks vary significantly depending on the problem…
Stochastic optimization methods have been hugely successful in making large-scale optimization problems feasible when computing the full gradient is computationally prohibitive. Using the theory of modified equations for numerical…
In this paper we propose stochastic gradient-free methods and accelerated methods with momentum for solving stochastic optimization problems. All these methods rely on stochastic directions rather than stochastic gradients. We analyze the…
Two of the most prominent algorithms for solving unconstrained smooth games are the classical stochastic gradient descent-ascent (SGDA) and the recently introduced stochastic consensus optimization (SCO) [Mescheder et al., 2017]. SGDA is…
Algorithmic reproducibility measures the deviation in outputs of machine learning algorithms upon minor changes in the training process. Previous work suggests that first-order methods would need to trade-off convergence rate (gradient…
We study the convergence of Optimistic Gradient Descent Ascent in unconstrained bilinear games. In a first part, we consider the zero-sum case and extend previous results by Daskalakis et al. in 2018, Liang and Stokes in 2019, and others:…
We study the effect of the stochastic gradient noise on the training of generative adversarial networks (GANs) and show that it can prevent the convergence of standard game optimization methods, while the batch version converges. We address…
This paper considers minimax optimization $\min_x \max_y f(x, y)$ in the challenging setting where $f$ can be both nonconvex in $x$ and nonconcave in $y$. Though such optimization problems arise in many machine learning paradigms including…
Variational inequalities have recently attracted considerable interest in machine learning as a flexible paradigm for models that go beyond ordinary loss function minimization (such as generative adversarial networks and related deep…
In this letter, we employ and design the expectation--conditional maximization either (ECME) algorithm, a generalisation of the EM algorithm, for solving the maximum likelihood direction finding problem of stochastic sources, which may be…
Optimal experimental design (OED) seeks experiments expected to yield the most useful data for some purpose. In practical circumstances where experiments are time-consuming or resource-intensive, OED can yield enormous savings. We pursue…
The need for fast and robust optimization algorithms are of critical importance in all areas of machine learning. This paper treats the task of designing optimization algorithms as an optimal control problem. Using regret as a metric for an…
We provide several applications of Optimistic Mirror Descent, an online learning algorithm based on the idea of predictable sequences. First, we recover the Mirror Prox algorithm for offline optimization, prove an extension to Holder-smooth…
Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, while understanding the dynamics of gradient algorithms for solving such formulations has remained a…
A framework is introduced for solving a sequence of slowly changing optimization problems, including those arising in regression and classification applications, using optimization algorithms such as stochastic gradient descent (SGD). The…
The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…
We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…
We study the iteration complexity of the optimistic gradient descent-ascent (OGDA) method and the extra-gradient (EG) method for finding a saddle point of a convex-concave unconstrained min-max problem. To do so, we first show that both…
Most of the literature on learning in games has focused on the restrictive setting where the underlying repeated game does not change over time. Much less is known about the convergence of no-regret learning algorithms in dynamic multiagent…
This paper proposes a new family of algorithms for the online optimisation of composite objectives. The algorithms can be interpreted as the combination of the exponentiated gradient and $p$-norm algorithm. Combined with algorithmic ideas…