Related papers: Constants of Motion: The Antidote to Chaos in Opti…

The beauty of physics is that there is usually a conserved quantity in an always-changing system, known as the constant of motion. Finding the constant of motion is important in understanding the dynamics of the system, but typically…

We consider multi-player games played on graphs, in which the players aim at fulfilling their own (not necessarily antagonistic) objectives. In the spirit of evolutionary game theory, we suppose that the players have the right to repeatedly…

This paper begins with a dynamical model that was obtained by applying a machine learning technique (FJet) to time-series data; this dynamical model is then analyzed with Lie symmetry techniques to obtain constants of motion. This analysis…

The cornerstone underpinning deep learning is the guarantee that gradient descent on an objective converges to local minima. Unfortunately, this guarantee fails in settings, such as generative adversarial nets, where there are multiple…

Gradient based optimization algorithms deployed in Machine Learning (ML) applications are often analyzed and compared by their convergence rates or regret bounds. While these rates and bounds convey valuable information they don't always…

Tracking the solution of time-varying variational inequalities is an important problem with applications in game theory, optimization, and machine learning. Existing work considers time-varying games or time-varying optimization problems.…

Maximizing monotone submodular functions under cardinality constraints is a classic optimization task with several applications in data mining and machine learning. In this paper we study this problem in a dynamic environment with…

Games generalize the single-objective optimization paradigm by introducing different objective functions for different players. Differentiable games often proceed by simultaneous or alternating gradient updates. In machine learning, games…

A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…

Stochastic Gradient Descent (SGD) methods see many uses in optimization problems. Modifications to the algorithm, such as momentum-based SGD methods have been known to produce better results in certain cases. Much of this, however, is due…

A systematic framework for analyzing dynamical attributes of games has not been well-studied except for the special class of potential or near-potential games. In particular, the existing results have shortcomings in determining the…

We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for…

We show that accelerated gradient descent, averaged gradient descent and the heavy-ball method for non-strongly-convex problems may be reformulated as constant parameter second-order difference equation algorithms, where stability of the…

In this work, we establish a frequency-domain framework for analyzing gradient-based algorithms in linear minimax optimization problems; specifically, our approach is based on the Z-transform, a powerful tool applied in Control Theory and…

Scale-invariance in games has recently emerged as a widely valued desirable property. Yet, almost all fast convergence guarantees in learning in games require prior knowledge of the utility scale. To address this, we develop learning…

The constants of motion of the following systems are deduced: a relativistic particle with linear dissipation, a no-relativistic particle with a time explicitly depending force, a no-relativistic particle with a constant force and time…

The search for universal laws that help establish a relationship between dynamics and computation is driven by recent expansionist initiatives in biologically inspired computing. A general setting to understand both such dynamics and…

We study the performance of stochastic first-order methods for finding saddle points of convex-concave functions. A notorious challenge faced by such methods is that the gradients can grow arbitrarily large during optimization, which may…

Gradient-based methods for two-player games produce rich dynamics that can solve challenging problems, yet can be difficult to stabilize and understand. Part of this complexity originates from the discrete update steps given by simultaneous…

This paper synthesizes anytime algorithms, in the form of continuous-time dynamical systems, to solve monotone variational inequalities. We introduce three algorithms that solve this problem: the projected monotone flow, the safe monotone…