Following the remarkable success of the AlphaGO series, 2019 was a booming year that
witnessed significant advances in multi-agent reinforcement learning (MARL) techniques …

The theory of random dynamical systems continues, extends, and unites various
developments in probability theory and dynamical systems. Roughly speaking, a random …

Bilevel optimization (BO) is useful for solving a variety of important machine learning
problems including but not limited to hyperparameter optimization, meta-learning, continual …

Gradient Descent Only Converges to Minimizers Page 1 JMLR: Workshop and Conference
Proceedings vol 49:1–12, 2016 Gradient Descent Only Converges to Minimizers Jason D. Lee …

Motivated by applications in Optimization, Game Theory, and the training of Generative
Adversarial Networks, the convergence properties of first order methods in min-max …

We establish that first-order methods avoid strict saddle points for almost all initializations.
Our results apply to a wide variety of first-order methods, including (manifold) gradient …

Most existing analyses of (stochastic) gradient descent rely on the condition that for $ L $-
smooth costs, the step size is less than $2/L $. However, many works have observed that in …

Contemporary work on learning in continuous games has commonly overlooked the
hierarchical decision-making structure present in machine learning problems formulated as …

In this book we will study equations of the following form x= f (x, t; µ),(0.0. 1) and x↦→ g (x;
µ),(0.0. 2) with x∈ U⊂ Rn, t∈ R1, and µ∈ V⊂ Rp where U and V are open sets in Rn and …

" Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but
introducing language and ways of thinking from category theory and homological algebra. It …