59 research outputs found
Cycles in adversarial regularized learning
Regularized learning is a fundamental technique in online optimization,
machine learning and many other fields of computer science. A natural question
that arises in these settings is how regularized learning algorithms behave
when faced against each other. We study a natural formulation of this problem
by coupling regularized learning dynamics in zero-sum games. We show that the
system's behavior is Poincar\'e recurrent, implying that almost every
trajectory revisits any (arbitrarily small) neighborhood of its starting point
infinitely often. This cycling behavior is robust to the agents' choice of
regularization mechanism (each agent could be using a different regularizer),
to positive-affine transformations of the agents' utilities, and it also
persists in the case of networked competition, i.e., for zero-sum polymatrix
games.Comment: 22 pages, 4 figure
Continuous-time Analysis for Variational Inequalities: An Overview and Desiderata
Algorithms that solve zero-sum games, multi-objective agent objectives, or,
more generally, variational inequality (VI) problems are notoriously unstable
on general problems. Owing to the increasing need for solving such problems in
machine learning, this instability has been highlighted in recent years as a
significant research challenge. In this paper, we provide an overview of recent
progress in the use of continuous-time perspectives in the analysis and design
of methods targeting the broad VI problem class. Our presentation draws
parallels between single-objective problems and multi-objective problems,
highlighting the challenges of the latter. We also formulate various desiderata
for algorithms that apply to general VIs and we argue that achieving these
desiderata may profit from an understanding of the associated continuous-time
dynamics
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