59 research outputs found
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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