  One of the main challenges of multi-agent learning lies in establishing
convergence of the algorithms, as, in general, a collection of individual,
self-serving agents is not guaranteed to converge with their joint policy, when
learning concurrently. This is in stark contrast to most single-agent
environments, and sets a prohibitive barrier for deployment in practical
applications, as it induces uncertainty in long term behavior of the system. In
this work, we apply the concept of trapping regions, known from qualitative
theory of dynamical systems, to create safety sets in the joint strategy space
for decentralized learning. We propose a binary partitioning algorithm for
verification that candidate sets form trapping regions in systems with known
learning dynamics, and a heuristic sampling algorithm for scenarios where
learning dynamics are not known. We demonstrate the applications to a
regularized version of Dirac Generative Adversarial Network, a
four-intersection traffic control scenario run in a state of the art
open-source microscopic traffic simulator SUMO, and a mathematical model of
economic competition.
