2 research outputs found
Exploration-Exploitation in Multi-Agent Learning: Catastrophe Theory Meets Game Theory
Exploration-exploitation is a powerful and practical tool in multi-agent
learning (MAL), however, its effects are far from understood. To make progress
in this direction, we study a smooth analogue of Q-learning. We start by
showing that our learning model has strong theoretical justification as an
optimal model for studying exploration-exploitation. Specifically, we prove
that smooth Q-learning has bounded regret in arbitrary games for a cost model
that explicitly captures the balance between game and exploration costs and
that it always converges to the set of quantal-response equilibria (QRE), the
standard solution concept for games under bounded rationality, in weighted
potential games with heterogeneous learning agents. In our main task, we then
turn to measure the effect of exploration in collective system performance. We
characterize the geometry of the QRE surface in low-dimensional MAL systems and
link our findings with catastrophe (bifurcation) theory. In particular, as the
exploration hyperparameter evolves over-time, the system undergoes phase
transitions where the number and stability of equilibria can change radically
given an infinitesimal change to the exploration parameter. Based on this, we
provide a formal theoretical treatment of how tuning the exploration parameter
can provably lead to equilibrium selection with both positive as well as
negative (and potentially unbounded) effects to system performance.Comment: Appears in the 35th AAAI Conference on Artificial Intelligenc