76 citations · 264 across the 45 of their papers we have counts for
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A stochastic variant of replicator dynamics in zero-sum games and its invariant measures
Maximilian Engel, Georgios Piliouras
We study the behavior of a stochastic variant of replicator dynamics in two-agent zero-sum games. We characterize the statistics of such systems by their invariant measures which c…
Family of chaotic maps from game theory
Thiparat Chotibut, Fryderyk Falniowski, Michal Misiurewicz +1
From a two-agent, two-strategy congestion game where both agents apply the multiplicative weights update algorithm, we obtain a two-parameter family of maps of the unit square to i…
Gradient Descent Only Converges to Minimizers: Non-Isolated Critical Points and Invariant Regions
Ioannis Panageas, Georgios Piliouras
Given a non-convex twice differentiable cost function f, we prove that the set of initial conditions so that gradient descent converges to saddle points where \nabla^2 f has at lea…