76 citations · 140 across the 3 of their papers we have counts for
4 papers
Independent Natural Policy Gradient Always Converges in Markov Potential Games
Roy Fox, Stephen McAleer, Will Overman +1
Multi-agent reinforcement learning has been successfully applied to fully-cooperative and fully-competitive environments, but little is currently known about mixed cooperative/comp…
First-order Methods Almost Always Avoid Saddle Points
Jason D. Lee, Ioannis Panageas, Georgios Piliouras +3
We establish that first-order methods avoid saddle points for almost all initializations. Our results apply to a wide variety of first-order methods, including gradient descent, bl…
Multiplicative Weights Update with Constant Step-Size in Congestion Games: Convergence, Limit Cycles and Chaos
Gerasimos Palaiopanos, Ioannis Panageas, Georgios Piliouras
The Multiplicative Weights Update (MWU) method is a ubiquitous meta-algorithm that works as follows: A distribution is maintained on a certain set, and at each step the probability…
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…