76 citations · 226 across the 9 of their papers we have counts for
10 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…
Global Convergence of Multi-Agent Policy Gradient in Markov Potential Games
Stefanos Leonardos, Will Overman, Ioannis Panageas +1
Potential games are arguably one of the most important and widely studied classes of normal form games. They define the archetypal setting of multi-agent coordination as all agent…
First-order methods almost always avoid saddle points: the case of vanishing step-sizes
Ioannis Panageas, Georgios Piliouras, Xiao Wang
In a series of papers \cite{LSJR16, PP17, LPP}, it was established that some of the most commonly used first order methods almost surely (under random initializations) and with ste…
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…
Mutation, Sexual Reproduction and Survival in Dynamic Environments
Ruta Mehta, Ioannis Panageas, Georgios Piliouras +2
A new approach to understanding evolution [Val09], namely viewing it through the lens of computation, has already started yielding new insights, e.g., natural selection under sexua…
The Complexity of Genetic Diversity
Ruta Mehta, Ioannis Panageas, Georgios Piliouras +1
A key question in biological systems is whether genetic diversity persists in the long run under evolutionary competition or whether a single dominant genotype emerges. Classic wor…
Natural Selection as an Inhibitor of Genetic Diversity: Multiplicative Weights Updates Algorithm and a Conjecture of Haploid Genetics
Ruta Mehta, Ioannis Panageas, Georgios Piliouras
In a recent series of papers a surprisingly strong connection was discovered between standard models of evolution in mathematical biology and Multiplicative Weights Updates Algorit…
Average Case Performance of Replicator Dynamics in Potential Games via Computing Regions of Attraction
Ioannis Panageas, Georgios Piliouras
What does it mean to fully understand the behavior of a network of adaptive agents? The golden standard typically is the behavior of learning dynamics in potential games, where man…