2020/07/05 by Marc Harper, Harper, Marc, Joshua Safyan +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Social Sciences · #Dynamical Systems (math.DS) #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Reinforcement Learning in Robotics
paper · pdf · doi:10.48550/arxiv.2007.02449
openalex publication_date 2020/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
We combine momentum from machine learning with evolutionary dynamics, where momentum can be viewed as a simple mechanism of intergenerational memory. Using information divergences as Lyapunov functions, we show that momentum accelerates the convergence of evolutionary dynamics including the replicator equation and Euclidean gradient descent on populations. When evolutionarily stable states are present, these methods prove convergence for small learning rates or small momentum, and yield an analytic determination of the relative decrease in time to converge that agrees well with computations. The main results apply even when the evolutionary dynamic is not a gradient flow. We also show that momentum can alter the convergence properties of these dynamics, for example by breaking the cycling associated to the rock-paper-scissors landscape, leading to either convergence to the ordinarily non-absorbing equilibrium, or divergence, depending on the value and mechanism of momentum.