Momentum Accelerates Evolutionary Dynamics
This provides a method to speed up evolutionary algorithms for researchers in optimization and evolutionary computation, though it is incremental as it adapts an existing technique to a new context.
The paper tackles the problem of slow convergence in evolutionary dynamics by incorporating momentum, a concept from machine learning, as a form of intergenerational memory. The result shows that momentum accelerates convergence, with analytic predictions matching computations, and can alter dynamics to break cycles like in rock-paper-scissors.
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.