Evolution Under Strong Noise: A Self-Adaptive Evolution Strategy Can Reach the Lower Performance Bound - The pcCMSA-ES

According to a theorem by Astete-Morales, Cauwet, and Teytaud, “simple Evolution Strategies (ES)” that optimize quadratic functions disturbed by additive Gaussian noise of constant variance can only reach a simple regret log-log convergence slope \(\ge -1/2\) (lower bound). In this paper a population size controlled ES is presented that is able to perform better than the \(-1/2\) limit. It is shown experimentally that the pcCMSA-ES is able to reach a slope of \(-1\) being the theoretical lower bound of all comparison-based direct search algorithms.

[1]  Hans-Georg Beyer,et al.  The Theory of Evolution Strategies , 2001, Natural Computing Series.

[2]  Petros Koumoutsakos,et al.  A Method for Handling Uncertainty in Evolutionary Optimization With an Application to Feedback Control of Combustion , 2009, IEEE Transactions on Evolutionary Computation.

[3]  Olivier Teytaud,et al.  Evolution Strategies with Additive Noise: A Convergence Rate Lower Bound , 2015, FOGA.

[4]  J. Kenney.  Mathematics of statistics , 1940 .

[5]  Hans-Georg Beyer,et al.  The Dynamics of Self-Adaptive Multirecombinant Evolution Strategies on the General Ellipsoid Model , 2014, IEEE Transactions on Evolutionary Computation.

[6]  Dirk V. Arnold,et al.  Noisy Optimization With Evolution Strategies , 2002, Genetic Algorithms and Evolutionary Computation.

[7]  Bernhard Sendhoff,et al.  Evolution Strategies for Robust Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[8]  Hans-Georg Beyer,et al.  A New Approach for Predicting the Final Outcome of Evolution Strategy Optimization Under Noise , 2005, Genetic Programming and Evolvable Machines.

[9]  Hans-Georg Beyer,et al.  Towards an Analysis of Self-Adaptive Evolution Strategies on the Noisy Ellipsoid Model , 2015, GECCO.

[10]  Ohad Shamir,et al.  On the Complexity of Bandit and Derivative-Free Stochastic Convex Optimization , 2012, COLT.

[11]  Bernhard Sendhoff,et al.  Covariance Matrix Adaptation Revisited - The CMSA Evolution Strategy - , 2008, PPSN.

[12]  Jürgen Branke,et al.  Evolutionary optimization in uncertain environments-a survey , 2005, IEEE Transactions on Evolutionary Computation.