Lyapunov Design of Two Success-Based Step-Size Adaptation Rules

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• Elizabeth Wanner (Aston University)
• Thursday 30 November 2017, 12:00-13:00
• Sandbox (Watson).

If you have a question about this talk, please contact Sergey Sergeev.

Two success-based step-size adaptation rules for single parent Evolution Strategies is formulated, and the setting of the corresponding parameters is considered. Theoretical convergence on the class of strictly unimodal functions of one variable that are symmetric around the optimum is investigated using a stochastic Lyapunov function method in the context of martingale theory. General expressions for the conditional expectations of the next values of step size and distance to the optimum under (1 + λ)- and (1 , λ) – selection are analytically derived, and an appropriate Lyapunov function is constructed. Convergence rate upper bounds, as well as adaptation parameter values, are obtained through numerical optimization for increasing values of λ, allowing for an informed selection of this parameter, as well. Experimental results are well within the theoretical convergence bounds, and provide additional insight into the strengths and weaknesses of the design methodology adopted and of the concrete adaptation rules obtained.

This talk is part of the Optimisation and Numerical Analysis Seminars series.

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• Optimisation and Numerical Analysis Seminars
• Sandbox (Watson)
• School of Mathematics Events

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