Marie-Liesse Cauwet

Marie-Liesse Cauwet, Olivier Teytaud

We study a test-based population size adaptation (TBPSA) method, inspired from population control, in the noise-free multimodal case. In the noisy setting, TBPSA usually recommends, at the end of the run, the center of the Gaussian as an approximation of the optimum. We show that combined with a more naive recommendation, namely recommending the visited point which had the best fitness value so far, TBPSA is also powerful in the noise-free multimodal context. We demonstrate this experimentally and explore this mechanism theoretically: we prove that TBPSA is able to escape plateaus with probability one in spite of the fact that it can converge to local minima. This leads to an algorithm effective in the multimodal setting without resorting to a random restart from scratch.

Marie-Liesse Cauwet

It is known that evolution strategies in continuous domains might not converge in the presence of noise. It is also known that, under mild assumptions, and using an increasing number of resamplings, one can mitigate the effect of additive noise and recover convergence. We show new sufficient conditions for the convergence of an evolutionary algorithm with constant number of resamplings; in particular, we get fast rates (log-linear convergence) provided that the variance decreases around the optimum slightly faster than in the so-called multiplicative noise model. Keywords: Noisy optimization, evolutionary algorithm, theory.