Optimal quantization: Evolutionary algorithms vs stochastic gradient

Abstract

We propose a new method based on evolutionary optimization for obtaining an optimal Lp-quantizer of a multidimensional random variable. First, we remind briefly the main results about quantization. Then, we present the classical gradient-based approach (this approach is well detailed in [2] and [7] for p=2) used up to now to find a "local" optimal L p-quantizer. Then, we give an algorithm that permits to deal with the problem in the evolutionary optimization framework and illustrate a numerical comparison between the proposed method and the stochastic gradient method. Finally, a numerical application to option pricing in finance is provided.