Abstract
Design of experiments, random search, initialization of population-based methods, or sampling inside an epoch of an evolutionary algorithm uses a sample drawn according to some probability distribution for approximating the location of an optimum. Recent papers have shown that the optimal search distribution, used for the sampling, might be more peaked around the center of the distribution than the prior distribution modelling our uncertainty about the location of the optimum.We confirm this statement, provide explicit values for this reshaping of the search distribution depending on the population size \(\lambda \) and the dimension d, and validate our results experimentally.
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Notes
- 1.
Arxiv version [20] of the present document includes bigger plots and the appendices.
- 2.
This requires knowledge of \(\inf _{x} f(x)\), which may not be available in real-world applications. In this case, without loss of generality (this is just for the sake of plotting regret values), the infimum can be replaced by an empirical minimum. In all applications considered in this work the value of \(\inf _x f(x)\) is known.
- 3.
Detailed results for individual settings are available at http://dl.fbaipublicfiles.com/nevergrad/allxps/list.html.
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Acknowledgements
This work was initiated at Dagstuhl seminar 19431 on Theory of Randomized Optimization Heuristics.
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Meunier, L., Doerr, C., Rapin, J., Teytaud, O. (2020). Variance Reduction for Better Sampling in Continuous Domains. In: Bäck, T., et al. Parallel Problem Solving from Nature – PPSN XVI. PPSN 2020. Lecture Notes in Computer Science(), vol 12269. Springer, Cham. https://doi.org/10.1007/978-3-030-58112-1_11
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