Zero-Inflated Gaussian Distributions Enable Parameter-Space Sparsity in Estimation-of-Distribution Algorithms
Proposes multivariate zero-inflated Gaussian (ZIG) distributions as sampling laws for EDAs, enabling joint optimization of sparsity patterns and active values without hand-crafted operators. The latent parameters are identifiable, and practical amortized inversion estimators are provided. On the Lunar Lander benchmark, ZIG-EDA outperforms dense Gaussian EDA, hand-crafted sparse EA, and ad-hoc sparse EDA in convergence speed and final returns while using few active parameters.
[2606.19369] Zero-Inflated Gaussian Distributions Enable Parameter-Space Sparsity in Estimation-of-Distribution Algorithms
[Submitted on 11 Jun 2026]
Title:Zero-Inflated Gaussian Distributions Enable Parameter-Space Sparsity in Estimation-of-Distribution Algorithms
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Abstract:Estimation-of-distribution algorithms (EDAs) are a powerful class of evolutionary methods for black-box optimization, especially when little is known about the structure of the objective. Whereas classical evolutionary algorithms rely on hand-designed mutation and crossover operators, hard to devise for unknown problem structures, and a source of bias, EDAs sidestep operator design entirely: they fit a probability distribution to the best individuals and sample the next generation from it. EDAs are well established on continuous parameter spaces, but they have not previously been generalized to sparse ones, in which most coefficients of a good solution are exactly zero. Existing sparse black-box optimizers therefore reintroduce exactly what EDAs were designed to avoid: hand-crafted sparsity operators, bi-level schemes alternating between support set and active values, zeroing thresholds, and other baked-in assumptions. We close this gap by proposing multivariate zero-inflated Gaussian (ZIG) distributions as EDA sampling laws. A latent Gaussian model with separate indicator and value dimensions represents sparsity patterns, correlations among active parameters, and the interactions between the two, so sparsity patterns and active values are optimized jointly, hierarchy-free. We show that the latent parameters of this model are identifiable from observed samples, unlike in the missing-data settings where related constructions originate, and introduce practical amortized inversion-based estimators for them. The estimators accurately recover latent correlation structures, and on the Lunar Lander benchmark the resulting ZIG-EDA converges faster and reaches higher final returns than a dense Gaussian EDA, a hand-crafted sparse evolutionary algorithm, and an ad-hoc sparse EDA, while finding controllers with only a small fraction of parameters active.
Subjects:
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as: arXiv:2606.19369 [cs.LG]
(or arXiv:2606.19369v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.19369
arXiv-issued DOI via DataCite
Submission history
From: Sven Nitzsche [view email] [v1] Thu, 11 Jun 2026 18:43:18 UTC (1,841 KB)
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