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In the post-Moore era, main performance gains of black-box optimizers areincreasingly depending on parallelism, especially for large-scale optimization(LSO). Here we propose to parallelize the well-established covariance matrixadaptation evolution strategy (CMA-ES) and in particular its one latest LSOvariant called limited-memory CMA-ES (LM-CMA). To achieve efficiency whileapproximating its powerful invariance property, we present a multilevellearning-based meta-framework for distributed LM-CMA. Owing to itshierarchically organized structure, Meta-ES is well-suited to implement ourdistributed meta-framework, wherein the outer-ES controls strategy parameterswhile all parallel inner-ESs run the serial LM-CMA with different settings. Forthe distribution mean update of the outer-ES, both the elitist andmulti-recombination strategy are used in parallel to avoid stagnation andregression, respectively. To exploit spatiotemporal information, the globalstep-size adaptation combines Meta-ES with the parallel cumulative step-sizeadaptation. After each isolation time, our meta-framework employs both thestructure and parameter learning strategy to combine aligned evolution pathsfor CMA reconstruction. Experiments on a set of large-scale benchmarkingfunctions with memory-intensive evaluations, arguably reflecting manydata-driven optimization problems, validate the benefits (e.g., effectivenessw.r.t. solution quality, and adaptability w.r.t. second-order learning) andcosts of our meta-framework.

Distributed Evolution Strategies with Multi-Level Learning for Large-Scale Black-Box Optimization