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

TL;DR

This paper introduces a distributed multi-level learning framework for large-scale black-box optimization, enhancing the parallel efficiency of CMA-ES variants through hierarchical meta-learning and adaptive strategies.

Contribution

It proposes a novel distributed meta-framework for LM-CMA that combines hierarchical learning, strategy control, and adaptive updates to improve large-scale black-box optimization.

Findings

Improved solution quality on large-scale benchmark functions.

Enhanced adaptability through multi-recombination and step-size strategies.

Validated effectiveness and efficiency of the framework in memory-intensive scenarios.

Abstract

In the post-Moore era, main performance gains of black-box optimizers are increasingly depending on parallelism, especially for large-scale optimization (LSO). Here we propose to parallelize the well-established covariance matrix adaptation evolution strategy (CMA-ES) and in particular its one latest LSO variant called limited-memory CMA-ES (LM-CMA). To achieve efficiency while approximating its powerful invariance property, we present a multilevel learning-based meta-framework for distributed LM-CMA. Owing to its hierarchically organized structure, Meta-ES is well-suited to implement our distributed meta-framework, wherein the outer-ES controls strategy parameters while all parallel inner-ESs run the serial LM-CMA with different settings. For the distribution mean update of the outer-ES, both the elitist and multi-recombination strategy are used in parallel to avoid stagnation and regression, respectively. To exploit spatiotemporal information, the global step-size adaptation combines Meta-ES with the parallel cumulative step-size adaptation. After each isolation time, our meta-framework employs both the structure and parameter learning strategy to combine aligned evolution paths for CMA reconstruction. Experiments on a set of large-scale benchmarking functions with memory-intensive evaluations, arguably reflecting many data-driven optimization problems, validate the benefits (e.g., effectiveness w.r.t. solution quality, and adaptability w.r.t. second-order learning) and costs of our meta-framework.