Learning to Evolve for Optimization via Stability-Inducing Neural Unrolling

TL;DR

This paper introduces Learning to Evolve (L2E), a neural unrolling framework that learns stable evolutionary algorithms, improving adaptability and robustness in optimization tasks across various landscapes.

Contribution

L2E reformulates evolution as a neural fixed-point iteration with stability bias and combines learned proposals with numerical guidance for enhanced optimization.

Findings

Achieves high optimization performance on benchmarks

Scales effectively to high-dimensional problems

Demonstrates robust zero-shot transfer across tasks

Abstract

Evolutionary algorithms serve as a powerful paradigm for tackling optimization challenges, yet their reliance on manually engineered heuristics inherently limits their adaptability across diverse landscapes. However, the transition from the hand-crafted heuristics to data-driven algorithms faces a fundamental dilemma: achieving neural \emph{plasticity} without sacrificing algorithmic stability. Although learned optimizers offer high adaptivity, their unconstrained update rules often result in unstable dynamics and brittle generalization on unseen landscapes. To address this challenge, this paper proposes Learning to Evolve (L2E), a bilevel meta-optimization framework that learns evolutionary search via stability-inducing neural unrolling. First, L2E reformulates population evolution as an unrolled fixed-point iteration via a structured neural operator. In this design, the inner loop imposes a stability-biased update structure, while the outer loop meta-trains the operator to produce effective search trajectories across tasks. Second, to balance global exploration with local refinement, a gradient-derived composite solver adaptively fuses learned evolutionary proposals with proxy numerical guidance in a differentiable manner. Extensive experiments on synthetic benchmarks and real-world control tasks demonstrate that L2E achieves substantial optimization performance, scales to high-dimensional problems, and exhibits robust zero-shot transfer across diverse test distributions.