Why and When Neural Networks Improve Local Approximation in Optimization

The paper investigates why neural network surrogates sometimes improve and sometimes worsen derivative‑free optimisation performance. It identifies three key factors—role (whether the surrogate proposes candidates or replaces gradients), radius (the neighbourhood within which a local model is reliable), and room (whether the base method can still progress)—that determine when a learned local model is beneficial. Experiments on 117 benchmark instances show that providing surrogate‑approved candidates boosts success rates, while replacing gradients or ignoring the radius can reduce them.

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