GIFT-Evo: Feedback Adaptation through Geometric-Inductive Operators for Low-Budget Black-Box Optimization

Learned evolutionary optimizers encode cross-task strategies into fixed parameters via offline training, allowing direct search on new problems without per-task tuning for low-budget black-box optimization. However, existing methods do not retain real-time search feedback, preventing the policy from exploiting past outcomes to guide later decisions and accelerate convergence. Online parameter updates adapt to the target but require extensive samples, conflicting with low budgets. To this end, we propose GIFT-Evo, which introduces a lightweight search knowledge channel that accumulates individual acceptance and improvement history. This state modulates offspring generation to better suit the current problem, thereby accelerating convergence, while keeping parameters fixed. Since search knowledge must be translated through the model, and absolute-coordinate-based models fail under scale changes, we further design a geometric-inductive operator framework based on relative population geometry to ensure consistent semantics across problem scales. Experiments on multiple baselines show that GIFT-Evo achieves significant advantages in both low-budget and cross-scale deployment scenarios.