神经网络代理能否提升优化效率，取决于三因素：是否辅助而非替代梯度、是否在合理范围使用、是否匹配基础方法能力。
Why and When Neural Networks Improve Local Approximation in Optimization
- 通过三个关键因素判断代理模型是否有效：辅助角色、有限适用半径、与基础方法的适配空间。
- 在117个基准测试中，合理使用可使高精度求解实例从67升至84，而错误使用则降至65。
- 适合关注优化加速的工程师和研究者，尤其关注代理模型与算法协同设计的场景。
在无导数优化中，神经代理模型的表现矛盾：同一类模型可能显著减少某求解器的评估次数，却对另一求解器无效甚至恶化。我们揭示，这一矛盾源于三个核心因素：代理模型应作为候选建议者而非梯度替代者；其有效性仅限于有界邻域内；且仅当基础方法本身仍能推进时才有加速价值。我们形式化了半径感知的局部泛化，关联经典完全线性条件，并固定代理类别、训练流程和基础方法进行验证。117个基准实例显示，合理使用使高精度求解实例从67增至84，而梯度替换则降至65；移除训练损失中的梯度项使代理接受率从0.703降至0.148；1000组对比在十种噪声水平下表明，无噪声阈值，只有早期停止的基础方法。同样，模型信任域求解器因可用空间小，性能从88微降至86；释放插值软件保持领先，达103；蒙特卡洛库存模型中修复接受接口带来10.40成本收益，而代理为0.00。
原文摘要 · Abstract (English)
Published experience with neural surrogates in derivative-free optimisation is contradictory: the same family of models that cuts the evaluation count of one solver leaves another unchanged, or makes it worse. We show that the contradiction dissolves once three factors are stated, and that these, rather than the fit accuracy a training curve reports, are what delimit when a learned local model pays. Role: a surrogate that proposes candidates the true objective must still approve helps, while one that replaces a gradient the solver depends on hurts. Radius: a model fitted to an optimisation path is reliable only inside a bounded neighbourhood, and its error neither vanishes as that neighbourhood shrinks nor survives its growth. Room: a surrogate can only accelerate progress the base method is still able to make. We formalise radius-aware local generalisation, relate it to the classical fully linear condition, and test each factor with the surrogate class, training pipeline and base method held fixed. Over 117 benchmark instances safeguarded assistance raises the instances solved to high accuracy from 67 to 84 while gradient replacement lowers them to 65; removing the gradient term from the training loss cuts surrogate acceptance from 0.703 to 0.148; and 1000 paired comparisons over ten noise levels show no noise threshold, only a base method that stops early. The same factors bound the gain: a model-based trust-region solver, which leaves little room, drops from 88 to 86 when the identical surrogate is attached, and released interpolation software stays ahead at 103, and on a Monte-Carlo inventory model repairing the acceptance interface is worth 10.40 cost units against 0.00 for the surrogate.
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