用分数匹配生成梯度，统一求解带复杂约束的全局优化问题
Global Optimization By Gradient From Hierarchical Score-Matching Spaces
- 将各类约束优化问题转化为无约束的分层目标函数
- 通过分数匹配获取梯度，在复杂场景中有效避开局部最优
- 揭示了全局优化与扩散生成模型之间的深层联系
基于梯度的方法广泛用于求解各类优化问题，但常受限于局部最优、简单凸约束和连续可微要求，或仅适用于低维简单问题。本文通过将具有各种复杂约束的优化问题统一为一个无约束的通用分层优化目标，并利用分数匹配获得梯度进行优化，突破了上述限制。方法在构造简单的和实际复杂的实验中均得到验证。更重要的是，该工作揭示了全局优化与基于扩散的生成建模之间深刻的内在联系。
原文摘要 · Abstract (English)
Gradient-based methods are widely used to solve various optimization problems, however, they are either constrained by local optima dilemmas, simple convex constraints, and continuous differentiability requirements, or limited to low-dimensional simple problems. This work solve these limitations and restrictions by unifying all optimization problems with various complex constraints as a general hierarchical optimization objective without constraints, which is optimized by gradient obtained through score matching. The proposed method is verified through simple-constructed and complex-practical experiments. Even more importantly, it reveals the profound connection between global optimization and diffusion based generative modeling.
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