用符号回归生成可解释的凸模型，避免复杂验证
DiscoverDCP: A Data-Driven Approach for Construction of Disciplined Convex Programs via Symbolic Regression
- 结合符号回归与凸规划规则，自动发现满足凸性约束的模型
- 生成的凸代理模型比传统二次函数更灵活准确
- 适合安全关键的控制与优化场景，结果可解释可验证
我们提出DiscoverDCP，一种数据驱动框架，将符号回归与规则化的凸规划（Disciplined Convex Programming, DCP）结合，用于系统识别。通过强制所有候选模型表达式遵循DCP组合规则，确保输出表达式在构造上全局凸，从而规避耗时的后验凸性验证。该方法可发现具有更宽松、更精确函数形式的凸代理模型，优于传统固定参数凸表达式（如二次函数）。所提方法生成的模型具备可解释性、可验证性和灵活性，适用于安全关键的控制与优化任务。
原文摘要 · Abstract (English)
We propose DiscoverDCP, a data-driven framework that integrates symbolic regression with the rule sets of Disciplined Convex Programming (DCP) to perform system identification. By enforcing that all discovered candidate model expressions adhere to DCP composition rules, we ensure that the output expressions are globally convex by construction, circumventing the computationally intractable process of post-hoc convexity verification. This approach allows for the discovery of convex surrogates that exhibit more relaxed and accurate functional forms than traditional fixed-parameter convex expressions (e.g., quadratic functions). The proposed method produces interpretable, verifiable, and flexible convex models suitable for safety-critical control and optimization tasks.
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