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DiscoverDCP: A Data-Driven Approach for Construction of Disciplined Convex Programs via Symbolic Regression

Sveinung Myhre

TL;DR

DiscoverDCP combines symbolic regression with Disciplined Convex Programming to learn convex, interpretable surrogates directly from data. By restricting the search space to DCP-compliant operations, it guarantees convexity by construction and eliminates the need for post-hoc checks. The method demonstrates improved flexibility over fixed quadratic baselines in synthetic settings and offers a transparent alternative for safety-critical optimization tasks. Its data-driven, convex-by-design approach enables verifiable models suitable for control and optimization applications.

Abstract

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.

DiscoverDCP: A Data-Driven Approach for Construction of Disciplined Convex Programs via Symbolic Regression

TL;DR

DiscoverDCP combines symbolic regression with Disciplined Convex Programming to learn convex, interpretable surrogates directly from data. By restricting the search space to DCP-compliant operations, it guarantees convexity by construction and eliminates the need for post-hoc checks. The method demonstrates improved flexibility over fixed quadratic baselines in synthetic settings and offers a transparent alternative for safety-critical optimization tasks. Its data-driven, convex-by-design approach enables verifiable models suitable for control and optimization applications.

Abstract

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.

Paper Structure

This paper contains 11 sections, 2 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Our Contributions.
  3. Related Work
  4. Method
  5. 1. Convexity-Preserving Operations.
  6. 2. Constrained Evolutionary Search.
  7. 2. Constrained Evolutionary Search.
  8. Experiments
  9. Discussion
  10. Conclusion
  11. Code Availability

Figures (2)

  • Figure 1: Comparison of model fits on 1D synthetic data. Red: Ground truth ($y = \exp(x + \max(x, -5x) + x^{2}) + 4x$). Yellow: PSD Quadratic fit ($y \approx 61.6 x^2 - 20.4x - 4.9$). Blue:DiscoverDCP low-complexity approximation. Purple:DiscoverDCP high-complexity approximation.
  • Figure 2: Functional forms of the discovered models. Left: A parsimonious approximation found by DiscoverDCP ($y=e^{3.2x} + e^{-4.9x}$). Right: A higher complexity model that accurately captures the nested non-linearities of the ground truth.