OKRidge: Scalable Optimal k-Sparse Ridge Regression

TL;DR

OKRidge introduces a fast, provably optimal algorithm for sparse ridge regression, significantly improving efficiency in identifying governing equations in nonlinear dynamical systems.

Contribution

The paper presents a novel algorithm for sparse ridge regression that combines saddle point formulation, linear systems, and ADMM, enabling scalable and provably optimal solutions.

Findings

Achieves provable optimality with much faster run times than existing methods.

Uses a novel lower bound calculation involving saddle point formulation.

Employs a warm-start strategy with beam search for efficiency.

Abstract

We consider an important problem in scientific discovery, namely identifying sparse governing equations for nonlinear dynamical systems. This involves solving sparse ridge regression problems to provable optimality in order to determine which terms drive the underlying dynamics. We propose a fast algorithm, OKRidge, for sparse ridge regression, using a novel lower bound calculation involving, first, a saddle point formulation, and from there, either solving (i) a linear system or (ii) using an ADMM-based approach, where the proximal operators can be efficiently evaluated by solving another linear system and an isotonic regression problem. We also propose a method to warm-start our solver, which leverages a beam search. Experimentally, our methods attain provable optimality with run times that are orders of magnitude faster than those of the existing MIP formulations solved by the commercial solver Gurobi.