329. Bilevel hyperpaGlobal relaxation-based LP-Newton method for multiple hyperparameter selection in support vector classification
Invited abstract in session MB-7: Hyperparameter Optimization for Classification, stream Bilevel and multilevel optimization.
Monday, 10:30-12:30Room: B100/5015
Authors (first author is the speaker)
| 1. | Yaru Qian
|
| Electronics and computer science, University of Southampton |
Abstract
Support vector classification (SVC) is an effective tool for classification tasks in machine learning. Its performance relies on the selection of appropriate hyperparameters. This paper focuses on optimizing the regularization hyperparameter $C$ and determining feature bounds for feature selection within SVC, leading to a potentially large hyperparameter space. It is very well-known in machine learning that this could lead to the so-called {\em curse of dimensionality}. To address this challenge of multiple hyperparameter selection, the problem is formulated as a bilevel optimization problem, which is then transformed into a mathematical program with equilibrium constraints (MPEC). Our primary contributions are two-fold. First, we establish the satisfaction of the MPEC-MFCQ for our problem reformulation. Furthermore, we introduce a novel global relaxation based linear programming (LP)-Mewton method (GRLPN) for solving this problem and provide corresponding convergence results. Typically, in global relaxation methods for MPECs, the algorithm for the corresponding subproblem is treated as a blackbox. Possibly for the first time in the literature, the subproblem is specifically studied in detail. Numerical experiments demonstrate GRLPN’s superiority in efficiency and accuracy over both grid search and traditional global relaxation methods solved using the well-known nonlinear programming solver, SNOPT.
Keywords
- Non-smooth optimization
- Multi-level optimization
- Applications of continuous optimization
Status: accepted
Back to the list of papers