Relax and penalize: a new bilevel approach to mixed-binary hyperparameter optimization

• URL: http://arxiv.org/abs/2308.10711v1
• Date: Mon, 21 Aug 2023 13:24:52 GMT
• Title: Relax and penalize: a new bilevel approach to mixed-binary hyperparameter optimization
• Authors: Marianna de Santis (UNIROMA), Jordan Frecon (LHC), Francesco Rinaldi (Unipd), Saverio Salzo (DIAG UNIROMA), Martin Schmidt
• Abstract summary: We tackle the challenging optimization of mixed-binary hyper parameters. We propose an algorithmic framework that is guaranteed to provide mixed-binary solutions. We evaluate the performance of our approach for a specific machine learning problem.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In recent years, bilevel approaches have become very popular to efficiently estimate high-dimensional hyperparameters of machine learning models. However, to date, binary parameters are handled by continuous relaxation and rounding strategies, which could lead to inconsistent solutions. In this context, we tackle the challenging optimization of mixed-binary hyperparameters by resorting to an equivalent continuous bilevel reformulation based on an appropriate penalty term. We propose an algorithmic framework that, under suitable assumptions, is guaranteed to provide mixed-binary solutions. Moreover, the generality of the method allows to safely use existing continuous bilevel solvers within the proposed framework. We evaluate the performance of our approach for a specific machine learning problem, i.e., the estimation of the group-sparsity structure in regression problems. Reported results clearly show that our method outperforms state-of-the-art approaches based on relaxation and rounding

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