D. A. Herrera-Martí

D. A. Herrera-Martí, E. Guthmuller, J. Fereyre

The combinatorial problem Max-Cut has become a benchmark in the evaluation of local search heuristics for both quantum and classical optimisers. In contrast to local search, which only provides average-case performance guarantees, the convex semidefinite relaxation of Max-Cut by Goemans and Williamson, provides worst-case guarantees and is therefore suited to both the construction of benchmarks and in applications to performance-critic scenarios. We show how extended floating point precision can be incorporated in algebraic subroutines in convex optimisation, namely in indirect matrix inversion methods like Conjugate Gradient, which are used in Interior Point Methods in the case of very large problem sizes. Also, an estimate is provided of the expected acceleration of the time to solution for a hardware architecture that runs natively on extended precision. Specifically, when using indirect matrix inversion methods like Conjugate Gradient, which have lower complexity than direct methods and are therefore used in very large problems, we see that increasing the internal working precision reduces the time to solution by a factor that increases with the system size.

A. Yermekov, D. A. Herrera-Martí

Feature selection in high-dimensional genomic data ($d \gg n$) demands methods that are simultaneously accurate, sparse, and stable. Existing approaches either require manual threshold specification (mRMR, stability selection), produce unstable selections under data perturbation (Lasso, Boruta), or ignore biological structure entirely. We introduce StackFeat-RL, a meta-learning framework that optimises the hyperparameters of an iterative dual-criterion feature selection algorithm via REINFORCE policy gradients. The dual criterion, requiring both coefficient consistency and selection frequency, guards against two failure modes missed by single-criterion methods, while iterative accumulation provides convergence guarantees via the law of large numbers. On COVID-19 miRNA data (GSE240888, 332 features) and three Alzheimer's disease classification tasks (GSE84422, 13237 genes; Normal vs.\ Possible, Probable, and Definite AD), StackFeat-RL achieves the highest predictive accuracy among all evaluated methods, including ElasticNet, Boruta, mRMR, and stability selection, while requiring 3--4$\times$ fewer features. Keywords: feature selection, reinforcement learning, REINFORCE, elastic net, biomarker discovery, Alzheimer's disease, dual-criterion selection, protein interaction networks