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Learning to optimize (L2O) has gained increasing popularity, which automates the design of optimizers by data-driven approaches. However, current L2O methods often suffer from poor generalization performance in at least two folds: (i) applying the L2O-learned optimizer to unseen optimizees, in terms of lowering their loss function values (optimizer generalization, or “generalizable learning of optimizers”); and (ii) the test performance of an optimizee (itself as a machine learning model), trained by the optimizer, in terms of the accuracy over unseen data (optimizee generalization, or “learning to generalize”). While the optimizer generalization has been recently studied, the optimizee generalization (or learning to generalize) has not been rigorously studied in the L2O context, which is the aim of this paper. We first theoretically establish an implicit connection between the local entropy and the Hessian, and hence unify their roles in the handcrafted design of generalizable optimizers as equivalent metrics of the landscape flatness of loss functions. We then propose to incorporate these two metrics as flatness-aware regularizers into the L2O framework in order to meta-train optimizers to learn to generalize, and theoretically show that such generalization ability can be learned during the L2O meta-training process and then transformed to the optimizee loss function. Extensive experiments consistently validate the effectiveness of our proposals with substantially improved generalization on multiple sophisticated L2O models and diverse optimizees. 

Abstract Motivation There is growing interest in the biomedical research community to incorporate retrospective data, available in healthcare systems, to shed light on associations between different biomarkers. Understanding the association between various types of biomedical data, such as genetic, blood biomarkers, imaging, etc. can provide a holistic understanding of human diseases. To formally test a hypothesized association between two types of data in Electronic Health Records (EHRs), one requires a substantial sample size with both data modalities to achieve a reasonable power. Current association test methods only allow using data from individuals who have both data modalities. Hence, researchers cannot take advantage of much larger EHR samples that includes individuals with at least one of the data types, which limits the power of the association test. Results We present a new method called the Semi-paired Association Test (SAT) that makes use of both paired and unpaired data. In contrast to classical approaches, incorporating unpaired data allows SAT to produce better control of false discovery and to improve the power of the association test. We study the properties of the new test theoretically and empirically, through a series of simulations and by applying our method on real studies in the context of Chronic Obstructive Pulmonary Disease. We are able to identify an association between the high-dimensional characterization of Computed Tomography chest images and several blood biomarkers as well as the expression of dozens of genes involved in the immune system. Availability and implementation Code is available on https://github.com/batmanlab/Semi-paired-Association-Test. Supplementary information Supplementary data are available at Bioinformatics online.