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Data dependent regularization is known to benefit a wide variety of problemsin machine learning. Often, these regularizers cannot be easily decomposed intoa sum over a finite number of terms, e.g., a sum over individual example-wiseterms. The $F_\beta$ measure, Area under the ROC curve (AUCROC) and Precisionat a fixed recall (P@R) are some prominent examples that are used in manyapplications. We find that for most medium to large sized datasets, scalabilityissues severely limit our ability in leveraging the benefits of suchregularizers. Importantly, the key technical impediment despite some recentprogress is that, such objectives remain difficult to optimize viabackpropapagation procedures. While an efficient general-purpose strategy forthis problem still remains elusive, in this paper, we show that for manydata-dependent nondecomposable regularizers that are relevant in applications,sizable gains in efficiency are possible with minimal code-level changes; inother words, no specialized tools or numerical schemes are needed. Ourprocedure involves a reparameterization followed by a partial dualization --this leads to a formulation that has provably cheap projection operators. Wepresent a detailed analysis of runtime and convergence properties of ouralgorithm. On the experimental side, we show that a direct use of our schemesignificantly improves the state of the art IOU measures reported for MSCOCOStuff segmentation dataset.

Optimizing Nondecomposable Data Dependent Regularizers via Lagrangian Reparameterization offers Significant Performance and Efficiency Gains