Optimizing Black-box Metrics with Adaptive Surrogates
This addresses a practical challenge for machine learning practitioners dealing with non-differentiable or opaque evaluation metrics, though it appears incremental as it builds on surrogate-based optimization methods.
The paper tackles the problem of training models with black-box and hard-to-optimize metrics by expressing the metric as a monotonic function of easy-to-optimize surrogates, achieving performance on par with methods that know the mathematical formulation and adding notable value when the metric form is unknown.
We address the problem of training models with black-box and hard-to-optimize metrics by expressing the metric as a monotonic function of a small number of easy-to-optimize surrogates. We pose the training problem as an optimization over a relaxed surrogate space, which we solve by estimating local gradients for the metric and performing inexact convex projections. We analyze gradient estimates based on finite differences and local linear interpolations, and show convergence of our approach under smoothness assumptions with respect to the surrogates. Experimental results on classification and ranking problems verify the proposal performs on par with methods that know the mathematical formulation, and adds notable value when the form of the metric is unknown.