Decision-Focused Learning with Directional Gradients

• URL: http://arxiv.org/abs/2402.03256v4
• Date: Wed, 30 Oct 2024 22:01:13 GMT
• Title: Decision-Focused Learning with Directional Gradients
• Abstract summary: We propose a novel family of decision-aware surrogate losses, called Perturbation Gradient (PG) losses, for the predict-then-optimize framework. Unlike the original decision loss which is typically piecewise constant and discontinuous, our new PG losses is a Lipschitz continuous, difference of concave functions. We provide numerical evidence confirming our PG losses substantively outperform existing proposals when the underlying model is misspecified.
• Score: 1.2363103948638432
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a novel family of decision-aware surrogate losses, called Perturbation Gradient (PG) losses, for the predict-then-optimize framework. The key idea is to connect the expected downstream decision loss with the directional derivative of a particular plug-in objective, and then approximate this derivative using zeroth order gradient techniques. Unlike the original decision loss which is typically piecewise constant and discontinuous, our new PG losses is a Lipschitz continuous, difference of concave functions that can be optimized using off-the-shelf gradient-based methods. Most importantly, unlike existing surrogate losses, the approximation error of our PG losses vanishes as the number of samples grows. Hence, optimizing our surrogate loss yields a best-in-class policy asymptotically, even in misspecified settings. This is the first such result in misspecified settings, and we provide numerical evidence confirming our PG losses substantively outperform existing proposals when the underlying model is misspecified.

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