Learning Best-in-Class Policies for the Predict-then-Optimize Framework
CoRR(2024)
摘要
We propose a novel family of decision-aware surrogate losses, called
Perturbation Gradient (PG) losses, for the predict-then-optimize framework.
These losses directly approximate the downstream decision loss and can be
optimized using off-the-shelf gradient-based methods. Importantly, unlike
existing surrogate losses, the approximation error of our PG losses vanishes as
the number of samples grows. This implies that 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 and the noise is not centrally
symmetric. Insofar as misspecification is commonplace in practice – especially
when we might prefer a simpler, more interpretable model – PG losses offer a
novel, theoretically justified, method for computationally tractable
decision-aware learning.
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