  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 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.
