  A popular line of recent research incorporates ML advice in the design of
online algorithms to improve their performance in typical instances. These
papers treat the ML algorithm as a black-box, and redesign online algorithms to
take advantage of ML predictions. In this paper, we ask the complementary
question: can we redesign ML algorithms to provide better predictions for
online algorithms? We explore this question in the context of the classic
rent-or-buy problem, and show that incorporating optimization benchmarks in ML
loss functions leads to significantly better performance, while maintaining a
worst-case adversarial result when the advice is completely wrong. We support
this finding both through theoretical bounds and numerical simulations.
