  Many high-stake decisions follow an expert-in-loop structure in that a human
operator receives recommendations from an algorithm but is the ultimate
decision maker. Hence, the algorithm's recommendation may differ from the
actual decision implemented in practice. However, most algorithmic
recommendations are obtained by solving an optimization problem that assumes
recommendations will be perfectly implemented. We propose an adherence-aware
optimization framework to capture the dichotomy between the recommended and the
implemented policy and analyze the impact of partial adherence on the optimal
recommendation. We show that overlooking the partial adherence phenomenon, as
is currently being done by most recommendation engines, can lead to arbitrarily
severe performance deterioration, compared with both the current human baseline
performance and what is expected by the recommendation algorithm. Our framework
also provides useful tools to analyze the structure and to compute optimal
recommendation policies that are naturally immune against such human
deviations, and are guaranteed to improve upon the baseline policy.
