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. Our framework 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. This paper was accepted by Nicolas Stier-Moses, Special Issue on the Human-Algorithm Connection. Funding: J. Grand-Clément was supported by the Agence Nationale de la Recherche [Grant 11-LABX-0047] and Hi! Paris. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2023.01851 .

Novel Insights on Robust Markov decision Processes with Average Reward and Blackwell Optimality Criteria Robust Markov decision processes (RMDPs) have been studied extensively when the objective is the discounted return, but little is known for average optimality and Blackwell optimality. We show that average optimal policies can be chosen stationary and deterministic for sa-rectangular RMDPs, but perhaps surprisingly, we show that for s-rectangular RMDPs average optimal policies may not exist, and if they do exist, they may not be stationary. We also study Blackwell optimality for sa-rectangular RMDPs, where we show that approximately Blackwell optimal policies always exist, although exact Blackwell optimal policies may not exist. We provide a general sufficient condition for their existence. We then discuss the connection between average and Blackwell optimality, and we describe several algorithms to compute the optimal average return. Interestingly, our approach leverages the connections between RMDPs and stochastic games. Overall, our paper emphasizes the superior practical properties of distance-based sa-rectangular models over s-rectangular models for average and Blackwell optimality.