The Best Decisions Are Not the Best Advice: Making Adherence-Aware Recommendations

TL;DR

This work introduces an adherence-aware decision framework for expert-in-the-loop systems, modeling the gap between algorithmic recommendations and implemented actions via an adherence parameter $\theta$ and the effective policy $\pi_{\rm eff}(\pi_{\sf alg},\theta)$. It proves that optimal recommendations can be computed as stationary deterministic policies by reducing to a surrogate MDP, and it provides both value-iteration and linear-programming methods for solving the adherence-aware problem. The authors also characterize structural properties, such as monotonicity and piecewise-constant dependence on $\theta$, and establish equivalences with random and adversarial adherence models, including robustness to uncertain baseline policies. Numerical experiments in machine replacement and healthcare illustrate potential severe deterioration if adherence is ignored and demonstrate the practical value of adherence-robust recommendations, as well as extensions to heterogeneous, uncertain, and time-varying adherence. Overall, the paper offers a rigorous, computation-friendly framework for designing recommendations that remain effective when human deviations from machine suggestions occur, with clear implications for deployment in high-stakes settings.

Abstract

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.

Figures (9)

• Figure 1: Details on the transitions and rewards of our MDP instance.
• Figure 2: Illustrating the impact of the partial adherence phenomenon (hence the coexistence of a baseline and algorithmic policy) in the MDP instance from Figure \ref{['fig:mdp-instance.tot']}. We choose $\lambda=0.5$ in our simulations.
• Figure 3: Transition probabilities for the machine replacement MDP. There is a reward of $18$ in state $R1$, of $10$ in state $R2$ and of $0$ in state $8$. All others states have a reward of $20$.
• Figure 4: Numerical results for the machine replacement MDP with $\pi_{\sf base}$ always choosing action wait.
• Figure 5: Numerical results for the machine replacement MDP with $\pi_{\sf base}$ repairing in the absorbing states $8,R_{1}$ and waiting in the other states.

Theorems & Definitions (26)

• Remark 3.1: Finite-horizon setting
• Proposition 3.1
• Remark 3.2
• Theorem 3.1
• Theorem 3.2
• Remark 3.3
• Theorem 3.3
• Remark 3.4
• Proposition 4.1
• Corollary 4.1