Zeyang Jia

Zeyang Jia, Eli Ben-Michael, Kosuke Imai

Algorithmic decisions and recommendations are used in many high-stakes decision-making settings such as criminal justice, medicine, and public policy. We investigate whether it would have been possible to improve a security assessment algorithm employed during the Vietnam War, using outcomes measured immediately after its introduction in late 1969. This empirical application raises several methodological challenges that frequently arise in high-stakes algorithmic decision-making. First, before implementing a new algorithm, it is essential to characterize and control the risk of yielding worse outcomes than the existing algorithm. Second, the existing algorithm is deterministic, and learning a new algorithm requires transparent extrapolation. Third, the existing algorithm involves discrete decision tables that are difficult to optimize over. To address these challenges, we introduce the Average Conditional Risk (ACRisk), which first quantifies the risk that a new algorithmic policy leads to worse outcomes for subgroups of individual units and then averages this over the distribution of subgroups. We also propose a Bayesian policy learning framework that maximizes the posterior expected value while controlling the posterior expected ACRisk. This framework separates the estimation of heterogeneous treatment effects from policy optimization, enabling flexible estimation of effects and optimization over complex policy classes. We characterize the resulting chance-constrained optimization problem as a constrained linear programming problem. Our analysis shows that compared to the actual algorithm used during the Vietnam War, the learned algorithm assesses most regions as more secure and emphasizes economic and political factors over military factors.

Zeyang Jia, Kosuke Imai, Michael Lingzhi Li

We introduce the cram method as a general statistical framework for evaluating the final learned policy from a multi-armed contextual bandit algorithm, using the dataset generated by the same bandit algorithm. The proposed on-policy evaluation methodology differs from most existing methods that focus on off-policy performance evaluation of contextual bandit algorithms. Cramming utilizes an entire bandit sequence through a single pass of data, leading to both statistically and computationally efficient evaluation. We prove that if a bandit algorithm satisfies a certain stability condition, the resulting crammed evaluation estimator is consistent and asymptotically normal under mild regularity conditions. Furthermore, we show that this stability condition holds for commonly used linear contextual bandit algorithms, including epsilon-greedy, Thompson Sampling, and Upper Confidence Bound algorithms. Using both synthetic and publicly available datasets, we compare the empirical performance of cramming with the state-of-the-art methods. The results demonstrate that the proposed cram method reduces the evaluation standard error by approximately 40% relative to off-policy evaluation methods while preserving unbiasedness and valid confidence interval coverage.