MiniMax Learning of Interpretable Factored Stochastic Policies from Conjoint Data, with Uncertainty Quantification

We study offline policy optimization over exponentially large factorial action spaces from randomized preference data, showing how conjoint experiments can estimate interpretable stochastic policies with asymptotically valid uncertainty under regularity conditions. Conjoint analyses typically report Average Marginal Component Effects (AMCEs) by averaging over opponent attributes and thus ignore strategic interdependence. We instead learn *stochastic interventions*—product-of-Categorical policies over factor levels—that (i) optimize expected outcomes in an average-case setting and (ii) extend to a two-player *minimax* (adversarial) setting that realistically captures simultaneous strategic candidate selection. Methodologically, we derive a closed-form optimizer for a tractable two-way interaction regime with $L_2$ variance regularization, and provide a general gradient-based procedure for richer model classes. Uncertainty from the outcome model propagates asymptotically to both the optimal policy and its value via a Delta method approximation. We further model institutional details (e.g., primaries) inside the minimax objective and introduce a data-driven measure of strategic divergence between parties. On synthetic data, we empirically characterize finite-sample error and coverage as dimensionality and $n$ vary. On a U.S. presidential conjoint, adversarially learned policies produce restricted-equilibrium vote shares that align with historical election ranges in our data, in stark contrast to non-adversarial (averaging) optimizers.

Researchers often use choice surveys to study how people evaluate complex options, from products and job applicants to political candidates. In these surveys, people compare hypothetical options with randomly assigned features, such as a candidate’s age, background, personality, and policy views. Standard analyses usually ask how much one feature helps or hurts on average. That is useful, but it misses two important realities: features can work together, and in competitive settings each side reacts to what the other side might do. This paper turns such survey data into a way to learn whole strategies rather than isolated feature effects. Instead of asking, “Is this one feature good or bad?”, it asks, “What mix of features would perform well, and how sure are we about that answer?” The method produces easy-to-read probabilities for each feature, such as how often a candidate profile should emphasize the economy, immigration, foreign policy, or other priorities. These probabilities summarize families of strong profiles, rather than pretending that one single profile is the only best choice. The paper also handles competitive settings, such as elections, where one side’s best choice depends on the other side’s likely response. It builds simple models of institutions like party primaries followed by general elections, so the learned strategies reflect both voter preferences and the rules of competition. In simulations, the method finds better strategies as more survey data become available and reports how uncertain those strategies are. In an application to U.S. presidential candidate surveys, strategies that account for competition produce predicted vote shares closer to historical election outcomes than strategies that ignore the opponent. Overall, the paper offers a more realistic and transparent way to learn from preference surveys, especially when choices are complex and competitors are strategic.