Speaker: Connor Jerzak
Transcript
Welcome to our presentation on the paper: MiniMax Learning of Interpretable Factored Stochastic Policies from Conjoint Data, with Uncertainty Quantification. Let’s begin.
From marginal effects to decisions
Conjoint experiments are useful because they randomize complex profiles and reveal multidimensional preferences in contexts ranging from policy analysis to marketing and beyond. But they are often analyzed in a marginal fashion. The effect of one feature after averaging over the rest. This paper asks a decision-relevant question about how all the features combine to determine choices: what full-profile strategy — full over all features — should be learned from those randomized data, especially strategies that will be robust to adversarial environments
What makes this hard?
At least three things make this hard. First, actions are exponential: every candidate profile is a combination of factor levels. Second, interactions: good marginal parts may form a bad bundle if those parts, when combined together, counteract each other. Third, once we optimize a policy, inference has to follow through the optimization.
Conjoint as offline policy data
More concretely, a forced-choice conjoint already gives us logged actions. Respondents compare two randomly generated profiles, and the outcome is whether A beats B. Randomization gives clean counterfactual information, but the profile space grows quickly— so many bundles are unseen or sparsely observed.
Why marginal effects are not enough
Marginal effects can miss exactly the structure that matters for decisions. Outsiders may look good on average, and moderates may look good on average, while outsider-moderates are worse together. AMCE averages that interaction into one marginal number. Instead, here, the target is not an isolated feature effect; it is performance across full profiles, including ALL interactions.
Factored stochastic policies
The target here is therefore a factored stochastic policy. For each attribute, the policy assigns probabilities to its levels, and the probability of a full profile is the product across attributes. This mean-field restriction replaces an enormous joint distribution with attribute-level marginals. It is interpretable: we can see which issues, traits, or positions the learned strategy emphasizes.
Average-case optimizer
In the average case, one side optimizes against a fixed reference opponent, usually the experimental assignment distribution. We fit an outcome model for counterfactual rewards, then optimize the expected outcome minus a trust-region penalty toward the logging policy. The paper gives a closed-form solution for a two-way linear model. It develops a gradient-based optimization approach for GLMs or neural reward models.
Optimizer-aware uncertainty
After optimization, uncertainty has to pass through the map from the fitted reward model to the learned policy. One option is to unroll every gradient step and differentiate the whole trace. A cheaper option, at a converged interior solution, is implicit differentiation. Combined with the outcome-model covariance, the Delta method yields standard errors for both policy probabilities and the value (Q).
Minimax extension
We also explore strategic settings, which are different because the opponent is not passive. Both sides choose factored distributions, and the payoff is the institution-aware win probability. The minimax objective captures simultaneous strategic adjustment. In the election application, institutions map strategies through primaries into nominee distributions, then nominees face the general electorate.
Simulation checks
The simulations check whether this procedure behaves like a statistical estimator. As the sample size grows, RMSE falls, and coverage improves across the average and adversarial cases both.
Presidential conjoint application
In the U.S. presidential conjoint — Average-case optimization against a uniform opponent can imply vote shares outside the historical two-party range. The adversarial, institution-aware restricted equilibrium falls inside that range and much closer to the 2016 result. Because the output is a distribution over profiles, the paper can also score observed candidates under the learned strategies and summarize candidate-level strategic divergence.
Takeaway
Methodologically, the takeaway is to learn policies in conjoints, not just effects. Randomized conjoint data can support a policy estimand over combinatorial profiles; a factored stochastic class keeps it interpretable and variance-controlled; optimizer-aware Delta-method inference attaches uncertainty; and minimax extensions bring in strategic opponents and institutions without giving up attribute-level readability.
References
@article{connor t. jerzak 2026minimax,
title={MiniMax Learning of Interpretable Factored Stochastic Policies from Conjoint Data, with Uncertainty Quantification},
author={Connor T. Jerzak and Priyanshi Chandra and Rishi Hazra},
journal={International Conference on Machine Learning (ICML)},
year={2026},
volume={},
pages={},
publisher={}
}