Preference-based Conditional Treatment Effects and Policy Learning

TL;DR

The paper tackles the misalignment between traditional CATE-based policies and complex, hierarchical or ordinal outcomes by introducing the Conditional Preference Treatment Effect (CPTE), defined via a known preference function $w$ and independent counterfactual copies to yield an identifiable target $CPTE(x)$. It develops two practical CPTE estimation strategies—distributional matching and quantile-regression sampling—and couples them with policy learning under a preference-based objective $V(\pi)$, including an optimal rule $\pi^*(x)$ and plug-in estimators. To address plug-in bias and achieve statistical efficiency, the authors derive an Efficient Influence Function (EIF) and propose a 1-step corrected policy estimator that improves finite-sample performance. The method is validated through synthetic and semi-synthetic experiments, showing CPTE-based policies often outperform CATE-based policies, especially in settings with heterogeneous and multivariate outcomes, and demonstrating robustness to certain violations of identifiability assumptions. Overall, the CPTE framework provides interpretable, policy-relevant targets and practical tools for learning personalized decisions across complex outcome spaces.

Abstract

We introduce a new preference-based framework for conditional treatment effect estimation and policy learning, built on the Conditional Preference-based Treatment Effect (CPTE). CPTE requires only that outcomes be ranked under a preference rule, unlocking flexible modeling of heterogeneous effects with multivariate, ordinal, or preference-driven outcomes. This unifies applications such as conditional probability of necessity and sufficiency, conditional Win Ratio, and Generalized Pairwise Comparisons. Despite the intrinsic non-identifiability of comparison-based estimands, CPTE provides interpretable targets and delivers new identifiability conditions for previous unidentifiable estimands. We present estimation strategies via matching, quantile, and distributional regression, and further design efficient influence-function estimators to correct plug-in bias and maximize policy value. Synthetic and semi-synthetic experiments demonstrate clear performance gains and practical impact.

Figures (11)

• Figure 1: Policy learning results on synthetic and semi-synthetic experiments with no outcome correlations
• Figure 2: Potential outcome distributions
• Figure 3: Policy Learning with PNS policy value, no correlations. (a–c) Homogeneous RCT setting; (d–f) Heterogeneous RCT setting; (g-i) Homogeneous Observational setting; (j-l)Heterogeneous Observational setting. Legends as in \ref{['fig:synthetic_policy_learning_heterogeneous_RCT_uncorr']}.
• Figure 4: Policy Evaluation of optimal policy in the synthetic, heterogeneous RCT setting
• Figure 5: Policy Learning with correlation between potential outcomes in the synthetic, heterogeneous RCT setting. (a–c) Linear Regression; (d–f) DKNN. Legends as in \ref{['fig:synthetic_policy_learning_heterogeneous_RCT_uncorr']}.

Theorems & Definitions (14)

• Definition 1: Preference function
• Lemma 1
• Definition 2: Preference-based conditional effect
• Definition 3
• Definition 4: Structural treatment effect modifiers
• Theorem 1
• Theorem 2
• Proposition 1
• proof
• proof