Smooth Multi-Policy Causal Effect Estimation in Longitudinal Settings

Conventional treatment policies map patient covariates to a single recommended intervention in order to maximize expected clinical outcomes. Although a rich body of causal inference methods has been developed to estimate such policies, point-valued recommendations can be highly sensitive to estimation uncertainty, model specification, and finite-sample variability, while typically providing little guidance about how confident one should be in the recommended action. In this work, we propose a set-valued policy learning paradigm for the multiple-treatment setting, in which policies output a set of plausible treatments rather than a single recommendation. This formulation enables intrinsic uncertainty quantification, with the size of the predicted set reflecting the degree of decision ambiguity. We extend the learning-to-defer framework to multiple treatments via a novel \textit{greatest Lower Bound} method, and introduce \textit{conformal policy learning}, which bridges the gap between unobserved ground-truth optimal treatments and estimated optimal treatment rules. Drawing on insights from the noisy-label literature, we develop a randomness-injection approach that guarantees marginal coverage without requiring assumptions on underlying black-box optimal treatment rules. Through experiments on synthetic data and a real-world application to In-Vitro Fertilization (IVF), we demonstrate that our methods produce robust and actionable policies that naturally incorporate clinical considerations while effectively balancing performance and reliability.

Imitation learning enables learning a policy in an unknown environment with a latent reward signal using expert demonstrations, but it struggles when the imitator's and expert's observations are mismatched and unobserved confounders are present in expert demonstrations. By identifying appropriate adjustment sets via the sequential $π$-backdoor criterion, causal imitation learning (CIL) provides a framework for approximating the expert's policy from confounded data. However, existing CIL methods, Causal Behavioral Cloning (Causal BC) and Causal Generative Adversarial Imitation Learning (Causal GAIL), are designed for short-horizon, low-dimensional settings. When applied to continuous control tasks with long horizons and high-dimensional state-action spaces, these methods exhibit poor performance: Causal BC suffers from compounding errors, Causal GAIL is unstable and sample-inefficient, and sequential $π$-backdoor adjustment becomes impractical. We introduce Causal Soft Q Imitation Learning (SQIL) and Causal Inverse soft-Q Learning (IQ-Learn), two off-policy causal imitation learning algorithms that combine the causal adjustment framework with state-of-the-art inverse reinforcement learning objectives. Both algorithms operate on causally-adjusted state representations produced by an efficient approximation of the sequential $π$-backdoor criterion, exploiting the causal structure of continuous control environments to reduce the full-horizon adjustment to a fixed-size sliding window. We evaluate all methods in a suite of confounded environments and find that Causal SQIL and Causal IQ-Learn substantially outperform prior CIL algorithms on long-horizon tasks, sometimes surpassing the expert, whereas all causally unaware imitation methods fail to learn meaningful behavior.

Longitudinal treatment decisions from multivariate time-series data require predicting potential outcomes under future treatment sequences in the presence of time-varying confounding, heterogeneous patient dynamics, and limited domain-specific data. Existing longitudinal causal estimators typically address this problem by training a new model for each cohort or simulator. We introduce Causal Longitudinal Prior-Fitted Networks (CausalLongPFN), a prior-fitted network for time-series causal inference in longitudinal treatment-response data and zero-shot in-context counterfactual outcome prediction. The model is pretrained entirely on synthetic episodes sampled from a broad prior over temporal structural causal models, exposing it to treatment-confounder feedback, latent heterogeneity, nonlinear state evolution, delayed effects, and cumulative treatment responses. At test time, CausalLongPFN remains frozen and is used zero-shot: it conditions on support trajectories, a query history, and a planned future treatment sequence, and returns a predictive distribution over future outcomes without gradient updates or propensity-model fitting. Multi-step predictions are obtained by recursively applying the one-step predictor under the specified treatment sequence. We evaluate the model on branchable cancer, HIV, and warfarin benchmarks with ground-truth counterfactual labels, and on factual-only rolling-origin prediction in MIMIC-III ICU trajectories. CausalLongPFN is competitive with domain-trained longitudinal baselines on counterfactual benchmarks and performs strongly on factual MIMIC-III prediction, suggesting that broad synthetic causal pretraining can provide a frozen, amortized alternative for zero-shot longitudinal treatment-response prediction when repeated domain-specific training is costly or impractical.