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Doubly Robust Fusion of Many Treatments for Policy Learning
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Proposes calibration-weighted fused-lasso treatment fusion that groups many treatments into latent clusters doubly robustly, then runs policy-tree learning on the grouped treatments.
Problem
Learning individualized treatment rules when there are many treatment levels, where data are sparse within arms and covariate distributions are unbalanced across arms, making policy learning unstable.
Approach
Calibration-weight each treatment group to match the overall covariate mean, then apply a weighted fused lasso on linear working-model projection vectors to recover latent treatment groups; recovery holds if either the calibration weights or the outcome model is correct, after which any multi-armed policy learner (e.g., policy trees with CAIPWL) is run on the grouped treatments.
Key results
- With K=16 treatments, calibration-weighted fusion reached ARI 0.96 (vs 0.26 without calibration weighting) and recovered 4.3 groups on average, with policy value 8.89 vs 8.77 for the policy-tree baseline.
- Under a misspecified weighting model with a correct linear outcome model, CW + fusion achieved ARI 0.96 and value 6.43 vs 6.35 baseline.
- The real-data analysis groups CLL/SLL therapies and produces a depth-5 policy tree using six covariates; no quantitative policy-value gain is reported in the text.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add calibration weighting to treatment fusion | fusion + policy tree · Synthetic simulation, K=16 | ARI: 0.26 (0.14) -> 0.96 (0.06) | Helped |
| Add calibration weighting to treatment fusion | fusion + policy tree · Synthetic simulation, K=16 | policy value: 8.78 (0.09) -> 8.89 (0.11) | Helped |
| Add calibration weighting to treatment fusion | fusion + policy tree · Synthetic simulation, K=32 | ARI: 0.21 (0.09) -> 0.85 (0.10) | Helped |
| Add calibration weighting to treatment fusion | fusion + policy tree · Synthetic simulation, K=32 | policy value: 8.63 (0.18) -> 8.80 (0.21) | Helped |
| Add calibration weighting to treatment fusion | fusion + policy tree · Synthetic simulation, K=48 | ARI: 0.16 (0.08) -> 0.74 (0.10) | Helped |
| Add calibration weighting to treatment fusion | fusion + policy tree · Synthetic simulation, K=48 | policy value: 8.40 (0.30) -> 8.52 (0.23) | Helped |
| Add calibration weighting to treatment fusion | fusion + policy tree · Simulation with misspecified weighting model | ARI: 0.88 (0.13) -> 0.96 (0.06) | Helped |
| Add calibration weighting to treatment fusion | fusion + policy tree · Simulation with misspecified weighting model | policy value: 6.41 (0.04) -> 6.43 (0.02) | Helped |
| Fuse treatments before learning the policy | policy tree baseline · Synthetic simulation, K=16 | policy value: 8.77 (0.08) -> 8.78 (0.09) | Helped |
Surprising findings
- Without calibration weighting, fusion achieves ARI of only 0.26, and the Ma et al. (2022) fused-lasso linear method yields a policy value (8.51) worse than the unfused policy-tree baseline (8.77) under misspecified outcome models.
Limitations
- Fusion is performed once, with no iterative alternation between fusion and weight estimation.
- Performance may be unstable when some treatment arms have very few or no observations.
- Group recovery relies on the oracle group structure defined by exact equality of outcome means, with a tolerance supplied by fused lasso.
Experimental setup
Datasets: Flatiron Health CLL/SLL EHR database (10,346 patients) simulated data
Benchmarks: simulated treatment grouping (ARI, number of groups, policy value) Flatiron CLL/SLL real data
Metrics: adjusted Rand index number of groups policy value
Baselines: policy tree (no fusion) fusion + policy tree (no calibration weighting) Ma et al. (2022) fused-lasso linear fusion
Builds on: CAIPWL (cross-fitted AIPW policy learning) policy trees fused lasso Cressie-Read calibration weighting
Closest papers by meaning
- An effective framework for estimating individualized treatment rules (NeurIPS 2024 · similarity 0.88)
- Assessing the robustness of heterogeneous treatment effects in survival analysis under informative censoring (NeurIPS 2026 · similarity 0.85)
- PairNet: Training with Observed Pairs to Estimate Individual Treatment Effect (ICML 2024 · similarity 0.84)
- Orthogonal Survival Learners for Estimating Heterogeneous Treatment Effects from Time-to-Event Data (NeurIPS 2025 · similarity 0.83)
- Contrastive Balancing Representation Learning for Heterogeneous Dose-Response Curves Estimation (AAAI 2024 · similarity 0.83)
- Continuous Treatment Effect Estimation Using Gradient Interpolation and Kernel Smoothing (AAAI 2024 · similarity 0.83)
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