An arXiv preprint reports a statistical method for choosing among several treatments when an important source of confounding cannot be measured. In synthetic tests, its kernel and neural-network versions were reported as superior to comparator rules once the simulated confounding parameter rose above 2; at a value of 10, agreement with the study's oracle - the best treatment in the simulation - was about 57% for Tree OutcomeReg and around 70% for NeuralOutReg and MOML.
A method built around uncertainty
At its core, the target is an individualized treatment rule: a data-based rule that selects a categorical option from observed covariates. The framework uses partial-identification bounds - ranges of values that remain plausible when the data cannot support one exact causal answer - and chooses the option with the best worst-case loss. It combines that minimax objective with a symmetric regular-simplex treatment embedding and a differentiable weighted surrogate risk.
The instrument was the hinge
The method's advantage was not universal. In the no-unmeasured-confounding simulation, NeuralOutReg had the highest agreement with the oracle and the lowest oracle risk at large training sizes. The proposed methods instead converged to the minimax rule, which was suboptimal relative to the oracle in that setting.
Instrument strength mattered. When the simulated instrument had no strength, represented by a value of 0, the proposed methods were no better than an uninformed baseline. Their performance improved monotonically as instrument strength rose and converged to the oracle policy once it reached at least 5.
The same information bottleneck appeared when the number of treatment choices increased. Holding the instrument at three levels, the methods suffered a sharp drop once treatments outnumbered those levels, with drastic agreement loss at four treatments and complete reported degradation by six.
A synthetic test with a built-in caveat
The evidence came from synthetic observational-style data, not human or clinical outcomes. The default setup used five continuous covariates, three categorical treatments, three instrument levels, binary outcomes and a discrete latent confounder. Each simulation was evaluated on an independent test set of 5,000 samples and repeated at least 10 times, with means and bootstrapped confidence intervals reported.
Outside the sample-size experiment, the main simulations used 12,000 training samples. They also supplied true probabilities to the causaloptim bound calculations and true propensity scores to MOML, removing probability estimation and sample splitting from those comparisons. That leaves open how the method would perform when bounds and related quantities must be estimated from finite observational data.
What the mathematics does - and does not - say
The mathematical results point to why information quality matters. The analysis says narrower identification bounds shrink the gap between the bound-based policy and the theoretically optimal policy. A theorem also states that, under its regularity conditions, reaching the minimum surrogate risk leads to the optimal worst-case-risk policy; a finite-sample oracle inequality gives convergence guarantees under those conditions.
Those guarantees remain conditional. They rely on the causal assumptions needed to derive valid bounds, while the surrogate optimization is generally nonconvex, so practical results can depend on initialization, tuning and regularization. Because the evidence is synthetic, the preprint does not show improved patient outcomes, safety or clinical effectiveness in humans, and it does not establish performance for continuous or ordinal treatments, outcomes or instruments.
The authors frame the approach as most useful when no-unmeasured-confounding assumptions are not credible. In the reported simulations, however, its edge depended on narrower bounds, stronger instruments and a treatment count supported by the available instrument.
Paper data and sources
Original title: Partial Identification Learning with Categorical Treatments for Individualized Treatment Rules
Authors: Johannes Hruza, Paweł Morzywołek, Jakob Zeitler et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text