Overlap-weighted orthogonal meta-learner for treatment effect estimation over time
Authors: Konstantin Hess
Dennis Frauen
Mihaela van der Schaar
Stefan Feuerriegel
Venue: ICLR 2026 Poster (2026)
Keywords: causal inference
heterogeneous treatment effects
time-varying treatments
meta-learners
machine learning for healthcare
Primary area: causal reasoning
TL;DR: We develop a novel overlap-weighted Neyman-orthogonal meta-learner for heterogeneous treatment effect estimation over time.

Abstract: Estimating heterogeneous treatment effects (HTEs) in time-varying settings is particularly challenging, as the probability of observing certain treatment sequences decreases exponentially with longer prediction horizons. Thus, the observed data contain little support for many plausible treatment sequences, which creates severe overlap problems. Existing meta-learners for the time-varying setting typically assume adequate treatment overlap, and thus suffer from exploding estimation variance when the overlap is low. To address this problem, we introduce a novel overlap-weighted orthogonal WO meta-learner for estimating HTEs that targets regions in the observed data with high probability of receiving the interventional treatment sequences. This offers a fully data-driven approach through which our WO-learner can counteract instabilities as in existing meta-learners and thus obtain more reliable HTE estimates. Methodologically, we develop a novel Neyman-orthogonal population risk function that minimizes the overlap-weighted oracle risk. We show that our WO-learner has the favorable property of Neyman-orthogonality, meaning that it is robust against misspecification in the nuisance functions. Further, our WO-learner is fully model-agnostic and can be applied to any machine learning model. Through extensive experiments with both transformer and LSTM backbones, we demonstrate the benefits of our novel WO-learner.

Published as a conference paper at ICLR 2026
ORTHOGONAL META- FOR TREATMENT EFFECT ESTIMATION OVER TIME
Konstantin Hess! 1.2," Dennis Frauen 12, MiMaella der Schaar?,, Stefan Feuerriege!
I LMU Munich Munich Center for Machine Learning
*University of Cambridge
Alan Turing Institute *Corresponding author: k hess@ mmudde
ABSTRACT
Estimating heterogeneous treatment effects (HTFs) in time-varying settings is partieularly challenging, as the probability of observing certain treatment sequences decreases exponentially with longer prediction horizons. Thus, the observed data contain little support for many plausible treatment sequences, which creates severe overlap problems. Existing meta-learners for the time-varying setting typically assume adequate treatment overlap, and thus suffer from exploding estimation variance when the overlap is low. To address this problem, we introduce a novel overlap-weighted orthogonal (WO) meta-learner for estimating HTES that targets regions in the observed data with high probability of receiving the interventional treatment sequences. This offers a fully data-driven approach through which our WO-learner can counteract instabilities as in existing meta-learners and thus obtain more reliable HTTE estimates. Methodologically, we develop a novel I population risk function that minimizes the overlap-wett weighted oracle risk. We show that our WO-learner has the favorable property of Neyman- orthogonality, meaning that it is robust against misspecification in the nuisance functions. Further, our WO-learner is fully model-agnostic and can be applied any machine learning model. Through extensive experiments with both transformer and LSTM backbones, we demonstrate the benefits of our novel WO-learne..
INTRODUCTION
Traatnert seguercs
Estimating heterogeneous treatment effects (HTEs) such as conditional average potential outcomes (CAPOs) and conditional average potential outcomes (CAPOs) (Frauen jet al. 2025a) over time from patient trajectories is cen- tral for advancing personalized medicine (Allam et al.)
Thead?
Treat
2021 Battalio et al. 2021 Bica et al.) 202 Feuerriegel al. 2024). Such estimates can, for example, guide treat- ment adaptation in chronic disease management or inform personalized intervention strategies in digital health.
Prodiction horizon
Figure 1: Overlap problems in time- varying settings. With longer prediction horizons, treatment sequences become more complex, and the probability of observing each treatment sequence de- creases exponentially. Hence, standard meta-learners often have poor perfor- mance due to low overlap.
Unlike standard predictive tasks, HTE estimation is inher- ently causal and, in time-series settings, requires adjust- ments for vimeinarying confounders (Bica et al. 2020). Without such adjustments, time-varying confounding can induce infinite-sample bias and lead to incorrect estimates, To address this, model-agnostic meta-learners (Frauen et al. 2025a) have been proposed to provide principled strategies for causal adjustments in time- varying settings Prominent examples include adaptations of the inverse propensity weighting (IPW) learner and the doubly robust (DR) learner to time-varying settings (Frauen et al. 2025a).
'The term meta-learner refers to general estimation strategies ("recipes") " to learn causal quantities Künzel 2019 Frauen et al, 2025b), which can be instantiated with different machine learning backbones (e.g..
neural networks).

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with respect Published as a conference paper at ICLR 2026
However, existing meta-learners (Frauen et al. 2025a) for estimating HTEs over time suffer from instabilities in settings with low overlap. which renders them inapplicable to medical scenarios. Here, overlap refers to the probability of receiving each of the two different treatment sequences of interest; if overlap is low, standard meta-learners have severe estimation variance (Jesson et al. 2020) Melnychuk al. (026). This issue is especially serious in time-varying settings: with increasing prediction horizons, the probability of a treatment sequence consists of products of propensity scores (Hess& & Feuerriegel 2025), which makes the treatment overlap decrease exponentially (see Fig. [ As result, in low-overlap regimes, adjustment strategies based on inverse propensity weighting (IPW) will lead extreme weights due to the product structure and, hence, division by values that are close to zero.
In this work, we propose novel peerlap-weighte orthogonal meta-learner (WO-learner) for estimating HTEs over time:
1. Our novel WO-learner addresses low-overlap regimes with carefully designed population risk function that minimizes a novel, overlap weighttd oracle risk. Hence, by focusing on high-overlap regions in the data, our WO-learner avoids extreme inverse propensity weights and unreliable response function estimates. As a result, our meta-learner provides stable HTE estimates, even in low-overlap regimes.
2.
We further ensure that our weighted population risk function is to all nuisance functions. Hence, our WO-learner is robust to misspecification in the nuisance parameters, meaning that estimation errors in the nuisance functions do not propagate as first-order biases into the final HTE estimate, which is a crucial advantage over simple plug-in estimators (Hines et al. 2022 Kennedy 2022).
3. Our WO- WO-learner is fully agnostca and can be used in combination with any machine learning backbone, such as transformers or LSTMs. Further, we derive our WO-learner for estimating conditional average treatment effects (CATEs). On top of that, we also extend our theory to conditional average potential outcome estimation (CAPOs); see Section
We make three key contributions: (1) We introduce novel overlap weighted meta-learner for HTE estimation over time that minimizes the overlap-weighted oracle risk. (2) We further derive a Neyman- orthogonal population risk that eliminates first-order bias from the nuisance functions in the HTE estimates. (3) Through extensive experiments, we demonstrate that our WO-leamne outperforms existing meta-learners, especially in settings with low overlap. In addition, we demonstrate the benefits of our meta-learner in settings where Neyman-orthogonality is crucial, such as limited sample size and complex nuisance functions.
2 RELATED WORK
We now review prior literature on treatment effect estimation over time, namely: ! average treatment effect (ATE) estimation, ② model-based HTE estimation, and meta-leamerss for HTE estimation. Our WO-learner belongs to the latter category, and this is where our primary contributions are.
1 ATE HTE estimation over time: The literature estimating ATES over time dates back to works in epidemiology and classical statistics (Robins] 1986 1999; Robins et al. 2000). Examples are G-computation (Bang & Robins, 2005| Robiiss| 1999 Robins & Hernán 2009). marginal structural models (Robins& & Hernán 2009 Robins et al. 2000) and structural nested models (Robins) 1 1994] Robins & Hernán 2009), which belong the broader class of so-called G-methods. More recently. targeted maximum likelihood has been adapted for the time-varying setting (van der Laan & Gruber 2012) van der Laan & Rose 2018). There is also some literature on model-based methods for estimating ATES over time (Frauen et al. 2023 Shirakawa et al., 2024). Importantly, all of these works focus on average potential outcomes estimation and, therefore, ignore patient heterogeneity, because of which these works are not suitable for personalized medicine.
2 Limitations of model-based HTE estimation over time: There has been much research on modellbased estimation of HTES over time (Bica et al. 2020 Hess et al. 2024 Hess & Feuerriegel 2025) Hess et al.) 2026 Li al. 2021 Lim et al., (018) 8 Ma et al. [025 Meinychuk et al. 2022
Seedat et al. 2022 Wang et al. 2025). Importantly, the focus in this literature stream is primarily
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on how to adapt the underlying neural backbone, but not how to find the best adjustment strategy (i... the learning strategy to address time-varying confounding). Further, the above model- based methods are known to be instanriations of different meta-learners (see Frauen et al. (2025a) for discussion). Importantly, none of these model-based methods relies on either sverlap-weighte or Neyman-orthooonal meta-learness In contrast, we design overlap-weighted meta-learner that is Neyman-orthogonal with respect to all its nuisance functions and that can be applied to any neural backbone.
3 Meta-learners for HTE estimation over time: Research on meta-learners for HTE estimators over time is still very limited, and we are aware of only a few works. Lewis & Syrgkanis (2021) developed a method that, however, relies on parametric assumptions on the data-generating process and is, therefore, not fully model agnostic.
Recently, Frauen et al. (2025)) formalized a suite of meta-learners for the time-varying set-
Proper time varsing ol). er > 0)
Nerricn oohogozzl
Designed for low overlap regines
ting, namely: (a) history adjustment (HA), (b) re- gression adjustment (RA), (c) inverse propensity weighting (IPW), (d) doubly-robust (DR), and weteeevaarinneeeeeeeee
HA
RA
IPW
(8) DR
(6) FYW
(IVW) learner. However, they all have important shortcomings (Table D: First, the HA is biased and does not target the correct estimand. Second, the RA, IPW, and IVW learners have plug-in bias and are not Neyman-orthogonaa with respect their estimated nuisance functions. Frauen et al. (2025a) refer to the IVW-learner as IVW-DR learner. However, it is not orthogonal with respect to its weights, and eπrors in the propensities propagate as first order biases to estimated inverse-variance weights, and hence, the reweighted population risk. Hence, for clarity, we refer to it as IVW-learner, as robutteso does not hold. Third, the IPW and DR learners rely on inverse propensity weighting, which can lead to extreme weights for long treatment sequences, especially in settings with low overlap. In contrast, we develop novel WO-learner that is Neyman-orthogonal and designed to deal with low overlap.
an (c)
Table 1: Meta-learners for HTE estimation over time. Our WO-learner is the only method that adjusts for time- varying confounding, is Neyman-orthogonal with respect to all its nui- sance functions, and avoids extreme weights in low-overlap regimes.
Why low overlap is non-trivial challenge for existing meta-learners: When the interventional treat- ment sequences have low overlap. inverse propensity scores may lead to extreme weights. Further, small errors in estimated propensity scores lead to large errors in the constructed pseudo-outcomes and, therefore, to extreme variance for the IPW and the DR learner. Importantly, this issue even more pronounced in the time-varying setting, where inverse propensity weighting relies on products of propensity scores and, thereby, the treatment propensity decreases exponentially with longer prediction horizons (Frauen al. 2025a Hess et al. 2026 Lim al. 2018). Here, propensity-score clipping is sometimes used as heuristic that introduces uncontrollable bias, since the truncation level cannot be calibrated without access to counterfactual outcomes. In contrast, our WO-leamner provides principled stabilization under limited overlap. Similar issues also arise for the response functions learned the RA and in the DR learner, where low overlap leads to poorly learned, biased response surfaces, especially in high-dimensional covariate spaces. Finally, as the IVW learner is not Ncyman-orthogonal w.r.t its weight functions, estimation errors propagate as first-order bias through all time steps. which makes it unstable in low-overlap regimes.
Research gap: To the best of our knowledge, there is no meta-learner designed to counteract low- overlap regimes while being Neyman-orthogone As remedy, we propose novel overlap-weighted orthogonal meta-learner (WO-learner) for HTE estimation over time.
PROBLEM FORMULATION
Setup: Let E No be the time index. Further, let Y, E 12dx the outcome variable of interest (e.g.. variable indicating the health status of a patient), X, E gd, the covariates that contain relevant patient information (including static features), and A₁ E {0. 13 the treatment variable. For any stochastic process V2 XY, A.}. }. we write V2 Vo. (Vo...., Vi) for the history of V up to time t. Then, let H, = (Y,-1. Ne, A.11) ) be the collective history observed at time step t, and 2, = (Yz, X,, A²) the history including the final treatment and outcome. Finally, 7 is the prediction
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horizon such that treatment sequences of the form a4:1+7 {0. 1| (see Figure Db. We further
build upon the potential outcomes framework (Neyman 1923] Rubin 1978) for the time-varying
setting (Robins 1999 Robins & Hernán 2009). Formally, let Y ++r [+:t+ be the potential outcome that would have been observed under the interventional treatment sequence.
Estimation task: Given history H, h4 and two interventional sequences of treatments dutt7 (oe,..., ((4r) and beat7 = (bz,... ..,....b... b(+r), our main objective to estimate the CATE
N4 a.h (hx) = E [ - [batt] H2 ha
We extend our theory to the conditional average potential outcome (CAPO), which is defined as 4 (h+) = EE [acst<] H, he
Identifiability: In order to ensure identifiability from observational data, we need to make the following as- sumptions that are standard in the literature (Bica et al.
B.
Yeur Redee
2020:
Frauen al., 2025a Hess et al.) 2024 Li et al.
2021 Melnychuk et al. 2022): (i) Consistency: When-
Betur
the observed treatment A, equals the interventional treatment a,, the observed outcome Y; corresponds to the
Xe-r Ganohwaried
potential outcome Y,(a,]- (ii) Positivity: Given history
H, = h with PH,,- = h2) > 0, there is non-zero probabil- ity P(A, 0g H, h₂)) of receiving any treatment
Helory
Inteverdoo
A, = az. (ii) Sequential ignorability: Given a history
Figure 2: Causal graph. Shown are the observed history, the interventional treatment sequence, and the potential outcome, along with their causal con- nections. When intervening on future treatments, we do not observe the fu- ture covariates (in purple), which leads time-varying confounding.
H,- he, the treatment assignment A₁ independent of the potential outcome Y++ (1=++T).
Time-varying confounding: The key difficulty in esti- mating HTEs over time lies in time-varying confounding whenever r > 0, i.e., when we are interested a sequence of future treatments dett+r (see Fig. 2 Then, at time I, we intervene both on the current treatment A, and treatments A4+5 for 0 < 8 < that lic several time steps in the future. However, future covariates Xe+6 and outcomes Y Y(+8-1. that are unobserved during inference time, will confound the treatment assignment of A4+5- This induces feedback loop that needs to be accounted for (see Fig. 1 backdoor-type history-adjustment) is biased in this scenario. Specifically, for O.
Importantly, simply conditioning on the observed history H₃ (i.e., a
E
Yetr M. = 7rg
+ E Y #B(Yetz
A- = h4, Auttr a+t++
proper adjustment (zour metbod)
naive history adjustment
which means that methods for the right-hand side (i.e., in the HA-learner) target an incorrect estimand that is different from our causal quantity interest. Instead, proper adjustments for time- varying confounding strategies lead to poor performance when the interventional treatment overlap is low. The inverse variance weighted adjustment in the IVW learner tries circumvent this issue but suffers from first-order plug-in bias from its estimated weights that propagate through all timesteps. As a remedy, we develop our novel weighted orthogonal (WO) meta-learner.
required, such as in the RA, IPW, or DR learner. However, these adjustment
To perform proper adjustments for time-varying confounding, all meta-learners rely on so-called nuisance functions; that is, functions that are not of direct interest but must be estimated accurately to enable valid estimation of the target parameter. Both existing meta-learners and, later, also our WO-learner rely on estimating response functions and/or propensity scores, which we define below.
Standard nuisance functions:
Definition 3.1 (Response functions and propensity scores). For interventional trealment sequences à ats++ and b = br.ttr, let the response functions for CATE be defined as
3,b (h₂) = 14 (h₂) - (hz),
IIn the static setting, a similar issue is known as runtime confounding, where not all confounders are observed during inference time (Coston al. 2020
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where 14 (g(C))))))h))) are the response functions for the CAPOs with
Mi+r (hu+T) = EE [Y HL+T = h Actr ac+t]
(5)
and, recursively, for ,t, + 11. 19 (hg) = E
Hj = -hj, A₁ = =az]
(6)
Further, let the propensity scores for j E {t, [ +T) r} be
すj ()1) (AA 0g H, = hg)-
Finally, introduce the pseudo-outcomer of the DR learner, which are subcomponent of weighted population risk. Here, pseudo-outcomes are variables that are estimated from nuisance functions, for which the conditional expectation equals the target causal estimand (in our case: CATE / CAPO) and, hence, enable consistent estimation.
Definition 3.2 (DR pseudo-outcomes (Frauen al.) 2025a)).
For interventional treatment sequences ā att+r and b = bEtTT, let the DR pseudo-outcomes for CATE be
a.b (2--) = (2( (Z(Z
(8)
where the corresponding DR pseudo-outcomer for CAPO are
At (2++7)
II j=t
1+ (A
1 YeT
1+
(H))
(1-1
[A,=, (H,)
(A,=as)
T (H²)
j=1
Different from existing meta-leamers, the population risk function minimize in our WO-learner minimizes a weighted, Neyman-orthogonal risk to address low-overlap regimes.
WEIGHTED ORTHOGONAL META-LEARNER
The key idea of our WO-learner is up-weight sam- ples in the training data that have higher probability of receiving the interventional treatment sequences. By up- weightittng samples with larger overlap (in the case of CATE estimation) larger propensity (in the case of CAPO estimation), we ensure that we target samples that are more relevant for estimating the HTE of interest (Figure 3. This requires non- trivial derivations to guarantee that our WO-learner (i) correctly adjusts for time-varying confounding, (ii minimizes the weighted oracle risk, and (iii) is Neyman-orthogonal with respect to all its nuisance functions.
Properaity (f(h))
downsowiggt CATE
Propertely weight of (P.))
Oredlop weight oi Doak
Up
CATE
2-2
6 0
Observational sampples
hiattry f7, Res
Figure 3: Weight functions. Our weight func- tions are designed to up-weight samples with large treatment overlap (CATE), or treatment propensity (CAPO). Thereby, we effectively overcome estimation variance issues in low- overlap and low- www-rppensstyy regimes in a fully data-driven way.
Below, we first introduce novel weight func- tions in Section 4.1 Then, we present our pseudo- outcomes for both CATE and CAPO estimation, and develop our weighted population risk; by minimizing our population risk, we adjusts for time-varying con- founding while minimizing the weighted oracle risk. Finally, we ensure -eymaan-rrthoonaale of our population risk with respect to nuisance functions in Section 4.2
4.1 WEIGHTED POPULATION RISK
We now introduce our weighted population risk for both CATE and CAPO estimation. We start by defining the weight functions, followed by weighted population risk function. We then show that is guaranteed to minimize the oracle risk (-+ Proposition 4.3) and, additionally, that it properly
adjusts for time-varying confounding (-> Corollary 4.4
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Definition 4.1 (Weight functions). Let the weight functions for CATE be the overlap weights
w (he) w/ (he).)
(10)
where we define the weight functions for CAPO the propensity weights
b+
wg
II T (Tx)
He Me= heg p(Ar:tt = agatt He he)
(11)
for j. E :l...., J.. Finally, summarize the set of nuisance functions for CATE as na. =1 Un, with the set of nuisance functions for CAPO r/" {m]. 11 w ز
Intuitively, our weight functions work as follows. For CATE, they act as overlap weights, i.e., they up-weight samples with higher probability of receiving both interventional treatment sequences. Likewise, for CAPO, the weight functions correspond to propensity weights. That is, they seek to up up-weight samples in the data that have higher probability of receiving single interventional treatment sequence of interest (see Fig. B). Thereby, we effectively circumvent key issues of existing meta-learners that lead to highly unstable inverse propensity weights and response function estimates.
Next, we develop our weighted population risk that minimizes the oracle risk; specifically, our weighted risk function minimizes weighted enror term that up-weights samples that have higher probability of receiving the interventional treatment sequences. Thereby, we counteract the issue in existing meta-learners (IPW, RA, DR) that suffer from poor data support when the overlap is low. For this, we first define the pseudo-outcomes for our WO-learner, which we will later need to satisfy deyman-orthhoonallee
in Section 4.2 Our pseudo-outeomes directly arise by orthogonalizing our weighted oracle risk. They inherit part of the structure of DR pseudo pseudo-outcomes, part from the orthogonalization of the overlap weights, and part of their combined structure.
Definition 4.2 (WO pscudo-outcomes), Let
(.b(Zet)) = pt )o Pt
pb
(HI) + pi )wf (HI, w.t
(12)
(2++7) II n. (H,) j=t
Σ
-1,==A1)- -9 (H w/ (11g II (HHx)
(13)
ISkC)
Then, we define our WO pseudo-outcomes for CATE as
a.b
hh (Z+4)) = 14 a.. (H.) +
Wt
0. -
0.b (H))
(14)
a.b
(Z(+7)
Pt
and, likewise, the WO pseudo-outcomes for CAPO
(H() p (Z(44)
(Zett))
(15)
We state first theorem, which guarantees that weighted population risk minimizes the weighted oracle risk. That is, our weighted population risk assigns the appropriate weights from Definition 4.1 while correctly adjusting for time-varying confounding.
Theorem 4.3 (Weighted population risk). Let o E ((a,b), a} for CATE and CAPO, respectively. Then, the population risk function
L(g,"f) =
E
pi (i(2)+)) (E((2t)))))))))
(16)
E wi (Hi)

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minimizes the oracle risk
C' (r
1
E wi (Ri) ((FP))
(17)
wi (Ha))
Proof. The proof for CAPO can be found in Supplement C.1 and for CATE in Supplement C.2
Therein, we derive several helping lemmas, including the result that Elpp (2+++ M.) w/ (H)).
which we leverage to prove our main theorem.
Finally, we show that minimizing our weighted population risk guarantees that we target the correct estimand and, therefore, that our WO-learner adjusts for time-varying confounding.
Corollary 4.4 (Time-varying adjustment). The minimizer of the weighted population risk Clgs nf) adjustt for time-varying confounding.
Proof. We leverage Theorem 4.3 and notice that, since wi (Hi,) > 0 by positivity, (g; (f) (and. hence, L(g: 1y)) is minimized if and only if g 14g which is exactly the target estimand.
Weighted orthogonal learning: We summarize the training of our WO-learner with the empirical weighted risk in Algorithm [. For this, we first learn the response functions P3 and the propensity scores $g.J E ft....,t + T.. and then, using the pull-out property of expectations, the weights via
++ 2 (HA) A=
H+ II
(g, = E
Hイ= = hg =
# (HL))
H, = h2 #3 (hg).
(18)
k=
Algorithm 1 WO learning
4.2 NEYMAN-ORTHIOGONALIY
Input: Data D, ( nuisance
In the following, we show that our weighted population risk from Theorem 4.3 is Neyman-orthogone with respect to all its nuisance tunctions. This is different from IPW, RA, and IVW, all of which suffer from severe plug-in bias, which means that estimation errors in their estimated nuisance functions propagate as first-order biases into their (Kennedy (022).. Bias
function estimators fi, parametric second-
stage estimator ge, sample split À E (0, 1).
1: Perform sample split Di [[=)))]> D
2: Learn nuisance functions A D P((1))))] and evaluate on Dix..] Construct 92 and po from evaluated nui- sance estimators
final estimated pseudo-outcome propagation is even more severe in the time-varying setting, where multiple nuisance functions are learned on top of each other, and incorrectly estimated nuisance functions in earlier stages lead to even worse bias in nuisance functions at later stages (and, hence, the final target estimate). In con- trast, our WO-learner is robust against estimation errors in its nuisance functions; = bias from nuisance function estimates only propagates as lower-order errors to the final HTE estimate. Importantly, this includes estimation errors from the weights in Equation 18
4: Construct WO pseudo outcomes & Minimize empirical weighted risk
[ SlAn of (H,,)
Etde:n")
x (E+ so (o(
W.r.L. 0 on D [An] (e.g.. with gradient descent). 6: Return optimized WO-learner ğo
If we directly minimize the oracle risk L (g: 17 as Theorem 4.3 do not achieve Norhoonorhhyygnalliyy with respect the nuisance functions 17". Instead, we need our tailored population risk L(g:
Theorem 4.5 (Neyman-orthognnaltty Let E {āā, b), a} for CATE and CAPO, respectively. The weighted population risk
C(g.n))
=
E pi (((2)))) 9((,)
(19)
E wi
(H,))
is Neyman-orthogonal with respect all nuisance functions 7
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Proof. The proof for CAPO is in Supplement C.I and for CATE in Supplement C.2 Therein, first calculate D, D.L(g: lg - g). ie., the path- wise derivative of L(g: n²) w.I.t. the target parameter check that the cross-derivative with respect to any
g. Then, establish Neyman orthogonality, nuisance function vanishes, i.e., that the second-order derivative Dr, (g 17 g, hi hj] for all h2 E 77. Intuitively, this ensures that the influence of nuisance function estimation errors enters only at second order, which makes the score function locally robust to small perturbations (i.e.. estimation errors) of 17?
Remark I: For a single-step-ahead prediction r = 0 (i.e., when there is time-varying confound- ing as in the static setting), the R-learner (Nie & Wager| 2021) has the same overlap weights as our WO-learner for CATE. In other words, our WO-leamne for CATE is non-trivial generalization of the R-learner to the time-series setting. We show this property formally in Supplement C.3
Remark 2: Further, we show in Supplement C.4 that our overlap weights lead uniformly bounded
variance of our pseudo-outcomes, which enables stable estimation even in low-overlap regimes.
Implementation: All meta- meta-leamers, including our WO-learner, can be implemented with any state- of-the-art neural network. Analogous to Frauen et al. (2025a), our main results in Section 5 are with transformers (Vaswani et al. 2017) as neural backbones for both the nuisance function estimators and the second-stage estimators. To ensure a fair comparison, all nuisance estimators and second-stage regressions share the same transformer-based architecture (implementation details are in Supple- mentBp. In our experiments, we evaluate our WO-learner against the entire family of meta-learners, and hence the comparison is exhaustive. As model-based methods are instantiations of specific meta-learners, including (or any specific mocel-archiitecture) them would distort the comparison which meta-learner is the best-perforning strategy, and make the evaluation fundamentally unfair. Following Frauen et al. (2025a). we highlight that these implementations serve as example; the op- timal model architecture depends on many different factors such as sample size or data dimensionality (Curth & van der Schaar 2021.
NUMERICAL EXPERIMENTS
In this section, we empirically evaluate our WO-learner against existing meta-learners. The purpose of our experiments (i) to verify the theoretical insights developed in Section 4 and (ii) to show that our WO-learner consistently improves upon standard meta-learners across a diverse set of settings with low overlap where Seyman-orthogonalln is crucial such as limited sample size and complex nuisances. Our main results are with transformer instantiations (see Supplement EE] for implementation details, hyperparameters, and runtime). Further, we provide additional ablations with LSTM instantiations. All experiments are repeated over five different seeds.
Datasets: We provide experimental results across several datasets, including synthetic, semi semi- synthettt and real-world data. * We simulate four synthetic datasets, where we isolate different complexities for CATE estimation in the time-varying setting. We then show that our WO-leamer real-world covariates, and provide experiments on semi-synthetic data based on the MIMIC-III dataset (Johnson al. 2016). Different from observational data, the advantages of both synthetic and semi-synthetic data are that we have access to the ground-truth CATEs and, thereby, can correctly validate all meta-learners (Poinsot al. 2025
deal with
We provide results on real-world observational
dataset in Supplement
Synthetic data: In order to isolate the different complexities in the time-varying setting, we run experiments on different synthetic datasets D E (D", , DN Therein, we show that our WO-learner (1) benefits from its overlap weights in low-overlap regimes (D"); (2) has crucial advantages over propensity based-methods when the propensity score function is complex (D"); (3) outperforms regression adjustments when the response function is complex (D"); and (4) remains robust even in low-sample settings
(DN). ). On high level, (1) and (2) highlight the importance of our overlap weights, while (2) show the benefits of seyman-orthogonaliin
All experiments are conducted for multi-step-aheet predictions, and all datasets have time-varying confounding. Details about the deta-gene processes are in Supplement D.I
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Published as a conference paper at ICLR 2026
191 IEA
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Table 2: Low-overlap regime D Reported are the average RMSES + standard deviation for CATE
estimation, and the relative improvement of our WO-Iearner over the best performing baselines across different levels of overlap (larger values of y correspond to lower overlap). Due to our weighted population loss, our WO-learner is highly stable even when the overlap is very low.
PW
(1) Low-overlap regime D"; We control the overlap in the data generating process with an overlap parameter 7). By increasing y, we decrease the overlap in the observed data, i.e., the prob- ability of receiving both interventional treatment sequences.
Pharage RaaE for Gat edimttionn
12
Results: Table 2 shows that our WO-learner outperforms all existing meta-leurners over all levels of overlap. This confirms the effectiiveness of our overlap weights. We further find that the RA-learner performs fairly stable, as it avoids inverse propen- sity weights that become increasingly more unstable in low- overlap regimes. Nonetheless, our WO-learner consistently outperforms the best baseline with relative improvement of up to 58.4%.
Prediction
Figure 4: Complex propensity score DD: Reported are the aver- age RMSES for CATE estimation. Our WO-learner significantly im- proves upon existing meta- leta-learners, even for large prediction horizons.
(2) Complex propensity score D"; We simulate data with a complex propensity score. We further increase the prediction horizon T, and study the performance of meta-learners that are based on the propensity score. Thereby, we gain insight into how errors propagate over time, and how the meta-learners behave under exponentially decreasing overlap for increasing prediction horizons.
Results: In Figure 4 can clearly the benefits of WO-learner over propensity-basee based baselines due to its overlap weights, and its seyman-orthogone population risk fusctionn Our WO- learner is robust against estimation errors in the estimated propensity scores and weight functions, and errors do not propagate as for the IPW and the IVW learner. Further, the performance deteriorates for the IPW and DR learners is due to the exponentially decreasing overlap for increasing prediction horizons In contrast, our WO-learner remains highly stable.
(3) Complex response function DP: In this dataset, we sim- ulate complex response function, and further vary the com-
WC (ust
Aoerage HAEE Cal edt mradon
plexity by increasing the dimension of the covariate space. The purpose of this experimental setup is to empirically validate that our WO-learner Neyman-orthogone its estimated response functions. Hence, we compare it with
with respect to
the RA learner, which solely relies on estimating the response functions and is not orthooolll
Results; Figure 5 shows the results for the complex response with
function. As WO- is also respect to its estimated response functions, we can clearly see that outperform simple RA-learner. As the response function becomes more complex with increasing dimension of the covariate space, WO-learner stays largely unaffected.
14 Dimension counriatte space
Figure 5: Complex response func- tion D Reported are the av- erage RMSEs for CATE estima- tion for increasing dimensionality of the covariate space. Our WO- learner clearly outperforms the non- orthogonal RA learner.
(4) Low-sample setting DN: We study the performance in settings with low sample size. By decreasing the number of samples for training. we demonstrate the importance of Neyman- orthogonality with respect all estimated nuisance functions. That is, we show empirically that increasing errors in the nuisance function estimates due to decreasing sample size only propagate as lower-order errors to the CATE estimates of our WO-learner.
Results: Table 3 shows that, for decreasing sample size, our WO-learner maintains a stable perfor- mance, even as errors in its estimated nuisance functions increase. This because our learner is with respect to all nuisance functions, and, thereby, errors do not propagate as first-order biases through all time steps up to the final CATE estimate.
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Published as a conference paper at ICLR 2026
Semi-synthetic data: We analyze the performance of all intaa-leamers for increasing prediction horizons on semi-synthetic data. For this, we sim- ulate treatments and outcomes based on real-world patient covariates of the MIMIC-III dataset with intensive care unit patients (Johnson et al., 2016). Therein, we (i) show that our WO- learner can easily handle the complex- ities of observational covariates, while we (ii) ensure that we have access to ground-trutt truth values for CATE in order to properly validate our results. We provide details on the data setup in Supplement [.2 In short, the data combines all the difficulties from synthetic experiments: the data has low overlap, a complex propensity score, a complex response function, low sample size, and time-varying confounding.
A,300
7.699
5,000
4.060
3,00C
235-2 5/12
0.36- 0/33
034.8
535.4
0.25 1633
0.33
0.31::0333
333.4 5/h
0.14 6/7
036
247 6.36
0:34 103
536 0..33
6:41 2-133
330-45000 2/03
0.33 6/6
0:3.4 105
5354 635
0.13 605
WO
0.08
0.04 0.0
0.0
0.0 0.04000 000
0:3:2000
0.38.-0.07
Table Low-sample setting DA Reppoted are the average RMSEs + standard deviation for CATE estimation, and the relative improvement of our WO-learner with decreasing sample size. Due to seyman-orthogonalle with respect to all nuisance functions, our WO-leamer remains stable across all sample sizes.
Results: Table shows the results for semi- synthetic data. Our WO-learner is the only method that remains stable for all prediction horizons. This confirms that our learner can deal with all the aforementioned difficulties in the time-varying setting, and clearly outperforms existing meta-learners.
Prediction borizon
(h) RA
0.12+0.0) 0.01
0.27 - 0.04
0.40 + 0.00
(c) IPW
0.66 0.50
0.91 0.62
5.25 2 6.55
(di DR
0.20 0.11
1.57 1.79
(6) IVW
0.01 = 0.02
31.27 = 41.02
879.80 2: 1213.54
(+) WO (owrs)
0.03 + 0.01
0.15 + 0.01
0.17 + 0.07
improv.
23.1%
22.4%
28.5%
Table 4: Semi-synthetic data: Reported are the average RMSEs for CATE estimation. With all complexities in the time-varying setting combined, WO-learner is the only meta-leamnr with con- sistent performance over all prediction horizons.
We report results for real- world outcome estimation in Supplement G
Real-world data:
Ablations: We repeat the experiment with de-
creasing overlap on the dataset DD Here, instan- tiate all meta-learners with simple L.TTMs (Hochreiter & Schmidhuber, 1997). That is, we substitute the transformer instantiations for both the nuisance function and the second-stage estimator from the main experiments in Section with LSTM architectures. As meta-learners can be instantiated with any neural backbone, this shows that our main results are robust for different instantiations.
Deelgit
60
E.5 3.05
4.53 11
000 133
000
1US DAG
DAL
4.5 457-0000
135
10.00
685 8.0
L49 1.32
EJB 133
0.0
8.33
622 113
3.85
0.8 6.12
6J5
18:
KWB
12:
1.20
25. 622
721
7610
133148
110-331
D8 000
D0L mm
818-1
D0M 812
0:0 616
Iet (eleoo...1 (9)
-20%
-7.66
54.35
Table 5: Ablations: Reported are the average RMSES + standard deviation for CATE estimation
on DV, and the relative improvement of our WO-learner over the best performing baselines across
different levels of overlap.
Results: Table Showw that WO-learner again improves over all existing meta- meta-learners for decreasing overlap. This is expected and in line with our theoretical findings, which are agnostic of the neural backbone. Hence, our novel WO-learner has clear advantages over existing standard meta-learners. especially when the overlup is low (large 7).
two edge cases, simpler meta-learners may suffice: (i) when nuisance functions are known or estimated with exceptional accuracy, in which case the DR learner's double robustness can be of advantage; and (ii) when propensities remain uniformly balanced, so that exponential overlap decay occurs at a lower rate and only becomes problematic for large r. Further, is standard in the causal literature (Curth & van der Schaar 2021 Frauen et al., 2025a] Melnychuk et al. 2022 Seedat et al. 2022), our method has been validated validated mainly (semi-)synthetie data. Evaluating counterfactuals on real-world data remains an open research direction (Poinsot et al. 2025).
Limitations:
In this work, we present novel weighted orthogonal meta-learner for HTE estimation over time. Therein, we introduce novel overlap weights that counteract exploding variance of existing meta-learners in low-overlap regimes, and we provide orthogonalized population risk that is insensitive to nuisance misspecification. Our experiments confirm that our WO-learner presents an important step towards reliable decision-making for domains such as personalized medicine.
Conclusion:
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REFERENCES
Ahmed Allam, Stefan Feuerriegel, Michael Rebhan, and Michael Krauthammer. Analyzing patient trajectories with artificial intelligence. Journal of Medical Internet Research, 23(12):e29812 12, 2021.
Heejung Bang and James M. Robins. Doubly robust estimation in missing data and causal inference models. Biometrics, 61()):662-9)) 9999993,, 2005.
Samuel L. Battalio, David E. Conroy, Walter Dempsey, Peng Liao, Marianne Menictas, Susan Murphy, Inbal Nahum- -Sanni, Tianchen Qian, Santosh Kumar, and Bonnie Spring. Sense2Stop: A micro- randomized trial using wearable sensors to optimize just-in- -it-in--time--aativeee stress management intervention for smoking relapse prevention. Contemporary Clinical Trials, 109:106534, 2021.
Ioana Bica, Ahmed M. Alaa, James Jordon, and Mihaela van der Schaar. Estimating counterfactual treatment outcomes over time through adversarially balanced representations. In ICLR, 2020.
Ioana Bica, Ahmed M. Alaa, Craig Lambert, and Mihaela van der Schaar. From real-world patient data individualized treatment effects using machine learning: Current and future methods to address underlying challenges. Clinical Pharmacology and Therapeutics, 109(1)887-100, 2021.
Victor Chernozhukov, Christian Hansen, Nathan Kallus, Martin Spindler, and Vasilis Syrgkanis. Applied Causal Inference Powered by ML and AI. CausalML-book.org 2024.
Amanda Coston, Edward H. Kennedy, and Alexandra Chouldechova. Counterfactual predictions under runtime confounding. In NeurlPS, 2020.
Alicia Curth and Mihaela der Schaar. Nonparametric estimation of heterogeneous treatment effects: From theory to learning algorithms. In AISTATS, 2021.
Stefan Feuerriegel, Dennis Frauen, Valentyn Melnychuk, Jonas Schweisthal, Konstantin Hess, Alicia Curth, Stefan Bauer, Niki Kilbertus, Isaac S. Kohane, and Mihaela van der Schaar. Causal machine learning for predicting treatment outcomes. Nature Medicine, 2024.
Aaron Fisher. The connection between r-learning and inverse-variance weighting for estimation of heterogeneous treatment effects. In ICML, 2024.
Dennis Frauen, Tobias Hatt, Valentyn Melnychuk, and Stefan Feuerriegel. Estimating average causal effects from patient trajectories. In AAAI, 2023.
Dennis Frauen, Konstantin Hess, and Stefan Feuerriegel. Model-agnostic meta-learners for estimating heterogeneous treatment effects over time. In ICLR, 2025a.
Dennis Frauen, Maresa Schröder, Konstantin Hess, and Stefan Feuerriegel. Orthogonal Survival Learners for Estimating Heterogeneous Treatment Effects from Time-to-Eyent Data. In NeulPS, 2025b.
Konstantin Hess and Stefan Feuerriegel. Stabilized neural prediction of potential outcomes in continuous time. ICLR, 2025.
Konstantin Hess, Valentyn Melnychuk, Dennis Frauen, and Stefan Feuerriegel. Bayesian neural controlled differential equations for treatment effect estimation. In ICLR, 2024.
Konstantin Hess, Dennis Frauen, Valentyn Melnychuk, and Stefan Feuerriegel. IGC-Net for condi- tional average potential outcome estimation over time. In ICLR, 2026.
Oliver Hines, Oliver Dukes, Karla Diaz-Ordaz, and Stijn Vansteelandt. Demystifying statistical learning based on efficient influence functions. The American Statistician, 76(3):292-304, 2022.
Sepp Hochreiter and Jürgen Schmidhuber. Long short-term memory. Neural Computation, 9()): 1735-1780, 1997.
Andrew Jesson, Sören Mindermann, Uri Shalit, and Yarin Gal. Identifying causal effect inference failure with uncertainty-awarr models. In NeurlPS, 2020.

---

Published as a conference paper at ICLR 2026
Alistair E. W. Johnson, Tom J. Pollard, Lu Shen, Li-wei H. Lehman, Mengling Feng, Mohammad Ghassemi, Benjamin Moody, Peter Szolovits, Leo Anthony Celi, and Roger Mark. MIMIC-III, freely accessible critical care database. Scientific Data, 3(1):160035, 2016.
Edward H. Kennedy. Semiparametric doubly robust targeted double machine learning: review. arXiv preprint, 2203.06469, 2022.
Sören R. Künzel, Jasjeet S. Sekhon, Peter J. Bickel, and Bin Yu. Metalearners for estimating heterogeneous treatment effects using machine learning. Proceedings of the National Academy of Sciences (PNAS), I 166(10):415-44165, 2019.
Greg Lewis and Vasilis Syrgkanis. Double/debiased machine learning for dynamic treatment effects via g-estimation. In NeurIPS, 2021.
Rui Li, Stephanie Hu, Mingyu Lu, Yuria Utsumi, Prithwish Chakraborty, Daby M. Sow, Piyush Madan, Jun Li, Mohamed Ghalwash, Zach Shahn, and Li-wei Lehman. G-net: A recurrent network approach to g-computation for counterfactual prediction under dynamic treatment regime. In ML4HI, 2021.
Bryan Lim, Ahmed M. Alaa, and Mihaela van der Schaar. Forecasting treatment responses over time using recurrent marginal structural networks. In NeurlPS, 2018.
Alex Luedtke. Simplifying debiased inference via automatic differentiation and probabilistic pro- gramming, arXiv preprint, 2405.08675, 2024.
Haorui Ma, Dennis Frauen, and Stefan Feuerriegel. DeepBlip: Estimating Conditional Average Treatment Effects Over Time. arXiv preprint, 2511.14545, 2025.
Valentyn Melnychuk, Dennis Frauen, and Stefan Feuerriegel. Causal transformer for estimating counterfactual outcomes. In ICML, 2022.
Valentyn Melnychuk, Dennis Frauen, Jonas Schweisthal, and Stefan Feuerriegel. Overlap-adaptive regularization for conditional average treatment effect estimation. In ICLR, 2026.
Pawel Morzywolek, Johan Decruyenaere, and Stijn Vansteclandt. On general class of orthogonal learners for the estimation heterogencous treatment effects. arXiv preprint, arXiv:2303. 126677, 2023.
Jerzy Neyman. On the application of probability theory agricultural experiments. Annals of Agricultural Sciences, 10:1-51, 1923.
heterogeneous treatment effects. Biometrika, Xinkun Nie and Stefan Wager. Quasi-oracle estimation of ostmaaiono 108(2):299-319, 2021.
Judea Pearl. Causality. Cambridge University Press, New York City, 2009. ISBN 9780521895606.
Audrey Poinsot, Panayiotis Panayiotou, Alessandro Leite, Nicolas Chesneau, Özgür Simsek, and Mare Schoenauer. Position: Causal machine learning requires rigorous synthetic experiments for broader adoption. In ICML, 2025.
James M. Robins. A new approach to causal inference in mortality studies with a sustained exposure period: Application to control of the healthy worker survivor effect. Mathematical Modelling, 1512, 1986.
James M. Robins. Correcting for non-compliance in randomized trials using structural nested mean models. Communications in Statistics Theory and Methods, 233))2379--241,, 1994.
James M. Robins. Robust estimation in sequentially ignorable missing data and causal inference models. Proceedings of the American Statistical Association on Bayesian Statistical Science, pp- 6-10, 1999.
James M. Robins and Miguel A. Hernán. Estimation of the causal effects of time-ng exposures. Chapman & Hall/CRC handbooks of modern statistical methods. CRC Press, Boca Raton, 2009. ISBN 17845888865
12

---

Published as a conference paper at ICLR 2026
James M. Robins, Miguel A. Hernán, and Babette Brumback. Marginal structural models and causal inference in epidemiology. Epidemiology, (1(5):50--560, 2000.
Donald B. Rubin. Bayesian inference for causal effects: The role of randomization. Annals of Statistics, 6(1):34-58, 1978.
Nabeel Seedat, Fergus Imrie, Alexis Bellot, Zhaozhi Qian, and Mihaela van der Schaar. Continuous- time modeling of counterfactual outcomes using neural controlled differential equations. In ICML, 2022.
Yi Shirakawa, Toru; Li, Yulun Wu, Sky Qiu, Yuxuan Li, Mingduo Zhao, Hiroyasu Iso, and Mark van der Laan. Longitudinal targeted minimum loss-based estimation with temporal-difference heterogeneous transformer. In JCML, 2024.
Mark J. van der Laan and Susan Gruber. Targeted minimum loss based estimation of causal effects of multiple time point interventions. The International Journal of Biostatistics, 8(1), 2012.
Mark van der Laan and Sherri Rose. Targeted learning in data science. Springer, Cham, 2018.
ISBN
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention all you need. In NeurlPS, 2017.
Shirly Wang, Matthew B.A. MeDermott, Geeticka Chauhan, Marzyeh Ghassemi, Michael C. Hughes, and Tristan Naumann. MIMIC-extract: data extraction, preprocessing, and representation pipeline for MIMIC-III In CIIIL, 2020.
Xin Wang, Shengfei Lyu, Chi Luo, Xiren Zhou, and Huanhuan Chen. Variational counterfactual intervention planning to achieve target outcomes. ICML, 2025.
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A DISCUSSION OF PRACTICAL CONSIDERATIONS WHEN TO USE OUR WO-LEARNER VS. OTHER META-LEARNERS
While our WO-learner outperforms existing meta-leamers in low-overlap regimes, there narrow scenarios which simpler approaches may be adequate or equally effective.
(i) When nuisance functions are known or exceptionally accurate. In this edge case, the classical DR learner benefits from its double robustness property: if either the outcome model or the propensity model is correctly specified, the DR estimator remains unbiased. Our WO-learner Neyman- orthogonal but not doubly robust, in the rare scenario where practitioners have exceptionally accurate nuisance models, DR may perform similarly or slightly better. However, in realistic longitudinal observational data, nuisance estimation is high-dimensional and difficult, which makes our WO-learner the more robust and stable choice.
(ii) When treatment assignment exhibits uniformly strong overlap and prediction horizons are small. If propensities are far from the boundaries and do not degrade too quickly over time, the benefits of overlap weighting only occur for larger prediction horizons, i.e., the exponential rate at which overlap reduces is slightly lower. Hence, for small prediction horizons and very balanced overlap, this benign regime where simpler methods may be sufficient. Our experiments show, however, that realistic longitudinal datasets rarely exhibit low overlap, and hence the significant empirical advantage our WO-learner.
Beyond these specific edge cases, are not aware of meaningful practical conditions under which our WO-leamer would not be favored. In high-dimensional or sparse-data regimes, our WO-lcarner remains well behaved: (i) orthogonality makes the method robust to nuisance mis-specification, and (ii) our theoretical results guarantee uniformly bounded pseudo-outcome variance even when propensities become small. This is reflected consistently in empirical results.
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B DISCUSSION: IDENTIFYING ASSUMPTIONS
Throughout our work, we rely on the identifying assumptions consistency, sequential ignorability, and positivity. These assumptions are the standard identifying conditions in longitudinal causal inference and are used uniformly across the literature on epidemiology and biostatistics (Robins) 1986 1999 Robins et al. 2000 Robins& Hernán 2009 van der Laan Gruber 2012 van der Laan
& Rose 2018), model-based methods (Bica et al., 2020 Hess & Feuerriegel 2025 Li et al. 202 I
Melnychuk et al., 2022, Seedat et al. (022), and HTE meta-learners (Frauen et al. 2025a). In the
following we discuss their practical meaning and why they are generally viewed as reasonable in
real-world longitudinal applications.
Consistency requires that the observed outcome under the realized treatment equals the corresponding potential outcome. This is an uncontroversial assumption in causal inference. In practice, it holds whenever the treatment is clearly defined and does not vary in unmodeled ways across time or individuals. This condition is typically met in longitudinal applications such as medical dosing decisions, behavioral interventions, policy sequences, and recommendation systems, where the treatment at each step has an explicit operational definition.
Consistency:
Sequential ignorability assumes that, conditional on the observed covariate history H,, treatment assignment A, does not depend on unobserved factors that jointly affect future outcomes. This assumption is the direct longitudinal analogue of standard unconfoundedness, and is required by all existing approaches for estimating time-varying treatment effects. In practice, it is considered plausible because the covariate history H, captures the clinician's 's or decision-maker information set at the time of treatment. Longitudinal datasets in medicine, policy, and online recommendation systems typically record rich state variables, risk indicators, prior outcomes, and past responses, precisely to model how decisions are made. When these histories include the drivers of treatment choice (which modern datasets increasingly do), the assumption is regarded as reasonable.
Sequential ignorability:
Positivity requires that each treatment option has nonzero probability for the covariate histories of interest. This does not require equal or -ndeee-indeeendentt probabilities as in an RCT only that each action occurs occasionally in practice. In practice, violations of positivity show up as near-deterministic treatment rules or extremely rare treatment paths. These issues are well-know well--nowwn in the causal literature and directly motivate our contribution: estimation in settings with limited but nonzero overlap by nown-weighting sequences with very low overlap and up- up-weighting sequences with large overlap. As long propensities do not collapse to zero, identification remains valid and our method addresses the resulting finite-sample instability.
Positivity:
WO-Icarner is designed to stabilize
the same assumptions used throughout the causal inference literature and are widely viewed as appropriate for longitudinal observational data. Our method operates under this well-established framework and specifically addresses the remaining practical difficulty of limited overlap, which is a finite- sample challenge that arises even when the underlying identifying assumptions hold.
Summary: Overall, the identifying assumptions
rely
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C PROOFS
C.I CONDITIONAL AVERAGE POTENTIAL OUTCOMES (CAPOS)
We split the following section into two parts: first, we derive several supporting lemmas to prove our main results (- Lemma C. I to C.4). Then, we derive the theorem from the main paper (-> Theorem C.5 and Theorem C.6p.
C.1.1 LEMMAS (CAPOS) In order prove our main theorems for CAPOs, first introduce series of helping lemmas.
Lemma C.1. Ler
H+ (A.=at (2++7) = II j-t
Y
+
Σ 14 (H3)
++
1 =A,= (1- TT(H)
(A.=aal
(20)
(H,)
(Fx)
g
where
Tg(hg) = P(A, = ajlHH = h₂)
(21)
the propensity score, and
((++7) E Yeetr
Hetr hITTi Actr = actt
(22)
and
(g3)) = E ((ggzt())ts) Hy = haj Aj = =as]
(23)
such that
(h.) EF. (eetr(aatt)) H. = Trg
(24)
the conditional average potential outcome. Then, 78 ( (Ze+r) Neyman-orthogonal with respect 103;:,03,.
all nuisance functions 1/a { 13] wu Jz=t-
(+T
Proof. First, 7f' (7e+r) is trivially Neyman-orthogonal with respect to w as it is independent of
Second, we notice that ? (
) is the uncentered efficient influence function of TE 14 (H..) (Frauen
cct al. 2025a van der Laan Gruber 2012), which is Neyman-orthae orthogonal with respect to all nuisance functions.
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Lemma C.2. Let
++ (m
++
pi (Z( =
+
- -
w[+1(())
II (H(),
(25)
jun
j=t
where
Tz(hy) = P(A, = - h₂)
(26)
the propensity score, and
(he) p(AAett = agatt He hτ)
II k=j
क (H&)
He he]
(27)
the weight function. Then, pt (Ze+r) is Neyman-orthogonal with respect to all nuisance functions 77th fm3, M 13=t.
w Wet
Proof. First, pf (2++r) is trivially Neyman- with respect to 24 as it is independent of Second, we show that pt ( (7++r) is the uncentered efficient influence function of E w (Fra) and
1147 For this, make hence, Neyman-orthogona, with respect to the nuisance functions {T. w (j=t"
use of the chain rule for pathwise derivatives (Kennedy 2022 Luedtke 2024). First, we compute the efficient influence function of wt (he) via
IIF
Wi (h+)
(28)
1+T
=IF E II
H. = Tn]))
(29)
j=t
=IF
Σ
phhet1atr (he)
II TT (ha)) ==t
(30)
hetlit+r
1+
(+T
Σ
IF (p(he+iatt Rw))
II
Tj (hz) + p(he41447
(31)
g=t
s=t
(x)
(40)
For (*), we have that
1+ II
IF (phe+iatt (h))
(he)
(32)
j=t
t+T
-IF (p(hee+r)//((h))
(he)
(33)
1 [k,) m..)
(L Honner p(he+1147 (h))
II
(h))
(34)
p(h))
j=t
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Further, we obtain (**) via
E+T
TIF
II m3
(hz))
(35)
==t
t+T
=p(he+1:04 h1)
Σ
IF
T (hy)
T& (hxx
(36)
kサj
=p(he41047 [4)
t+
1 {
(1 (0,,=A,) - mgg)))
II
(37)
p(h))
5=
1 (h, = H1) [ (1(o)=A5)- - -m3(k)))
=p(he+10tr h4)
II kØj
Th (hx)
(38)
p(h,)
1 ( f7.) p(h+)
1 Han hT)) (16,,=A,) - (hg)) kgj
II
(
(39)
Combining both results, the efficient influence function of wi (hr) is given by
IF IF (T)(
(40)
1 (hitHtt p(he)
1+7
Σ
( Horrat)) p(ho-1:447 ha))
II 1=1
(41)
be lett
H+
Σ jun
I He M 1ol Rt)) (y)) (1(omAA)) - Fÿ mby)))
II
क (ha)
(42)
kdj
1 (1i=At)
Σ
(M p( p(he-ritt1(he)) (he))
1+.
(43)
p(he)
he-tierr
j=l
Llhrpss- Mass)((haatt I (1(1)-1s)-
(44)
x
T (he)
T (hx)
(45)
ISk<i
k>j
1 (
1++
(He+1:s he)-
II (1,) fl, he] g=z
(46)
p(h()
Llaj=At) - (H441:33))11))
(47)
m 1He h
m kzj
II
Hott:g; - hu/
(48)
tgkej
1 (h, [1) p(h))
(The) II
H Hetti he) + Σ
(Hlo==A)) - (HH
(49)
j=t
f=t
x
(H he E
m
Hittyg H.. = hn]
(50)
k>
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Using this result, we derive the efficient influence function of IE le (Ele) via
IIF 1R (FF()(F))))
(51)
Σ IF (p(he)sf (Ti)
(52)
he
IF (p(his) w (Fas) (hh,)) (wf (hi)
(53)
he
(H,, - E w (1.)) - wH((H)
(54)
1+
1+7
+ II (
+
Σ -
II
(( E
T
(Hx)
H1]
(55)
j=1
j=1
tgkej
(1(())
E (F.)
pe (Z)+r),
(56)
which concludes the proof.
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Lemma C.3. Let
H+ 1l =A
++
(1-
1 [
(A.=al
7/ (2++7) = II
Ytr +
Σ 1g (A₁) gm
(57)
j=t mj (H₂)
m3(H)
& (Hx)
where
()g) = P(A) = ag 1 Hy h1)
(58)
is the propensity score, and
= E Yeets Hetr = lEtTs Actr = actt
(59)
and
mg(h)) = E ((g Hi = hejs Aj = as}.
(60)
such that
(h.) EE. (estrlauttt) H. = hı
(61)
is the conditional average potential outcome. Then, it holds that
( Hi] (H..)
(62)
Proof.
IP 2 (7++T)
H..
(63)
1+
(A,=as}
Yetr +
Σ j=1
1+7
M (H,) (1- [Ay=o)))
[A==a)
H1
(64)
x (H₃)
(H,)
कo (Hx)
f=t
(A, (A,= Yetr
E
H2
(65)
J H3)
jut
(Hfe)
H+
(1- m3 HH,)
=di= Th Hx)
(4j (H²)
As) Hl
(66)
A==
1+T
11- |B [4p
j-1
(H.)
+
E
1 (H,)
He
(67)
(H,,
te Hxx)
++-
(1ا (H,)
(B.( +
Σ
E
1 (HL)
LAv=ai x (H+)
He
(68)
(A.)
(69)
The DR- pseudo outcomes, which are a sub-component of our pseudo-outcomes, have been introduced in Frauen et al. (2025a) van der Laan & Gruber (2012).
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Lemma C.4. Let
++
++
pi (Z(Z) = m] (m,) +
Σ - ((H1)))@++105 w]+h(H,) (,0))))==3(1))),+++()
II (H())
(70)
jun
jut
where
Tz(h,) = P(A, = a hhj)
(71)
the propensity score, and
(he) p(AAu4t = azatt He he)
II k=j
(Ha))
He = he]
(72)
is the weight function. Then, it holds that
E pt (cerr Ho = (H..)
(73)
Proof.
Pi (2(+T)
(74)
++
1+
(Hr)
+
Σ
1
1ay=
w (H₂) II (HA)) H.
(75)
j=t
j=
[Sk<j
14.7
E
3 (Hz)
11
+E
((ay=1,)) T. (1dg v (H,
II xR(((h)
H1
(76)
j=t
j=t
(Sk<j
=w{(H.) (H.)
6+
(H..
IE
IE
((aa)=A)) - - w (1t (Hzz II (g(())) i5kej
Hj}
He
(77)
5=(
++-T
(H.. + Σ
TE
E2 ((a)=AA) H. - m3 (H,)
II (FAx
(78)
-H{(H)) + -ー
E
(Rz(H,,) - (H3
II * He
(79)
(H.).
(80)
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C.1.2 THEOREMS (CAPOS)
We now prove the CAPO version of our theorems from the main paper. For both proofs, we leverage additional helping lemmas that we derived in Supplement C.I.I
Theorem C.5 (Weighted population risk (CAPO)). Ler
(Z++)) = (H,) + w/ (Hi)
(1e -1 (H())
-
(81)
Pi (Zetr)
where
++ (Z( II (Hz)
Σ
1 - ( II (Ha):
(82)
j=1
j=l
(
and
+ Eng (H)) j=t
(1 (1- [A,=a1 (H,)
(A, 7/ (217)) = II
(A,=all
Yerr
(83)
mf(H))
T (Hx)
j=t
k=t
with Zerr = (Hetr, Actr, Y.T)). Then, the population risk function
((
1
E
(Z(+r) -
(84)
E
w/
(H))
minimizes the oracle risk
(g(g))))=
E
wi
(1((F)))
(85)
E
w/ (ffe)
Proof. In order to show that L(g: n7*) and L (9:n)))) have the same minimizer we need to show that
(H.) (L)(H)) g( ((H))) 2
pt (Z(+7)
(E)(2+)) - 9
+
(86)
where C' some constant term that does not depend on g. For this, notice that
ot (ZeeT) (E)(((+))))) ((((2++)-s((t1)) s((1)))
E
(87)
pl 18 (Ze+z) ((
11. (HH, + 11 (H.) )(()))
-E
(88)
E
p8 (Ze+r) (E8(((+))
11 -if 2
21E
Pt (Zet7) (5 (ZetT) (5
1 (1 (11.)
(89)
2E
p (Z(tr) (((tt) (E (Z(+)) -
-4 (H)) (H.)
+ (Z(+7) (1((t))))((EE))) -((H))
(90)
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Here, the first two terms do not depend on g and are therefore constant. Next we focus on
-1 (H.) (( (FF())))( g(H.))
E
Pi pe (2
(91)
E
E pe (((+r)) (5:(2(+)))))) - ((((Hi))((())))
( g(Eti) Hi]
(92)
H4 (1 (H1r) + (H..)
=E
E 0c (2(( (( )
( -((ee) - (((() ( ((Ht))
(93)
Pi (((tT)
E
E w/ (Hi)
(/8 (2e4+) - -1 (H(,) g(Hft) Hep
(94)
=E
w/ (H,)
E (Z(tr)
He (H)) - g(H)))
(95)
(B)(
-0,
(96)
where the result we apply in Equation 95 follows from Lemma C,3 Finally, we focus on the last term in Equation 90 That is,
E Pi (z+++) (1E((t)) o(FF.)
(97)
E
E
Pt (Z(++) (u((Ft)) (
Hi
(98)
E2
IE
p8 (Zetr)
He
(p -
(99)
=wf
(Hte)
Bl4 (H.)) (g:""))
(100)
where the result we apply in Equation 99 follows from Lemma C.4
Hence, combining Equation
90 with Equation 96 and Equation 100 and multiplying with
1 1/ (H,,) yields
C(g:n*)) = L- (":"")) + +C,
(101)
which proves the theorem.
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Theorem C.6 (Neyman- -oomoontrrhhogonality (CAPO)). The weighted population risk
1
oe ((t) ( 9((t.) 2
D(g:nf))
E
(102)
w/
(He)
is Neyman-orthogonal with respect to all nuisance funciions v7² = { 14 wj " 18+
Jjmt.
Proof. In order to show Neymaa--rrhhogonnlliyy we first calculate the pathwise-derivatee with respect to the first argument, i.c., the target parameter g. via
DyLign nn) 19 gl
(103)
pi (2 (((47) - (o(Ht) +r(((HH) - - 2
E
(104)
dr
Pe ( (((+T)) (59 (2(+T) - [D(A)) r((((.)) ((FF))) (B(())) (B(FT)) ((FA))
2F
(105)
08 (Z (() (((+T) - s(H)) (B(Hls) =
2E
(106)
P8 (((t+)) (11((Hs) (1( + (Htr)
(2(+7)) - 11. (H(() -(((i)) (0(Hl)) - =(FF.)
2E
18 (2(+T)
(107)
(1(22t7)( - - wt (Hte) (1(())(((((1))) - - (O(E))))))
2E
(108)
Next, we compute the pathwise derivative of DyC(g:n""(15 - g] with respect to all nuisance functions 17th = {m3, MJ w watt When calculating the pathwise derivative of the functions Ie E {ut Vi pf. w/) with respect to of E ry8, we use (((gg) to make our notation more explicit to highlight which f depends on the nuisance 05.
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First, calculate the pathwise derivative of DyC(g:n") gl with respect the nuisances n/ for
j = .t...., . via
Pay DgL(gg n. m
g.
(109)
d Dg gi Lug دزز [,6...., 3 r -ni). 1............................. ........-.))6 s] 0
+
(110)
dr
d E (p mf ,(. イタ)) [u - g(Eli)
(111)
dr
+ wi (B + tr(āî - x5ه) (70 (2t + r - mU)) - 18 (Bb)) - -s(Ht)) (
(112)
E { dr Pi (2 + mラ)) r= (n((Htt) - g)( g((He))
(113)
+ d dr
w/ Wfle: + r - x3)) r=o (z((Z+4)) - (Eti))
(114)
d + wf((f (Hi)
dr 21 (Z of + +r - x9)) 1=0 } (0(EF))- - -((FF))
(115)
E
{
d
wi (H: + +
(o(HV) - ( [Hg 3. + +r(ag - -زز) 1= (1² - -( (B(EL))
イラン) -
- 5:5 (2++T) - 14. (HI,)
-
(116)
dr
E
wi
-((E)))
Hi
dr
(117)
=
(ar
d
(F + +r(, -m)) - R 78 (2++T)
Ad] -uā -A.) (B(P))) -((P)))
(118)
=0,
(119)
where the result we apply in Equation 113 follows from Lemma C.2 in Equation 115 from Lemma and in Equation 118 follows from Lemma
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Next, we compute the pathwise derivative of DyL(g: gl with respect the nuisances ná for j = tt....tt+ via
Dug DgLlgn 10- 9. -191
(120)
d DgL gi (T) W 146....,, + r(2]
119h...., (ftt...,,(it))))6 s] --
(121)
dr
d E dr
{ pf (p((Z (18 (Hei + +r(0g - 19)) s(Hi))
(122)
+ wf((H) (Z tr( 18)) (B
+ r -((1)-1)1)] (b(Ft)) o(Et))
-
1=0
(123)
E (2 (f + r -191) r=0
(124)
+ wf wF((F)) dr
76 (2 + r(is - 199) r=0
dr u (F +r(0--11000000
- (33) (B(
- -(())))(((
(125)
d E { pc (Ze+r)
dr uf + r(a pB})) -
(126)
wi (Ei) ( (Hi: + r(p اله) (o(())) -((l))
(127)
E
E
ā Pi (Z(tz)
( (Hr + r(( - nو)) 0-
Jr ui 2
(128)
with ( (+) d
dr 1i (1rs + +r(s n3)) - (0(Ft)) - -((t)) B.]
(129)
E
E {pi (z++r)
Ho dr
Mi (Ha + r(ag اووي) م r=u
(130)
[of(fte)
d wi (Eli)
Jo u8 11 r(0 -33) (a((t)) ( s((ii)
(131)
=0,
(132)
where the result we apply in Equation 125 follows from Lemma C.I and in Equation 130 from Lemma C.4
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Finally, we compute the pathwise derivative of DyL(g:n")1 with respect the nuisances wf
for j = t, .t....tt ++++ T via
Dug Do g. 0. w
(133)
Do gi (T. 1 1 U .......,u. + T - w(rr))) - sl m
(134)
dr
E
{ (2 + و(0 w99)) [1 9(Hi,)
(135)
dr
+ wl (He:w) + r(00 - w(و)) -
- (Bi) (B(BL) - -(HH))
(136)
E
dr Pi (Z + t - w(t)) r=0 (1E(H)) - g(Hr))
d
(137)
d dr
wi (Hi: + r(4 - wff) - (f -
(H.) -
(B(HF)) - -s(Ht))
(138)
w (H + r(af wff)) م-ر (8 (Z(+T) - (2 (B -O(EE))
(139)
wi W1 + +r(0g wf1) r [00l===((((_))))) -- (0111)-((110) -s((e))
(140)
E
d
wi (Hi:w} r(0] - wwf)) 1=0
E V6
(Ze++)
He - 1h (Ai) (o(H)) - g(FF))
(0(FF))
dr
(f(e)
(141)
0,
(142)
where the result we apply in Equation 137 follows from Lemma C and in Equation 141 from Lemma C.3
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C.2 CONDITIONAL AVERAGE TREATMENT EFFECTS (CATES)
We split the following section into two parts: first, as for the CAPOs, we derive several supporting lemmas prove our main results (-Lemmas C.7 to C.10 Then, derive the theorems from the main paper (~TTheorem C.IT and Theorem C.12
C.2.1 LEMMAS (CATES)
In order to prove our main theorems for CATEs, we first introduce a series of helping lemmas.
Lemma C.7. Let
a.b (2 (Z
(143)
Then, Yt' (Zerr) is Neyman-orthogonal with respect to all nuisance functions npa. r7"h U
Proof. The proof immediately follows from linearity of the efficient influence function and Lemma C.T
Lemma C.8. Let
Pt a.b
(Z =p (LH+) (H.))) w. (HT))
(144)
Then, pt ad (Z is Neyman-orthogondl with respect all nuisance functions rpa. 11a Un
we notice that P3 A.b (Z++7) is trivially Neyman-orthogonal with respect to u and u as does not dependent on Further, we show that pi (Ze+r) is the uncentered efficient influence function of E
Proof. As in Lemma C.2
[H.) and hence, Neyman-orthooond with respect to the nuisance bittr For this, we make once again use of the chain rule for pathwise derivatives (ennedy which is given by
2.5
functions W
w. a
2022
Luedtke 2024). We start with the efficient influence function of w/ (ht),
IF
w
(T+)
2.
(145)
IIF
w
(Tee)
(146)
IF
E
(H))
H. nu uf wh((he) wt (he IF E
(H₂)
H, Rd)
(147)
(*))
For both (*) and (**), we can follow the derivations in Lemma C.2 which yields
(he)
IIF
(148)
{ { w/ (he)
II
H (H++1:) hi) +
L [(a)=1,) T3 ( (H1+1,,
(149)
p(h+)
j=t
j=1
x
T (HI4I:k he EE
T (Hx)
Hesr, Hi he hi] Julthe
(150)
tSk<j
k>j
+
w/ (Fx))
wht (Tee)
II
H
Hen Tuo)
Σ
[11,=A,1 (5((Hettsss
(151)
y
j=l
f=t
Hesrig H. = Tur] Tun]}/
x II
(He h.))
(H(x)
(152)
tgkey
k>j
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Finally, we derive the efficient influence function of E (us t (Hi) via
II
TP We
a.
(FF)))
(153)
p(he)w? a. (he)
(154)
LIF' (p(hes Juse
w b.b (Fc) + p(he) HIF (wa))
(155)
be
wi B.b((H) (F.)) - IF w ..b. (F1.)
(156)
1+77
+ - wl (Efe) + II (b,) +
Σ j=t
II
(Hs) E
T (H+)
Hzg }aB(Ut)
j=t
igkej
kラj
(11
(157)
L+
HT
+ w/ (B.)) { - wf (Hi,) + II
Σ
-
II [Skc]
+k(()s) E
T (E
Hzs
j=t
-uf+. (Hf,)
(158)
=w - (F..) - EF wi (.ab(Hi)) (F1:) + (( + ((
+ -
- (..)) + P ((x++))
(159)
-w. - E wu b. (H.))
- 2w, Lbb (H.) + w. H.)p (Z (2++7) + (FI))(((
(160)
= - B B[u b (Fi,)
+ + a.b b (2e+r)-
(161)
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Lemma C.9. Let
a. -/8(2++)) (Z
(162)
for two treatment sequences aua+r. b and let
a.b (ha) 1t
= E YEst [atst++] + [rattr]
Hr = hig
(163)
be the conditional average treatment effect. Then, it holds that
Tt
a.
(2++))
Me 14 (H,)
(164)
Proof. The proof immediately follows from linearity of expectations and Lemma C.3
Lemma C.10. Let
Pi a.b
= (2++))) (H. + p. - (H.)
(165)
for two for two treatment sequences OuseT. breet,, and let
wi g.b((T))) = w/ (Tt) + (T+)
(166)
be the weight function. Then, it holds that
E
b.b (Ze++)
H1| w..b (Hi).
(167)
Proof. The proof follows from Lemma C.4
via
E
Pt a.b
(2+++)
Fl.
(168)
E
pi (Z Ja (Hle) + pi:Z2 (Hi) - w6a (Hi)
(169)
E
pi (Ze++) He w/ Hi) + E (p((z++)) Elg wi (Hi) w
(170)
-w He ((H Juel (H)) + w (H.)) (HH.) a.b (..:((H.)))
(171)
1 & (H)))
(172)
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C.2.2 THEOREMS (CATES)
Finally, we can prove the CATE version of our theorems from the main paper. For both proofs, leverage additional helping lemmas that we derived in Supplement C.2.1
Theorem C.11 (Weighted population risk (CATE)). Let
w (HL,)
(Zc+)) - a. 1%
0.6 -M b.b (H.)):
111
(173)
(2
a.
Pi
where
Pt
b.b (Z(+r) = (2 + +:p((((t))
(174)
and
71 3.b (..b(Ze (Z(ts) = 7/ (2(+7) (Ze-m)
(175)
with Zetr = (Hetr, Autri Y(tr). Then, the population risk function
C(g:naa>
abb
1
E 2.b (2(+)) (Ze+t) (1+ -((t)))
(176)
E ((H.)
minimizes the oracle risk
(gg
E
w/ p.b
(
(2g (H)) - ((B1))
(177)
E w a. (H))
Proof. The proof follows the exact same steps as for Theorem
C.5
where we can replace Lemma C.3
with Lemma C.9 and Lemma C.4 with Lemma C.10
For completeness, we repeat the derivations in the following:
As in Theorem
C.5
need to show that
(H.) [1 (H,)) s(Hr))
E
= E
+C,
(178)
where C/ some constant term that does not depend on g. For this, notice that
E
Pb b (Z.
(2tt()))((Hh)))
(179)
E
0.b Pr
(Zc- (E). - -14 (..((H.)) + pz (H.) - g s(HF.)
(180)
a.b (Ze++) (sa.)) (5a.((Z(+t)) - -1ab( 2
Pt a.b (.(+())))) (55.0) (Z.b(((e))) - 1/ a. (HH() 1 (HH))
Pt
+ +E
=C
(181)
Pr 5.5 (Z.(()())) (14. ((b.((H))) - ( 2
3.6 (Zeet) (ca.b(Ze)))) (aa(()))) (FF..)
2F
Pt
+E
(182)
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Again, the first two terms do not depend g and are therefore constant. Hence, focus
E
Pt a.h
(Z++T)
(5. (2++)) - 14 (Hr.) g(Ht))
(183)
-E
Pt. (r.0(Zz11 (Ze+T) (5x
14 1/. ((()))) Hi]
(184)
wi (H1.) |4z (Hi) +
-3
Pt (Z(tz)
(104(Z(4T) 14 (Hi)) te (Ht) (H,)
Hi
Ps (7++))
a.b
(185)
a.5 (H,)
2.. (Z+++)
a.b (Fle) g( (F+) F1.
(tt
14:
(186)
=E
W
b.b
(H))
b,b
(Ze+T)
Hg
H4
a.
(H+)) (H))))(FHl g(Ft))
(187)
=
(B.))
-0,
(188)
where the result in Equation Finally, we simplity Equation
187 follows from Lemma C.9
182 via
5.5 Z4+7 (1+ (Hab(HB)) 9(H)))
E
Pr
(189)
a.b b (Ze+z) (17 (1² - s(Et))) Hl
Pe
(190)
a. Pi (..0(22 (Ze+T)
He (1))) 2
(191)
E[w 8.6 (H.)) (()
(192)
where the result Equation 191 follows from Lemma C.10
Hence, combining Equation
182 with Equation
188 and Equation 192 and multiplying with
1 1/Elw, a.b
(Ho) yields
C(g:npab) L' (a +
(193)
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Theorem C.12 (Neyman
(Neyman-orthogonall) orthogonality (CATE)),
The weighted population risk
((g;
1
E
Pe
(Z++)) (2++)) -s(H))
n.
(194)
Wi a.b (H))
is Neyman--rrhogonal with respect to all nuisance finctiios rja.b = 118 Unp
Proof. The proof follows the proof for Theorem C.6 where we can replace Lemma
C. with
Lemma C.7 and Lemma C.2 with Lemma C.8
Again, for completeness, we provide the steps below.
In order show Neyman-orthogonality, first calculate the pathwise-derivative with respect the target parameter g via
DyL(g: " 2 gl
(195)
d E
Pi a.b
(Ze++) (E,.b)())) (((H)) + + -(((())))))(()))
(196)
dr
a.b (2,+7) (57:((Z))))
r - (o(PT)) 9(H1))
2E
Pt
(197)
2E
Pt a. (Zetr)
(g
(ca.b (50.)(Z(4r)) ((tle) -
(198)
w/ 3. (H.)
Pi B. (Ze+T)
(HH,)
a.b
7't 1z (H.)) (Ze47)
a.
=((F)) (g(Fl.) oFFF))
2E
144 146
b.b
(Z(+T)
Pi
(199)
0.b (Z+t(2 (HQ g(Hi))
(Hi) a. (2.b(Ze(4)) 14 a.b (Hi)) (g(Hi) 9((H))
(
2E
wi
(200)
Without loss of generality, we compute the pathwise derivative of DyC(g (. " to the nuisance functions r7a. The case for r/ follows completely analogously.
g] with respect
Again, for the pathwise derivative of the functions fe {n. a.5 a,b a.5 of E n7,, we use ft (:.g to make our notation more explicit to highlight which f. depends on the nuisance og.
77th Pt ,w, (.bb with respect to
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The pathwise derivative of DyL(g:n" ") g] with respect to the nuisances n3 for = t,...,, t ++7 is given by
DogDy Dyggggg n ) 9. #3 mÿ]
(201)
d Dff( 9: 11g wf. mj ببل . r xz)...., x2 m 60 g] r=
dr
(202)
d E x dr
{ 0 (Zitriz + r(a) n3)) (1t (H.)) - -s(Hl))
{
(203)
a.
(He:s] + r(( nf)) (1x : (Zetri m3 + =((a] -33) 1 (Hi)) } (0(A))- 9 (H.))
+ w/
r=0
(204)
=E ( d a.b
(Zitriz + r(a m3)) r=0 (1..) g((ti)
(205)
d
Lbb
(H(; uÿ. + -(न5 - mه)) r=u 2.b (Z(+7) - 14, 1 (Bii)
+ dr wi
(206)
+ w/ (Ht,)
dr 't (. (f m5 + r(( - xタÿ) r=0| } (B(FF.) - -
d
(207)
E
d
b.b
H m3 r(a) mو)) r=0 0 2.b - ((+) } (0(H.) -o(ta)
(208)
dr
-E
E
d
W
a.b
(Hz: m3 + -ff イ,!)
- 7/ (2.+t)
the a.5 (H.) } (O(HL) - s(Hri)
H.)
dr
(209)
E
{ (
dr
d
wi
ab
(Brimz+ + - - - (
BBaab a.
E
7 (1 (2++r)
He
-i
a.b (Bi) (0(H))- - -
a.6 (ftt)
pp
(210)
-0, where Equation 205 205 follows from Lemma C.8 in Equation 207 from Lemma C.I and in Equation 210 follows from Lemma C
(211)
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The pathwise derivative of DyL(g: 1y is given by
g] with respect to the nuisances 23 for j = t....,t t
Dug Dgg((gggg 1
160 9 13]
(212)
d Dg f gi [T]. (mj. 33. w m3 u (,o....,// r(A 19))............. (()).....((tr))
1) G - g]
dr
(213)
d x
b (2(+)) 3. (H:: + r((] - (g)) - g( g(H..)
R dr
(214)
+ wat (HH) (1..) (Zetrin1 + rr0] mf)) ,i 2 (Hr + +r(0 --111) (0(H.)) (FF))
r=0
(215)
=1 (2 Jo 22 (Hiin)) + r(āf pl))) r=
(216)
+ (Hi))
d aB (a + +r(f, -xg)) r=0
d a o Mi
(Hai + +r(n] - (1))) r=))
((((E)))(((i))
(217)
=E
PPr (Z++7)
ab
th a. (Hau) + r((s]] - m3)) r=
(218)
wi wBb(BB))) (ar 14
- a (He: + r(05- - x13)) (1())
(219)
E a. Ba (Zetr) (.
d 2. (He 13 + r(p] - nو)) -
(220)
w, "(H.))
d (Hss + r((a-- - 11))) - - (i)) (((P)) A..
Th
(221)
E
a.b Pr
(2++))
Hi
di
a. (He: + r((] (33) 1
(222)
ab (H)) dr
d a. (He + r(0g- (3) r=
- g( (((H)))
(223)
=0,
(224)
where Equation 217 follows from Lemma C.7 and Equation 222 from Lemma
C.10
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Finally, the pathwise derivative of nyth) 9l with respect the nuisances w/ for j f, t,...,t t + T is given by
Dug D, P(: n" "1 9. wfl
(225)
d Dol f gi {og) 2 19 m ا u fugg...,, ug + t(0 wg) wg)....., w..r) 60 g) r=0
dr
(226)
x
d dr
(
( a. (2+t:i5 + r((0) - wوف) (14 (H.) - g(HH.)
(A.)
(227)
+ w/
+ r(0 (Hi:w
a.b
w)t) (a.b(2 (Z++T) - wi (H1)) } ((((F))-((()))
-
(228)
r=0
d ab dr (Zet:iu3 + r(00 - wff) 1=o (1g (P))) sg(Hi))
(229)
d
-(0 ((0 -0017-00
a.
2. (H))) (++1
- -
+ dr
Wi
(230)
h Wi
(Hiiw) + r(05 - wfl) /.b (Z(+t) -1e (k.)
(B(EL) - -
E
(231)
dr
d
- a.b (Fle:w] + (aaf--++ra---@- wff)
- a.b (Zctt) - tie a. ( (((H))) - s((t))
H.
dr
(232)
a.
(Hliw + +r(0g wg9) r=o (E 2. (Ze+r)
Elg -Hi (1a)) (g(i1.) - 9 ((le)
=E
W/
dr
=M- (Btc)
(233)
0,
(234)
where Equation 229 follows from Lemma C.8 and Equation 233 from Lemma C.9
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C.3 GENERALIZING THE R-LEARNER
Remark: For single-step-ahead prediction T = O (i.e., when there is no time-varying confounding as in the static setting), the R-learner has the same overlap weights as our WO-learner for CATE.
Proof. We show how our weighted population risk function reduces for 7 = 0 and leverage previous findings on the identity of the R-learner (Nie & Wager 2021).
Notice that under our identifiability assumptions. for single-step ahead prediction 0. condition- ing on the observed history (i.e., a backdoor-adjustment)) is sufficient to adjust for all confounders, as there is no time-varying confounding.
Hence, for r = O, we can treat the observed history H, as a fixed set of covariates (typically denoted as X), the treatment variable A, E {0, 1} well as the intervention ā dr E {0, 1] as binary treatment (denoted as A and a, respectively), and the outcome Y, as the instantaneous outcome (denoted as Y). Finally, Z, summarizes all variables (H,, Ar, Yi), which corresponds to (X, A.A.Y) in the static setting (see Figure
Let 0. Then, the pseudo-outcomes and weights simplify
(Z,)
(235)
II m3 (Hz) j=t
Σ j=t
[aaz=AA) - TH. (1d,) ) W ((,)
II (H(
(236)
(gAe)
= = (Ft) + (1 (1(o-=A)) - oं( xF{ - (uft))(=ft+1 (Ht) 1skct
(237)
0
=m (Htt,
(238)
and
(H.) = E T (H+)) H1] (HH))
(239)
such that
a.b(Z.)) (Za)
P1
(240)
(241)
(8) -f (HI)
(242)
(FT.))
(243)
(244)
af
(245)
and finally
c..h (Z.)
(246)
Wt a.b (HH))
=p a. (H.))
?/t (Z.)(
-1. 12,((H))
b.b
+
(247)
Pi b. (Z,)
b (He) - T/ (11,)
=p a. (H.)
+
't (Z)((2))
0.b
-4t" (H.))
a.b
(248)
क (H+) - 72 ())))
14 (Ze))
(249)
-1 (()))
(250)
where a.1-a (Z,) simplify to the DR pseudo-outcomes for CATE in the static setting (Curth & van
der Schaar 2021 Frauen et al. 2025a). As shown by Morzywolek et al. (2023) and highlighted by
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other works (Chernozhukov al. 2024
Fisher 2024
the R-learner is overlap-weiglttd DR
learner and, hence, minimizes the loss
((g:n") E -X
I8 (X)](1)'(xx))
(251)
- (X))
Since for r O, only need set of nuisances for CATE, i.c. 17th = r/6 -/tth and it follows
that Equation 251 exactly mirrors
Fc 2 (1 - +((H) (T. (2.1-((2)) - ")
(( T (H) mp (H.))
(252)
our time-varying notation.
H
X
Y!(a|]
Y[a)
at
Figure 6: One-step ahead prediction. For a one-step ahead prediction = O, there no time- varying confounding, Hence, treat the observed history H, fixed set of covariates X, and the single intervention and instantaneous outcomes as in the static setting. Our WO-learner for CATE then simplifies the R-leamer in the static setting.
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C.4 UNIFORMLY BOUNDED VARIANCE LOW-OVERLAP REGIMES
In the following, we show how our overlap- stabilize the variance in low-overlap regimes. For this, simplify notation and focus the case. Longer prediction horizons follow completely analogously.
For our proof, we first show that the DR pseudo-outcome has conditional variance of order 1/w,""(Hl, (He), while our WO-learner uses pseudo-outcomes with uniformly bounded variance, that independent of overlap. Thereby, we demonstrate how our overlap weights stabilize estimation in lvw-overlap regimes.
Throughout, we assume bounded conditional variances of the potential outcomes:
min I Var(Yi[a]] |
Ht) S mmax < oc,
a E {0,
(253)
C.4.1 VARIANCE OF THE DR PSEUDO-OUTCOME
Recall that the DR pseudo-outcome for CATE where 7 0s
A
1- A: (Y, (Ye- (H.)).
1.0 (2.) 14 - (..)
+
T. (H.) (Y, - (H()))
(254)
T. (H.)
Lemma C.13 (DR variance inflation under low overlap). Let the potential outcome satisfy bounded conditional variance as in Equation 253 Then, the conditional variance satisfies
$ Var(n (Z,) H.) < O
min W (H,,
W.
(H,(H.
diverges at rate 1/wL (H,). In particular, as overlap (H,, - 0, the conditional variance of the DR pseudo-outcome
Proof. First, using Equation 254 and conditioning on H.,
Elt 1.0 (Zc) Hi]
(255)
A (Y, (2
A. (Yr (H()) H.
= (H+) 1º (H.) +
E
H.
E
T (H.)
x. (H))
(256)
The two expectations vanish because
E|Y, 11 (H))
He, At = 1|=0
(257)
and
E|Y, - -(((H)) He, A. 0] -
(258)
such that
Bl((2)) H1. = 14 1.0 (H..)
(259)
Now, let the correction term be
A
A- (Ye - ((()))))
U. = म7 (H, (Yr - (((HH))
(260)
so that
(2,) " + Up
(261)
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and
Varl (ar(22/(2,)) H,,) Var(U, H.).
(262)
Next, we condition further on Ar, which yields
Var(U, H1) = B Var(U; At) Hi).
(263)
A, then
U,= -Y, (H.))
(264)
and hence
Var(U: H1, A, = 1) =
(265)
If A, = 0, then
Var(U, A, 0) (
(266)
Using P(A,= H.) = (H.),
Var(U, H:) = of(Ht))
(H,,) + og(L!.)
(267)
क| (H+,)
Finally,
7| (Hi, + n (H+)
1
(268)
H.))
HH.)
m| (H,) 7 (H:)
(H)
wH,))
and applying the bounds Equation 253 yields the claim.
C.4.2 STABILIZED VARIANCE WITH OUR OVERLAP- Recall that for 0, our WO-learner minimizes by Theorem 4.3 the weighted oracle risk
C(g;n1.0 Elw; 10 (H.))
E w 1.0 (He) (n (1.(2)) g(()))))
(269)
In the following, we define the transformed pscudo-outcome and prediction as
(Z.) = (H)) g(Hi.) = / Vut 1.0 (Hi) s(H)).
(270)
Lemma C.14 (Equivalent transformed risk). For any g.
((g.n119) = E[w, (
1
172.01 (Z,) g((.))
(271)
Proof. We simply factor / ((H,) inside the square:
(H)) w/ (Hi, (nt (Zz) s(H+))² = (V (Hte) 2.0 (2.) -v (Ht) ((H)) 9(H))))
(272)
In the following, analyze the conditional variance of 2,1.0(Z.) (Ze).
Lemma C.15 (Bounded variance using overlap weights). Under the assumptions of Lemma C.13
Var 1/ (Z,) (l)) E [o a
a.s.
(273)
11,0 (Zi) is uniformly bounded and independent of In particular, the conditional variance of 7/ w (HH.)
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Proof. First, again write (Z,) 14 1.0 (Hi) + Us with BlU, H,] 0. Lemma C.13 shows that
Var(U: H.) E
2
Quax
(274)
W/ (H.))
wi wH.)
Since (2)) Vul (H.)) (Z,) (H.)) + U. with nn! w 1.0 and U,
ut 1/0 (H,) U.. it follows that
Var(5. (ar()20((2)) H₂) = Var(U:] | H.) wh (H,, Var(Ue Ht).
(275)
Substituting the bounds yields
o min - Var(Fit0022) (2,) H.) S m
(276)
as claimed.
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D DETAILS ON THE DATA-GENERATING PROCESSES
D.I SYNTHETIC DATA GENERATION
We now describe the data-generating processes for the synthetic datasets D (low-overlap regime), DR (complex propensity). 'Di (complex response function), and DDN (low-sample setting). All of them have the following general structure:
As in Frauen et al. (2025a), for each E {7, [H, N, we first simulate an initial confounder Xa [00, 1). Then, for time steps 1 1,..., T", we generate d fy-dimensional time-varying confounders via
X, = (X.l...... Xed;) (( Hx-1) +
(277)
and varying treatments via
A ~ (fae)t(
(278)
where (.) is the sigmoid function. The outcomes are then simulated via
Y f,,, + Cy.
(279)
with Ey ~ (N0.0.33 0.3 For each dataset, we simulate n' samples for training and 1000 samples for testing. For the test set, we always generate the ground-trun truth CATE of 7 stes always treat against r"-step never treat intervention.
We provide the specific configurations of fü Jä. Jy. =", dz T and n below:
(1) Low-overlap regime D'; For D we set T7 = 1, dj = 1, 5, and n² = 4000. The covariates are generated via (Y, A,-1,
0.5X,-1. the treatments via f2 (0.5X, + 0.5Y,-1 0.5( A,5(Ar Ar- 0.5)), where controls the overlap strength, and the outcomes via (A, H.) = 0.5 exp( - (A, 0.5). In order to decrease the overlap, we vary the overlap parameter 7 E (0.5, 1.0, 1.5....,
H1-1) A
(2) Complex treatment D"; For D" we set d= = 1, = 15, and n = 4000. The covariates are generated via f2 (Y,-1, Ac-1, H,-1) = 0.5X,-1, the treatments via (H. = sin (0.5X, - 0.5Y,-1 0.5(A.-1 0.5)), and the outcomes via f (A,, H,) 0.5 ex5xxp(xX?) order to increase the complexity of the treatment propensity, we increase the prediction horizon T" E (1,
0.5). In
(3) Complex response DH: For DH, we set T* TM 15, and n" 4000. The covariates are generated via A-,, = 0.5X,-1. the treatments via fo (HI,)
T
0.5 di
0.5). and the outcomes via f" (A,, H,) = (0.5(. 0.5) Σ =p=1 (0) cos(cos( X, ( 1/ dd) ). In order to increase the complexity of the response function, we increase the dimensionality d, of the time-narying confounders X, = (e,,!) via di (5, 10, 15, 20, 25, 30, 35).
p= -. 11..0,,---00.4444
(4) Low-sample setting DN: For DAV we set n. = de = 5, and T.N = 5. The co- variates are generated via 1 (Y--1, Ac-1, H.-1) 0.5X,-1, the treatments via SAN (H.) 3. 3.5 Σ / + 0.5Y 0.5(A,-1 0.5)), and the outcomes via f (A,, H.) = -
0.5 15exp(((EX) 1 cos( X., ) (2, 0.5). We vary the sample size for training the nuisance functions and second-stage estimators via V (8000, 7000, 6000, 5000, 4000, 3000, 2000).
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D.2 SEMI-SYNTHETIC DATA GENERATION
For our semi-synthetic experiments, we employ the MIMIC-III (Wang et al., 2020) extract based on the MIMIC-III dataset (Johnson al., 2016). Here, we use time-narying real-world covariates heart rale, red blood cell count, sodium, mean blood pressure, systemic vascular resistance, glucose, chloride urine, glascow coma scale total, hematocrit, positive end-expiratory pressure set, and respiratory rate. All mcasurements are aggregated at hourly levels. Further, we include gender and age as a static covariates. We summarize all covariates as X, (X,,,,..,,Xx. Then, we simulate treatments A, and outcomes Y, based on these covariates.
Our data generating process is designed to have time-varying confounding, has a complex propensity score, and a complex response function. Specifically, we simulate the treatments via
A a (Ja + Ea):
(280)
with Ea ~ (d,, H.) sin(Y - Ar-1 Ep sin (in(Xx))//d and the outcomes via fu(A,, H1) + E
(281)
with [A,, H.) = - 2 - 0.5) exp (( 0.5) sin(Y ΣΦ= cos( xt.p) and
By (0, 0.13). We include trajectories of length T 20, and simulate Puaain = 1 1500 samples for training. For evaluation of CATE, we again compare 7-step always treat against 7-step never treaf treatment intervention sequence.
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E
IMPLEMENTATION DETAILS
Implementation details: We report implementation details for our transformer instantiation in Section 5
Here, we closely follow the setup by Frauen et (2025a) (see 6)
All nuisance functions and second-stage estimators can be written regression models that take the history H, as input and learn some d-step-ahead outcome Y1+8 (e.g., for the HA-leamer, = Y
Hence, we parametrize each regression model as ge g h+)), where g) is a representation function (in our main experiments: standard transformer), and gø a read-out function standard multi-layer perceptron).
As in (Frauen et al. 2025a), we learn the propensity scores mit; in a joint model, whereas we learn the response functions μi+j and the weight functions wh+ in separate models.
Representation function ge (+): For our main experiments in Section we use an encoder trans- former Vaswani et al. (2117) with single transformer block and a causal mask to avoid look-ahead bias, as well as non non-trainable positional encodings. The transformer block has self-attention mechanism with dan attention heads and hidden state dimension dnia, followed by network with hidden layer size dæ. The self-attention mechanism and the feed-forward network use residual connections, followed by dropout layers with dropout probability 0.1, and post- normalization for regularization.
Read-out function oe (-): We use a simple multilayer-perceptronn with one hidden layer of size dmlp- ReLU nonlinearities, and either linear (regression) softmax (classification) output activation.
We summarize all parameterizations in Table To ensure a fair comparison, all nuisance models and second-stage estimators share, where appropriate, the exact same architecture and parametrization.
Runtime: For each wranformer-bbaee learner, training took approximately 1.5 minutes with Araain 4000 samples and AMD Ryzen Pro CPU and 32GB of RAM. The runtime was comparable for our WO-learner and the existing meta-lcarners.
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Estimator
Hyperparameter
Configuration
HA
RA
IPW
DR
IVW
WO
(ours)
dur
3
dhia di
30
20
/
/
4
Second-stage function
dmip Learning rate
20
0.001
Number of epochs
100
Batch size
64
dag dhid da dmip Learning rate
30
20
Response functions
0.001
Number of epochs
100
Batch size
64
dan dhid da dmlp Learning rate
3
30
20
x
X
1
1
Propensity score
20
0.001
Number of epochs
100
Batch size
64
dur thia du
3
30
20
x
X
X
X
x
IV weight functions
duip Learning rate
20
0.001
Number of epochs
100
Batch size
64
d chid da
3
30
20
X
X
X
Overlap weight functions
dmlp Learning rate
20
0.001
Number of epochs
100
Batch size
64
Table 6: Hyperparameters of transformer instantiations for the nuisance function estimators and second-stage estimators. To ensure a fair comparison, the nuisance functions for all meta-learners share the exact same parametrization.
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F SENSITIVITY ANALYSIS FOR NUISANCE MISSPECIHICATION
In Section 4 we show that our population risk is Neyman-orthogome with respect to the esitmated nuisance functions. This means that that errors in estimated nuisances should enter the final CATE estimator only at higher order. In the following, we empirically validate this property. Here, we conduct controlled sensitivity analysis in which we corrupt the estimated response-fumee functiio nuisance H4: a.6 by fixed bias and measure how this corruption propagates to the final-stage estimate of CATE,
For this, we use our data generating process D7 and fix 7 3.5 (for details, see Supplement D.I.
We fist estimate the response-function nuisance n.a and then construct perturbed versions
(.)(() = m4 (..
(282)
where å E {0.0, 0.1,0.,.. 1.0] is constant additive bias. Therein, we mimic systematic mis- specification of the response function. For each value 8, we retrain the final-stage CATE model using the corrupted nuisance while keeping all other nuisance components fixed. The results are reported in Figure 7
0.12
Average RMSE for CATE estimation
0.08
0.1
0.3
0.5
0.6
0.7
Corruption of response function estimate
Figure 7: Sensitivity of CATE estimation with WO-learner to corruption of the response-function nuisance. Reported are the average RMSE of the final CATE estimates against the injected bias.
The results show that even strong corruption of the response-funcion functionn nuisance leads only relatively low errors in the final CATE estimates. The error grows slowly and approximately linearly. This consistent with the higher-onder influence from our Reyman-orthogonallig result (Theorem 4.5):
the population risk is insensitive to first-order perturbations of nuisances such μ4 2.5 and errors enter only through second-order terms. other words, the final estimator remains stable even under sizeable misspecification of the response-function nuisance.
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G REAL-WORLD OUTCOME PREDICTION
In this section, we report the performance of our WO-learner on factual outcome prediction using real-world data. This experiment not designed evaluate causal validity; instead, it serves as standard sanity check to confirm that the model components used in our meta-learner behave sensibly on real outcome trajectories. Such auxiliary diagnostics are commonly included longitudinal causal studies, even though they do not speak to counterfactual accuracy.
In Table 7 we report the performance of the propensity-based meta-leameen and the HA baseline performance. For this, we use the MIMIC-III dataset (Johnson et al. 2016, Wang et al. 2020 The outcome variable of interest is diastolic blood pressure, and we consider mechanical ventilation as the treatment variable. We further use 19 time-varying covariates such as cholesterol, respiratory rate, heart rate, and sodium, and further include gender as static covariate for predicting the factual outcome. All measurements are aggregated at hourly levels.
We emphasize that factual outcome prediction is not the task our method is designed for, nor is it the target of any time- varein meta-learner that adjusts for causal, timevarying confounding. Predicting observed outcomes requires no adjustment for future treatment sequences and can be solved by standard regression on the observed history. Accordingly, the HA baseline performs best, exactly as expected: for factual prediction, a simple history adjustment is the statistically optimal approach.
The purpose of this experiment is different: to verify that the WO learner, which is primarily designed to estimate counterfactual quantities, still produces stable and reasonable predictions when applied to real-world outcome trajectories. It is simply confirmation that the nuisance components, final stage estimates, and representation layers behave sensibly on real data.
Unlike other propensity-basee bbased meta-learners, which exhibit instability or variance inflation even in this predictive setting, the WO-learner remains consistently well-behaved across all horizons. This fully aligned with our theoretical analysis: the weighting mechanism stabilizes estimation in the presence of small propensities, which affects not only causal adjustment but also any learning task involving propensity- based pseudo-outcomes.
Prediction horizon
HA
IPW
DR
IVW
WO (ours)
0.708 = 0.022
5.627 + 8. 49898
1.601 = 1.038
53,200 1 98.958
1.077 +:2 0.025
2
0.774 = 0.023
3.419 + 4.767
1.255 - 0.305
0.305
37.408 + 36.641
1.079 : 0.022
3 0.822 = 0.024
3.729
+ 5.094
3.978
+ 5.208
21.151 + 40.098
1.087 : 0.027
4
0.869 0.024
1.426 + 0.674
5.556 = 8.939
22.128 + 32.211
1.099 + 0.006
Table 7: Reported are the RMSEs for factual outcome prediction. We emphasize that factual outcome prediction is not the task our WO-learner is tailored for. Yet, different from the other propensity- based methods, it has very robust performance over all prediction horizons. In line with theoretical considerations, we conclude that the HA learner has the best performance since regressing on the observed history simple history-adjustment- is sufficient for factual outcome prediction.
This experiment is not intended as evidence of causal validity real data. Counterfactual treatment effects over time cannot be validated on observational data (Pearl 2009 Poinsot et al., 2025). as at least one of the required potential outcomes is never observed. Therefore, the correct and widely accepted evaluation strategy for time-varying CATE/CAPO estimation consists of synthetic and semi-synthetic experiments where ground-truth effects are known, which the protocol follow in our main results in Section
47


Reviews:
[{"review_id": "8GUSry5SIA", "reviewer": "Reviewer_u6pF", "summary": "The paper proposes an overlap-weighted orthogonal (WO) meta-learner to estimate time-varying heterogeneous treatment effects (HTEs) under low-overlap conditions. The framework aims to stabilize inverse-propensity-based estimators by re-weighting high-overlap regions.", "questions": "- The paper claims to estimate HTE but reports only CATE in the experiments. There is no discussion of heterogeneity across subgroups or covariate-dependent variation in effects. It may mislead readers about what “HTE” means in this context.\n- Please see weaknesses.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- The paper proposes a model-agnostic framework for adjusting time-varying confounders.\n- The paper provides a theoretical foundation for orthogonality.\n- An implementation code is available for review.", "weaknesses": "- The claim that weighting by overlap improves estimator stability is weakly justified. By emphasizing high-overlap regions, the learner avoids extreme inverse-propensity weights but can ignore potentially outcome-informative regions. Is there a trade-off between propensity and outcome predictions?\n- The motivation behind the study problem (treatment effect estimation over time) needs to be further clarified, particularly in relation to its real-world applicability. It is not evident whether the problem is testable, whether the authors have empirically validated it in real applications, or whether the underlying assumptions commonly hold in practical settings.\n- The experimental validation is primarily based on synthetic data. Even in the semi-synthetic MIMIC-III experiment, both treatments and outcomes are simulated, so there is no demonstration of applicability to real observational data. The study does not evaluate whether estimating CATE over time provides practical benefits or is actually necessary or useful in real-world contexts. The study shows performance under a controlled scenario rather than demonstrating practical utility.\n- The authors explicitly note that “factual outcome prediction is not the task our method is tailored for,” yet give no alternative validation criterion for real-world use. How would it be verified in practice? The authors should add a discussion and limitations on this point.\n- The baselines are narrow, limited to RA, IPW, DR, and IVW  from [1]. The paper omits several relevant baselines for CATE over time, e.g., G-Net [2] and G-Transformer [3].\n\n[1] Frauen, D., Hess, K., & Feuerriegel, S. Model-agnostic meta-learners for estimating heterogeneous treatment effects over time. In The Thirteenth International Conference on Learning Representations.\n\n[2] Li, R., Shahn, Z., Li, J., Lu, M., Chakraborty, P., Sow, D., ... & Lehman, L. W. H. (2020). G-Net: a deep learning approach to G-computation for counterfactual outcome prediction under dynamic treatment regimes. arXiv preprint arXiv:2003.10551.\n\n[3] Hess, Konstantin, Dennis Frauen, Valentyn Melnychuk, and Stefan Feuerriegel. \"G-Transformer for Conditional Average Potential Outcome Estimation over Time.\" CoRR (2024).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "FGgNvE8aTz", "reviewer": "Reviewer_gNhd", "summary": "The paper proposes an over-weighted meta-learner to estimate HTE in a very challenging time-varying scenario with a treatment sequence scenario. It also develops a new risk esimation to reduce the effects of first order bias in the estimation. The paper provides detailed theorectical analysis. The empirical results show that the proposed method achieve the best performance compared with other adjustment method.", "questions": "- In table 4, why the IVW performance get dramatically incresed when the prediction horizon increases? In the paper [1], the performance looks normal when $\\tau=2,3$.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "- Compared with other meta-learners in this field, the study proposes a novel method to address the challenges of other learners in the low overlap scenario, which is common in the time varying treatment assignment strategy. \n- The overlap weighted orthogonal \n- The study has conducted both theorectical and empirical analysis to demonstrate the advantages of their proposed method.\n- The results demonstrate dramatical improvement of the performance in Table 2. And the performance is uniformly the best over all the sample sizes.", "weaknesses": "- Can you please revise the writing of the problem setup? Maybe provide some examples to illustrate what the treatment looks like. Based on my understanding of your problem, the two sequences should be a list of 1 or 0, correct? i.e. $a = [1, 0, 0, 1], b = [0, 1, 1, 1]$\n- One very relevant study as mentioned in the paper is the IVW method. As stated in the IVW paper, the framework is a composition of IVW and DR learner [1]. The paper provides very brief description in line 116-125. I wonder here is the IVW refers to the same model as the IVW-DR learner in the original paper or just the IVW only.  \n- Another concern about the time-varying treatment strategy is that, the proposed method only considers confounders happen before $t$. But in the real-world setting, the propensity scores are usually depend on what happened during $t:t+\\tau$. I know it makes the problem much harder, but it is very realistic in healthcare domain. \n\n[1] Frauen, D., Hess, K., & Feuerriegel, S. Model-agnostic meta-learners for estimating heterogeneous treatment effects over time. In The Thirteenth International Conference on Learning Representations.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "gVFQSnHNTC", "reviewer": "Reviewer_jn4J", "summary": "This paper proposes a new framework, Overlap-Weighted Orthogonal Learning (OWL), for estimating heterogeneous treatment effects in time varying settings where covariate overlap between treatment groups decreases exponentially with time horizon. The method incorporates the a propensity/overlap weights that up-weights samples with a higher probability to having the treatment sequence of interest. Moreover, the proposed estimator is Neyman orthogonal which makes the estimator insensitive to nuisance estimation error.", "questions": "- Do we expect the performance of the proposed estimator to deteriorate more that the DR-learner when propensity is hard to learn, as the weights also rely on the propensity estimates?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Clear motivation and the proposed estimator addresses the problem of insufficient overlap. \n- The estimator is flexible and is robust to nuisance errors as well. \n- Performed comprehensive experiments that addresses different settings. Results demonstrates the effectiveness of the proposed method at addressing the different issues discussed in the paper.", "weaknesses": "- While the paper showed that the proposed population risk is Neyman orthogonal, papers on mete-learners usually also provide error analysis and show that the error terms from the nuisance functions are higher order, which is not presented in the paper. \n- The main innovation is to address the problem of limited overlap, so it would be nice to have some theorems that showcase how this estimator have better behavior (e.g. variance) in those regimes.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "7wOTsoV7Qw", "reviewer": "Reviewer_hGFP", "summary": "This paper tackles the challenge of estimating HTEs in time-varying settings, where treatment sequence overlap decreases with longer horizons. The authors propose a Weighted Orthogonal (WO) meta-learner, which introduces an overlap-weighted, Neyman-orthogonal population risk function to focus learning on regions with sufficient treatment overlap. This design stabilizes estimation variance and enhances robustness to nuisance model misspecification. The method is model-agnostic and demonstrated with transformer and LSTM backbones, showing improved reliability and accuracy over existing time-varying meta-learners.", "questions": "**CATE vs. CAPO Weighting:** Why is the overlap weight for CATE (Eq 10) defined as the *product* of the individual propensity weights ($\\omega^{\\overline{a}}\\omega^{\\overline{b}}$)? Why not estimate the CAPO for each arm separately (using the CAPO propensity weight $\\omega^{\\overline{a}}$) and then simply subtract them? What is the theoretical motivation for this specific product-based weighting for CATE?", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "* **Problem Significance:** The paper addresses a highly relevant and challenging problem at the intersection of causal inference and time-series analysis. Estimating HTEs over time is crucial for personalized medicine, and the issue of exponentially decreasing overlap is a core, practical barrier that the paper directly confronts.\n* **Methodological Novelty:** The proposed WO-learner is methodologically novel and sound. The key idea of designing a population risk function that explicitly minimizes an *overlap-weighted* oracle risk, while simultaneously enforcing Neyman-orthogonality, is the primary technical contribution.\n* **Theoretical Guarantees:** The method is supported by strong theoretical guarantees. The proof that the weighted population risk is Neyman-orthogonal with respect to all nuisance functions (including the newly defined weight functions) is a non-trivial and important result.\n* **Experimental Design:** The paper presents a broad set of experiments, including four synthetic datasets designed to isolate specific challenges (low overlap, complex nuisance functions, small sample size) and a semi-synthetic experiment based on real-world MIMIC-III covariates.", "weaknesses": "* **Marginal Absolute Improvement:** While the paper reports large *relative* improvements the *absolute* improvements in RMSE are often in the $10^{-2}$ magnitude. The practical significance of such a small absolute gain is questionable, especially given the significant added complexity of estimating the new WO pseudo-outcomes and weight functions.\n* **Flawed Real-World Validation:** The validation on real-world data is fundamentally flawed. The authors state this is a \"real-world outcome estimation\" task, which is a standard *prediction* (supervised learning) task, not a *causal inference* (HTE estimation) task. Demonstrating that the WO-learner is \"not worse\" than baselines on a predictive task provides **no evidence** of its efficacy for its stated purpose (HTE estimation). This experiment does not support the paper's core claims and raises questions about the method's applicability.\n* **Omission of Key Baselines:** The paper omits a crucial and common baseline: a standard DR learner or IPW learner with **propensity score truncation (clipping)**. This is a very common heuristic to handle low-overlap regimes. It is unclear if the WO-learner's complexity is justified over this much simpler, strong baseline.\n* **Lack of Intuition for Key Formulas:** The derivation of the key components, particularly the WO pseudo-outcomes $\\xi_{t}^{\\circ}$ and the weighting term $\\rho_{t}^{\\circ}$ in Definition 4.2, lacks intuition. They appear to be complex formulas derived to make the orthogonality proof work, rather than being motivated by a clear, first-principles-based explanation. This makes the method difficult to understand and build upon.\n* **Unclear Practicality of New Nuisance Function:** The new weight function $\\omega_{j}^{\\overline{a}}$ (Eq 11) is itself a complex expectation of products of future propensity scores. The practical challenges and stability of estimating this new, non-trivial nuisance function (especially for long horizons $\\tau$) are not sufficiently discussed.\n* **Missing Discussion of Failure Cases:** The paper does not adequately discuss the potential failure cases or limitations of the WO-learner. When would this method *not* be preferred? How does it behave in very high-dimensional or extremely sparse data settings? A \"Limitations\" section is missing.\n* **Overall Impression and Presentation:** Overall, while the problem is valid and the method is technically correct, the contribution feels incremental. The solution is an orthodox application of established causal inference principles (weighting, orthogonality) to the time-series setting, but the practical gains appear marginal, and the real-world validation is not fit-for-purpose. The work lacks a \"surprising\" element. Furthermore, the paper's presentation is overly dense, and it notably lacks a \"Conclusion\" section, which weakens the paper's summary and impact.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)