Uncertainty-Aware Systems for Human-AI Collaboration
Authors: Vasco Pearson
Jean V. Alves
Jacopo Bono
Mario A. T. Figueiredo
Pedro Bizarro
Venue: Accepted by TMLR ()

Abstract: \textit{Learning to defer} (\textbf{L2D}) algorithms improve human-AI collaboration (\textbf{HAIC}) by deferring decisions to human experts when they are more likely to be correct than the AI model. This framework hinges on machine learning (\textbf{ML}) models' ability to assess their own certainty and that of human experts. L2D struggles in dynamic environments, where distribution shifts impair deferral. 
We argue that robust HAIC in dynamic environments requires uncertainty-driven policy switching rather than reliance on a single deferral strategy. To operationalize this principle, we introduce two uncertainty-aware approaches that estimate epistemic uncertainty to guide the deferral policy choice. Both methods are the first uncertainty-aware approaches for HAIC that also address limitations of L2D systems including cost-sensitive scenarios, limited human predictions, and capacity constraints. Empirical evaluation in fraud detection shows both approaches outperform state-of-the-art baselines while improving calibration and supporting real-world adoption.

Published in Transactions on Machine Learning Research (03/2026)
Uncertainty-Aware Systems for Human-Al Collaboration
Vasco Pearson
wasco.pearsonn@feeaaaaccomm
Peedzai
Jean V. Alves
dean.alves@feedaaat
Heedzai
Jacopo Bono
www.ssboooooooooo Maccpo.bono@feeedaaae com
Feedzai
Mário A.T. Figueiredo
mario. merro.fuuueired@tecciie
Instituto Superior Téénico, Universidade de Lisboa Instituto de Telecomunicações
Pedro Bizarro
aidrobbiaarr@@@eezza..oo com
Feedzai
Reviewed on OpenReview; https: openreview. net/ fttl/ffrmm? id- PERYCNNBl
Abstract
Learning to defer (L2D) algorithms improve human-Al collaboration (HAIC) by deferring decisions to human experts when they are more likely to be correct than the AT model. This framework hinges on machine learning (ML) models' ability to assess their own certainty and that of human experts. L2D struggles in dynamic environments, where distribution shifts impair deferral. We argue that robust. HAIC dynamic environments requires uncertainty- driven policy switching rather than reliance on a single deferral strategy. To operationalize this principle, we introduce two uncertainty-aware approaches that estimate epistemic un- certainty to guide the deferral policy choice. Both methods the first uncertainty-awwr approaches for HAIC that also address limitations of L2D systems including cost-sensitive scenarios, limited human predictions, and capacity constraints. Empirical evaluation in fraud delection shows both approaches out outperform stale-of-the-arl baselines while improv- ing calibration and supporting real-world adoption.
1 Introduction
While artificial intelligence (AI) and machine learning (ML) models rival human expert performance and efficiency in various domains, including finance (Khandani et al. 2010 Awoyemi et al. 2017 criminal justice (Goel et al. 2021), and healthcare (Gulshan et al. 2016 Somanchi et al. 2015 Esteva et al. 2017), their use in high-stakes settings still faces challenges. Their reliance on training data constrains their scope and they often struggle to generalize under dynamic conditions, such as in adversarial settings finance (Perdomo) ct al. 2020 Lunghi al.] 2023). or under concept drift (Gama al.) (014)). Furthermore, their predictions often lack transparency, posing diffieulties interpretability and trust (Saeed & Omlin 2023 Gohel et al. 2021 As result, their applicability in automated decision-making systems remains constrained.
In contrast, humans can access external information, adapt to changing environments, and provide causal reasoning and explanations for decisions (Gopnik & Wellman 2012). These altributes make human ex- perts indispensable scenarios where interpretability, adaptability, and broader contextual awareness are required. Consequently, combining the complementary strengths of humans and ML models through human- AI collaboration (HAIC) systems has emerged a promising approach to address the limitations of fully automated systems (Dellemmann et. al. 2019
De-Arteaga al.) 2020

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Optimizing the allocation of decisions humans or Al major challenge in HAIC. The simplest approach, rejection learning (ReL) (Chow) 1970; Hellman 1970; Cortes et al. 2016 Geifian & El- 2017). addresses this by deferring to human experts instances with high model uncertainty. However, an optimal solution would involve taking human cortainty into considcration, assigning instances to humans only when they are likely to perforrmm the model. Learning to defer (L2D) aims to achieve this by estimating the performance of both the model and the human decision-maker, thereby enabling a better allocation of tasks
to the decision-maker most likely to succeed (Madras et al. 2018 Mozannar & Sontag 2020] Mozannar
et al. 2023 Verma & Nalisnick 2022 Verma et al. 2023 Hemmer al. 2022 2023
Charusaie et al. 2022
Although L2D improves decision-making performance, it struggles in dynamic environments. L.2D methods rely on ML models to estimate the correctness of each decision-maker, whether human or Al. However, when faced with distributional changes, these models often become unreliable (Gama et al.) 2014). Beyond performance degradation, a critical issue that they can exhibit high confidence in their predictions on out- of-distribution (OOD) samples (Hein et al. 2019), which in an L2D system leads suboptimal assignments. In contrast, ReL, which leverages uncertainty measures (Hendrickx el. al., 2024 can detect. such changes inference time, deferring novel instances to human experts, thus ensuring robust handling of OOD data.
Unlike current ML models, humans can adapt to changing environments, a crucial advantage that HAIC systems should be designed to leverage. Ideally, one would rely on the models whenever they reliably perform well, which requires that model uncertainty be estimated in a way that allows humans to intervene when necessary. However, current L2D approaches remain limited in this respect, as they focus on obtaining calibrated performance prediction, without incorporating uncertainty estimation into the deferral process. Integrating uncertainty estimation techniques with optimal decision allocation in HAIC is nontrivial, since this combination introduces new theoretical and practical challenges and tradeoffs, which are not present when each is studied in isolation. To address this gap, we show that robust human-Al collaboration under distribution shift requires uncertainty-driven policy switching rather than reliance on a single deferral strategy (Figure 1. Instead of committing to either pure L2D or pure rejection-based deferral, HAIC systems must adapt their routing policy across uncertainly regimes. We implement this principle through two uncertainty- aware methods for HAIC and provide an empirical study of their advantages and limitations.
High
Deferral Policy
Epistemic Uncertainty
Rejection Learning
Uncertainty-Aware L2D
Leamning to Defer
Low
Figure 1: Uncertainty-drive policy switching in human-Al collaboration.
In addition to challenges posed by dynamic environments, T.2D systems have failed to address other practical constraints {Leitão et al. 2022 Alves et al.) 2024), including human work capacity limitations, reliance on extensive expert predictions for training, and limited consideration of cost-sensitive scenarios. While prior
work (Hemmer et al.) 2023 Tailor et al. 2024 Alves et al. 2024h has addressed some of these issues, our approach accounts for all of the aforementioned constraints, enabling robust and practical deployment.
In summary, this work makes three key contributions to HAIC:
We demonstrate that robust human-Al collaboration under distribution shift benefits from uncertainty- driven policy switching rather than reliance on single deferral strategy. We show that effective HAIC systems must adapt their routing policy based on epistemic uncertainty and distributional context.
systems that operationalize this principle: (i) an uncertainty-awaat L2D framework and (ii) a hybrid system combining conformal prediction with L2D, both explicitly ac- counting for misclassification costs and human capacity consts
We introduce two uncertainty
We provide an extensive empirical evaluation in a realistic, cost-sensitive fraud detection setting using a benchmark dataset (Alves et al.) (2025a) with synthetic expert decisions modeled after real analysts. Across variations in noise, data availability, and work capacity constraints, both systems consistently improve performance over state-of-the-art baselines.
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2
Related Work
ReL and uncertainty estimation. The simplest HAIC approach in the literature is ReL Chow 1970:
Hellman 1970 Cortes et al., 2016 Geiffnan & El- Yaniv, 2017), which often involves having the model abstain from predicting in high uncertainty cases (Hendrycks & Gimpel, 2017). Hendrickx et al. (2024) categorize rejection into two types: ambiguity rejection, which enables the model to abstain in scenarios where the target values are inherently ambignous, and novelty rejection, where the model refrains from predicting for instances that deviale significantly from the training data. These types of rejection align with different types of uncertainty: aleatoric uncertainty, which stems from irreducible randomness within the data (such class overlap), thus leading to ambiguity rejection; epistemic uncertainty, which ariscs from incomplete knowledge, whether due to distribution shifts uncertainty about the model fit to the data, leading to novelty rejection (Hüllermeier & Waegeman 2021]. Several studies have proposed methods to distinguish these types of uncertainty for applications like ReL. (Senge et al.) 2014]) and active learning (Nguyen et al. 2019). Generative models have been proposed as an intuitive way to quantify epistemic and aleatoric uncertainty [Hechtlinger et al. 2018 Sun et al. 2023 Postels et al. 2020), by leveraging estimates of the density function p(æ), where æ is a feature vector, to decide whether input points are located in regions of high or low density, in which the latter serves as proxy for high epistemic uncertainty.
Learning to defer. The L2D framework was introduced by Madras et al. (018) to address the shortcom- ings of confidenco-based ReL, which does not take into account the human decision makor's 's performance. Leveraging not only class labels but also predictions from the downstream human decision-maker, à classifier and a deferral mechanism are trained, meaning L2D considers both model and human errors when optimizing decisions. Mozannar & Sontag (2020) highlight that the loss function proposed by Madras et al. (2018) is not consistent, proposing a consistent surrogate loss that includes separate class for deferral. Verma & Nalisnick (2022) critique the T.2D surrogate loss developed by Mozannar & Sontag] (2020) for miscalibration issues, introducing one-vs-all (OvA) approach that improves calibration by training the classifier and de- ferral model independently. In the multi-cxpert setting, Keswani et al. (2021) extend L2D to assign instances to multiple experts, while Verma et al. (2023) propose a new consistent and calibrated loss, generalizing the loss of Verma& & Nalisnick (2022) to handle multi-expert scenarios.
However, L2D methods face several limitations in practical deployment (Leitão et al. 2022 They lack adaptability in dynamic environments, where data distributions can evolve over time due to concept drift (aama et al. 2014),, or in performative prediction (Perdomo et al. 2020). Changes in distribution degrade the performance of the ML models used in L2D to estinate the correctness of the decision-makers, which leads to sub-optimal assignments. Moreover, these frameworks rely heavily on labeled data sourced from all experts involved, rendering them impractical in real-world scenarios due to high labeling costs. Most existing L2D mothods also do not consider cost-sensitive scenarios where misclassification costs can vary. Finally, these mothods often neglect human work capacity constraints al. inference time.
Recent advancements in L2D research have aimed address some of these practical constraints, particularly the challenge of learning with limited expert data (Charusaic et al. 2022 Hemmer et al. 2023 Tailor et al., 2024h. Alves et al. 2 focus on cost and capacity constraints, which are crucial for real-world applications. Despite these advances, L2D research has not focused on its limitations in dynamic environments. Since human experts adapt to changing conditions, HAIC systems can mitigate this, but doing so requires reliable uncertainty estimates to defer cases where models may fail.
Synthetic human expert predictions. Datascts with human predictions are scarce and collecting anno- (ations is often prohibitively expensive. Prior work resorts simulating human decision-maker by injecting label noise. Verma & Nalisnick (2022), Mozannar & Sontag (202)), and Charusaie et al. (2022) use CIFAR-10 [Krizhevsky] 2012) to create experts with high accuracy on some classes while deciding randomly on others, while Keswani et al. 2021 simulate racially biased experts by varying error rates across groups.
While these methods provide a simple way to introduce heterogeneity across experts, they have a major limitation: their accuracy is determined solely by class labels or a single feature, ignoring the broader set of input features that influence real expert maaisi. To the best of our knowledge, the most principled approach to synthetic expert simulation in L2D is the OpenI.2D framework (Alves et al. 2025a
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This framework addresses the aforementioned limitations by generating synthetic expert predictions through instance-dependent label noise, where the probability of error is function of instance features and additional information available to decision-makers (e.g,, a risk score provided by a separate ML model (De- Arteaga ct al. 2020 ) This provides a more realistic approximation of human decision-making behavior. By applying this Tramework a public fraud detection dataset, Alves et al. (2025b) produce the Financial Fraud Alert Review (FiFAR) dataset, which contains predictions from synthotic fraud analysts over 30K instances.
Crucially, this dataset was constructed with the explicit goal of realistically simulating the behavioural properties (e.g., interrater agreement, consistency, performance distribution) of team of highly skilled experts. These synthetic experts are supported by decision-making literature and were modeled after real financial fraud analysts. By adopting this dataset, our empirical evaluation of L2D methods is, to the best of our knowledge, based on the most realistic set of expert decisions to date.
3 Uncertainty-Aware L2D
To address the limitations of T.2 systems in dynamic environments, we propose an uncertainty-aware L,2D framework that improves how correctness probabilities are estimated for both the classifier and human ex- perts. Deferral decisions in L2D rely directly on these estimates: instances are assigned to the socision-make predicted be most likely correct. When distribution shift occurs, standard ML models can become over- confident OOD instances (Hein et al. 2019), leading to unreliable correctness estimates and suboptimal assignment decisions. To mitigate this, incorporate density-aware modeling (Bui & Liu 2024) into the L2D framework (Figure 2. By using density information as proxy for epistemic uncertainty, the system attenuates confidence in low-support regions the feature space. This produces more reliable correctness estimates under distribution shift, thereby enabling more robust deforral decisions and improved export modeling when labeled data limited.
Uncertainty-Aware L2D
Optimize
Assignments
Expert model
Expert model
ML model
Capacity
New alert
Constralntss
Density function
Density function p(z; σ))
Denstly function
p(z; a)
p(z; Ø)
Figure 2: Uncerlainty-awarc L2D.
Density-softmax. Density-softmax Bui & Liu 2024) can be viewed data-dependent temperature scaling mechanism: logits are attenuated in low-density regions, increasing predictive entropy. This behavior qualitatively approximates epistemic variance shrinkage in Bayesian models, whore uncertainty over pa- rameters reduces confidence away from observed data. Unlike Bayesian methods, however, sensity--ofttmax achieves this effect deterministically without modifying model weights. It consists of a feature extractor, a density estimator based on normalizing flows (NF) (Dinh al. 2017). and classifier. The feature extractor f maps input æ into a latent space representation z, where the NF model estimates the ligeliood log pgzp(z;)) a:) under the training distribution, with representing the model parameters. The NF model is optimized via maximum likelihood estimation (MLE) and provides exact log-likelihoods. Importantly, Bui & Liu 2024) show that the density-softmax approach achieves lower test-time latency than stale-of-the-art uncertainty estimation methods, making lightweight addition to an L2D system with minimal compu- tational overhcad. To avoid numerical issucs from unbounded log-likelihoods, we scale them following Bui & Liu 20244] at test time, log- logliikelssodds divided by the maximum training log-likelihood and then min max normalized to 1). The scaled likelihood p(z;o) a) adjusts the classifier g's logits, modifying the predictive probability follows:
ply = i|x: = exp(p(z; a) gx(x))
(1)
exp(p(z0 a) (x())))
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where 9, is the logit of classifeer for class i. For OOD instances in low-density regions, this adjustment scales down the logits, resulting in predictive probabilities that reflect higher uncertainty and improve calibration. These calibrated probability estimates are then used in the optimization step described in Section 5
L2D Formulation. Our L2D system is built using the OvA framework introduced by Verma et al. (023 which aims to minimize the 0-1 loss defined as
(h-r = (m m [r(x)) = 0J L[h(z) # y] Σ 1[((x) = =] Mmy + x
where h X' +V the classifier, r: X + (0, } is the rejector, and my is the prediction from expert E (l,..., J}. When r(æ) O, the classifier l makes the decision, and when r(æ:) = j, the decision is deferred to the j-th human expert. Verma et al. (2023) show that minimizing the 0-1 loss leads to the following Bayes optimal classifier and rejector:
1'(x)= = arg max P(y x), DEY
(2)
0 P(y - (x) x)) > P x)
r (x)
(3)
arg max P(y my x3) otherwise, (E(O.....))
where Py(y | æ)) is the probability of the label under the data generating process and P(y = my | x)) is the true probability that the jth expert is correct.
To approximate this solution, the OvA framework constructs the classifier and rejector using |J]| functions gk : X' + R, where each function gk is related to the probability of the instance belonging to class k, and J functions gıjj X' + IR related to the likelihood of each expert j E J making the correct decision. These D[+J functions are combined in the OvA surrogate loss, defined as
VOLA= = (1))(())]+ +
Σ V'
(1-99 + Σ + (1-91
Tmm (0)0) ((-g1,(()))).
(4)
where my represents the j-th expert's decision, and 4: {+1} x R + R. is a strictly proper binary surrogate
loss function.
Verma et al. (0223) prove that the minimizer of the pointwise inner V V VovA-rish is composed of the minimizers of the inner Q-risk for each binary classification problem, meaning each Jy can be trained independently on its corresponding OvA binary classification task by minimizing proper binary loss (such as the log-loss), and calibrated estimates for given instance's probability of belonging to each class k are given by Φi (oy); where 15-1 is the inverse link function for the proper binary surrogate loss t (in the case of the log-loss, v is given by the sigmoid function o). Similarly, each J1,j can be trained independently on the subset of data where predictions from expert j are available, and calibrated estimates for the probability that expert j will predict correctly on instance are given by 4b (11.)))))
Aleatoric and Epistemic Uncertainty. By using the density-softmax approach, each of the |D++J binary classifiers is paired with density function to improve uncertainty estimation. The allocation of instances to decision-maker relies these correctness estimates, which must be calibrated and reflect instanco-specific unccrtainty. Equation I contains both alcatoric and epistemic uncertainty. To disentangle these, the likelihood value from the density model must. be separated from that of the main classifier, allowing it to represent epistemic uncertainty. In regions of high epistemic uncertainty, is reasonable to downweigh the classifier's predictions, as the classifier relies solely on training data and may not generalize well to OOD instances. Human experts, however, can adapt, learn, and access additional information not available to machine learning models, meaning we can expect them to outperform the classifier OOD
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instances. Consequently, use the human expert's average correctness the training data as proxy for their expected performance. Specifically, for instances with high epistemic uncertainty, the model blends the predicted logits of the binary classifier for expert j (ā1.) with the expert's average probability of correctness on the training data (fj.vg), using the donsity score p(z; a) from the normalizing flows model (p(2;a) 1]). The adjusted logits are defined as
a)Z + (1- p(z; (Fg.v
(5)
where a represents the sigmoid function, and are fed into the softmax function in Equation This adjustment ensures that the model reflects a more realistic estimate of expert performance in high epistemic uncertainty instances, balancing the model's own estimates with the historical expert performance.
4 Conformal Prediction for HAIC
In this section, we introduce our second approach to uncertainty-awan HAIC, which follows a different design principle. Whereas the previous approach focuses on providing calibrated estimates of correctness improve assignment within L2D framework, here we explicitly separale in-distribution and OOD instances and apply different deferral strategies to each. We hypothesize that, while L2D methods perform well on familiar, in-distribution cases, these should avoid handling instances lying outside the training distribution. For such OOD cases, the models' probability estimates can be poorly calibrated, resulting in suboptimal decisions. In these scemarios, human experts are better suited to make predictions, as they are able to generalize and adapt by leveraging broader contextual knowledge. Furthermore, in high-stakes environments, it may preferable, or even required, that OOD instances be reviewed by human experts to ensure accountability and explainability. To meet these requirements, we propose a system that defers OOD instances to human experts through ReL, while relying L2D for in-distribution cases (Figure
Rejection Learning
C(x)
0
OO G Human experts
Optimize Assignments
High Epistemic Uncortainty
New alert
C(x) +
Capacity Constraints
Density Bensstty-Based Conformal Prediction
4TB Learning Defer
Low Epistamic Uncertainty
Figure 3: Conformal prediction for HAIC.
Density-based conformal prediction. We use density-based conformal prediction (Hechtlinger et al. 2018 Messoudi et al., 2020) as a proxy for epistemic uncertainty by identifying inputs with low support under the training distribution as OOD. Generative density models distinguish high- and low-density regions, with low density commonly associated with OOD and increased epistemic uncertainty (Hüllereeier & Wacgeman, Hechtlinger et al. 2018 Messoudi et al., 2020). This links density-based uncertainty estimation to outlier detection and rejection learning, where models abstain in regions of low support. Importantly, conformal prediction guarantees coverage only under exchangeability, and these guarantees do not extend to arbitrary distribution shift, mcaning that conformal prediction is used here as a consorvative deferral signal. Limitations are discussed Section
2021
Density-based conformal prediction uses a two-step training process involving proper training set Drr (X"r, y*r) and calibration set Deal = (X yoal). First, class-conditional density estimator p(xly) is built using D The calibration set is then used to determine the empirical 1 quantile á, of the density values for each class,
hy = sup 1:
Σ
(p(a, 2 -0
(6)
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where I(Ø(2;ly)) 2 t) equals 1 if the estimated probability p(a,ly) is no less than t, and 0 otherwise, D {(,, 36) Deal 1/4 y) is the subset of calibration examples in class y, and ny is the cardinality of Dout This quantile effectively acts as a threshold, allowing the model to define, for any new observation Tn a prediction set
(an+ = (v E (( 2 Gg).
(7)
which includes all classes y for which the observed density is above the threshold. Hechtlinger et al.
(2018)
show that [P(y E C. (x)+ (1 - ai) a + 0 as miny"ly oc, ensuring the asymptolic validity of the model. The training and prediction algorithms for density-based conformal prediction are described in Section B of
the Appendix. At inference, the additional computation is limited to evaluating density scores and comparing them to pre-computed thresholds for each class. binary settings, this adds negligible overhead, but in multi-class scenarios with many labels (e.g., image classification), the cost scales with the number of classes and can become more substantial.
Aleatoric and epistemic uncertainty. Figure 3 provides a schematic representation of our system. Instances with high epistemic uncertainty, which deviate significantly from the training distribution, are classified as empty sets and deferred to human experts. For non-empty predictions, which indicate in- distribution instances, the L2D system (as previously formulated in Section 3 assigns instances by using the correctness estimates for both the ML model and human experts. The assignments are then optimized taking into account human work capacity constraints (Section 5
5 Cost and Capacity Constraints
Cost-sensitive learning. We adapt methods to cost-sensitive scenarios in which each instance i incurs misclassification cost c, Following Zadrozny et al. (2003) Elkan (2001) and Alves et al. (0024), we replace the standard objective of minimizing the expected error rate (m,))> / with minimizing the expected misclassification cost Em,y..s. [c [Aaa) where D is the data distribution and e is the instance-specific cost. To achieve this, Zadrozny et al.] (2003) show that we can weight each instance proportionally to its cost by redefining the data distribution as
D(I, v) Eewold D(., c),
c
(8)
and that, under this modified distribution, the expected error rate is
1
E E [n( Ee-pl ee (n()))ll
(9)
Thus, minimizing the error rate under ò is equivalent to minimizing the expected misclassification cost under the original distribution D. In practical terms, this entails modifying the empirical loss function C =EE, ((h(::).)) where E is the pointwisc loss, by weighing cach instance by its associated cost (Zadrozyy el al. 2003 Elkan 2001), resulting in loss function aligned with the cost-sensitive objective C= --> (2(()))),,)) M1). To implement this approach in our OvA framework, we modify the standard log- loss functions of each of the DJ++J binary classifiers. The weighted loss functions are described in detail in Equations 13 and 15 in the Appendix.
Capacity constraints. We address human work capacity constraints in both assignment systems. For the density-softmax approach, which is a pure L2D system, we apply the strategy proposed by [lves et al. (2024), optimizing assignments under capacity constraints. For the conformal prediction approach, we extend this framework by creating a method that dynamically balances L2D with ReL while respecting capacity limitations. From decision-theorretee perspective, this optimization corresponds to maximizing expected utility under uncertainty. Each action consists of routing instance either to the model or to a specific human expert. The estimated probabilities of correctness serve as instance-wise expected rewards, while misclassification costs and expert capacity constraints define the feasible decision space. The resulting objective can therefore be interpreted as a constrained expected-risk minimization problem, where the system selects the allocation policy that maximizes expected correctness subject to limited human resources.
Rather than processing the entire dataset at once, we impose constraints over batches of instances. This approach aligns with practical scenarios where data is processed in batches and allows the system to adapt
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dynamically to varying workload demands. We define batch vector b that assigns each instance i to batch b containing nh instances, and a human capacity matrix H, where Haj denotes the maximum number of cases that can be deferred to expert j within batch b. Each instance a; is subject to an action ag E J+...,,++[]) with an associated estimated probability of correctness P(correct Iz, 0z), obtained via the OvA classifiers. II a, = + 1, class y is automatically predicted with an estimated probability of correctness of P(correct 24 az) = (gy); while a, = j [ indicates deferral to the jth human expert with an estimated probability of correctness of ((correct|/z; /2: a.) = (g),)) A set of na assignments can then be represented as a matrix E 10 +_]])=((+(()))) x(++D')) where ara denotes whether action a, is taken for instance i. We can then frame the assignment optimization as
J+Y Σ
A = argmax
P(correct|ag; 0z) Ai,
(10)
AE(0.11"0x(H+1)
subject to two constraints: (1) Em Ar.: = Ho.a: ensuring each expert meets his capacity, and (2)
Edtt"1 Aia, = 1 to ensure each instance has a unique assignment.
For the conformal prediction approach, balancing between L2D and ReL necessary. The indicator function (a:))40 indicates whether instance will be assigned through L,2 ReT., based on the coverage level a for the conformal prediction method. We then optimize this balance alongside the assignment matrix A, with the following objective:
J+DI Σ
(A", aaaa)=
argnax
Σ>
le)())) P(correct vi, a.) + Iou(m))= Pccorrett Xuain, an) ALa.-
(11)
This optimization is subject to the same constraints mentioned above, and an additional constraint ensuring that when ReL is applied (x;) = 0). the instance is deferred to a human expert, preventing OOD) instances from being handled by the model. Additionally, we downweigh model predictions for some instances (through wy) based on the coverage level a at which they fall into the empty set, and if the proportion of empty set predictions excceds the expected rate from training data. The downwcighing is described in detail Section C This adaptation allows the system to respond distribution shifts by prioritizing expert work capacity for OOD instances when required. We solve the assignment problems 10 and 11 using the CP-SAT solver from Google Research's is OR-Tools (Perron & Didier).
6 Experimental Setup
The code used for the experiments is available at Systtess--o--uuaa--------------- Caanman-A--Colabben AlCColabbootiion also publicly available (Alves el al.] 2025a).
Reproducibility.
https:/ http:///ggtuuuuooo/eeeoo foodzai/ http//fceaaainnnnaanttttyyyeot
The dataset is
Dataset. As discussed in Section D datasets with real human predictions are scarce and collecting expert annotations is expensive. OpenL.2 (Alves al. 2025a) addresses this by providing open-source frame- work for generating highly customizable synthetic experts with control over feature dependence, bias towards protected attributes, and performance levels. In this work, we use the FiFAR dataset (Alves et al. 2025a generated with OpenL2D from the publicly available bank-account-fraam (BAF) dataset (Jesus et al. 2022 FIFAR simulates a team of fraud analysts whose decision- decision-making properties were validated against the lit- crature and compared to real analysts. In particular, the framework captures instance-dependent expert accuracy, heterogeneity across experts, and realistic inter- and intra-rater variability documented in high- stakes decision-making (Alves et al., 2025a). However, the current setup does not model expert adaptation over time, and while expert behavior is influenced by the model's score, other external factors affecting real-world decisions are not explicitly represented. Our experiments use team of five analysts, for which the dataset provides predictions on all 30K instances flagged as fraudulent by a fraud detection model, rep- resenting an "alert-review" scenario where analysts review high-risk applications. Each instance contains the original BAF fcatures, expert prodictions, and the fraud model's score. The BAF datasct spans 8 months: the first 3 were used in Alves et al. (2025a) train the fraud detection model, while the flagged 30K instances come from months 4-8 and comprise the FiFAR dataset.
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Misclassification costs. In account opening frand detection, a positive prediction leads to application rejection, while a negative prediction results in account opening. Consequently, misclassification costs differ, as false positives (rejecting legitimate applications) lead to customer loss, whereas false negatives (accepting fraudulent applications) may result in financial losses for the bank. Consequently, fraud detection requires balancing the costs of false positives (cpp) and false negatives (<EN), making commonly used metrics like accuracy inadequate. In our cost-scnsitive task, assuming no cost for correct classifications, the objective function to be minimized is the expected misclassification cost,
1 N N
(Ally, = 0 A 9. = 1] Ily: = 1 8. = 0]),
(12)
where À = CFP/CFN- As only the ratio À is relevant for minimization purposes, we choose to arbitrarily set CFp = À and CpN =1 for our misclassification cost re- re-weighting approach. For the FiFAR dataset, À is derived from the alert model threshold selected under the Neyman Pearson criterion, which maximizes recall at a 5% false positive rate, yielding 2 = 0.057 (Alves et al. 2025a).
Noise injection. The two foundational works in density-baset conformal prediction (Hechtlinger et al. 2018 Messoudi al., 2020) evaluate robustnnss by injecting Gaussian noise to simulate distribution shifts. The work introducing density-softman (Bui & Liu 2024) similarly applies Gaussian noise among other perturbations in its empirical evaluation. Such noise- based stress tests are standard in uncertainty estimation, where the goal is to assess performance and calibration on borderline or clearly OOD instances (Hein et al., 2019: Hendrycks & Gimpel| 2017 Depeweg et. al. 2018). In our case, the introduction of contrllled Gaussian noise allows isolating the contributions of each system component, including calibration and performance from density modcls, and OOD detection and deferral from conformal prediction. We modify the test set (last month of data) by int roduiingg noise to 20% of instances under three configurations: low, medium, and high noise. For each configuration, numerical features are standardized, perturbed with Gaussian noise (o 1.0, 1.5, 2.0), and mapped back to the original scale, with discrete values rounded and bounded features clipped. Categorical and binary features are randomly switched with probabilities 0.3, 0.4, and 0.5, respectively. To account for statistical variation, each configuration is repeated five times with different seeds.
Data availability and capacity constraints. We simulate scenarios with variable amounts of expert labels across four data conditions: all instances labeled by all experts, a common but unrealistic assumption in prior T.2D methods (Verma al., 2023 Hemmer et al. 2022), and subsets where experts label only 1 1/5, 1/20, or 1/40 of the data. These subsets are randomly distributed across experts using five random soeds per condition. In both systems, the expert-specific models are trained on the subset of data with labels for that expert, and in the density-softmax approach, the same subsets train the density models. We impose uniform work capacity constraints on experts by varying deferral rates (10%-50%) to evaluate the system's 's ability to manage OOD instances across four experimental variables: noise (low, medium, high), number of experts (1-5), deferral rates, and data availability. This leads to 300 different test settings, so results are analyzed for key subset of representative settings to assess the system's robustness under these constraints.
Baselines. We consider three baseline approaches. First, for the L2D baseline, we implement the OvA L2D algorithm by Verma et al. (202)) using LightGBM (Ke et al. 2017) models for each binary classification task, omitting the distance-aware awareness feature to isolate the impact of our proposed contributions. This setup also serves as a baseline for the conformal prediction approach, as the same L2D method handles instances not identified as OOD. Second, in the ReL baseline, density- conformal prediction measures uncertainty to docide whether to defer instances to human experts, deferring randomly when predicted as the empty set and assigning the remainder to the ML model, with coverage level a selected to match expert work capacity. This baseline serves measure of the effectiveness of conformal prediction in detecting and deferring OOD instances, independent of any optimization in the expert assignment step. Third, random assignment baseline allocates a random subset of test instances to experts, ensuring capacity constraints are met.
System Training, Both systems share a single MLP trained on the data from months 4 to to minimize weighted log-loss, with month 7 used for validation. The MLP's penultimate dense layer used as a feature extractor to map inputs into a continuous latent space for density estimation. In the density- based conformal prediction method, class-conditional densities are estimated using kernel density estimation
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(KDE) (Rosenblatt] 1956p. and empirical 1 - quantiles computed calibration data from month 7. For the density-softmax approach, RealNVP (Dinh et al. 2017) models are trained on the extracted features to estimate likelihoods, using subsets of the data labeled by each expert to reflect specific data availability scenarios. Both systems use LightGBM (Ke et al. 2017) models for the binary classifiers in L2D: the main classifier is trained predict the true labels, while expert-specific models estimate correctness. Because human experts often have access to the alert model's score, the human correctness models include as an additional imput feature. All classifiers are trained minimize the weighted log-loss, described in Section A.1 Details the training and hyper-paramen selection are available in Section A of the Appendix.
7
Results
Calibration improvements from the density-softmax approach. To assess how the density model interacts with predictions, we first extract the features from the penultimate layer of the MLP trained for feature extraction and project them in two dimensions with t-SNE. The first panel on the left of Figure shows the resulting feature map in the high-noise test setting, where in-distribution and OOD instances are clearly separated. The second panel displays density scores estimated by the normalizing flows density model, confirming the model's ability to capture the data likelihood under the prior distribution. The last two panels show the effect on classifier predictions: raw LightGBM probabilities (third panel) can be overconfident on OOD regions, but after adjustment with density scores (forth panel), probabilities in those regions are pulled closer 0.5. This demonstrates how the density-softman approach improves calibration by adjusting predictions data unlikely to belong to the training distribution.
Incorporating density models into our T,2D) classifiers consistently enhances calibration across all settings. Figure 5 reports the mean expected calibration error (ECE) with 95% confidence intervals, accounting for the randomness in noise injection and training set selection. Here, data availability is the fraction of training data with given expert's predictions: 1/1 means full coverage, while 1/40 means each expert labels only 1/40 of the data, and their models (both LightGBM and density) are trained on that subset. The figure shows ECE for the models that predict expert correctness, which are used in our system (Section 3 to assign instances to the most reliable expert. Calibration of these models is crucial, since we directly compare their predicted probabilities of correctness to decide which expert should handle a given instance.
t-SME: Original vs. Notsy
Density
Probabiliies
Adiusted Probabiities
20-
62-
UGB80 Probuooiyy
-25
-4
Nalry Frad
Ofgind
10-
42-
-6
caspiod inul
-00-
Figure 4: Effect of density-softmax on predictions under high noise. From left right: (1) t-SNE visual- ization of extracted feature representations showing separation between in-distribution and OOD instances; (2) density scores estimated by the normalizing flow model, with low-density regions corresponding to OOD data; (3) raw LightGBM predicted probabilities, which are overconfident in OOD regions; (4) adjusted prob- abilities after density-soflmaxx scaling, where predictions in low-density regions are moderated loward 0.5.
The results show that without density models, ECE increases sharply noise grows. On the other hand, incorporating density models significantly reduces the growth of ECE, creating widening gap in performance as noise increases. The benefit is especially pronounced under higher data availability, where having more expert predictions allows for more accurate modeling of human behavior and better estimation of densily scores, which in turn improves discrimination between in-distribution and OOD data. This improvement arises because density models balance the expert's predicted probability of correctness with their average correctness on the training data in regions of high epistemic uncertainty (as detailed in Section 3), yielding more reliable predictions for instances that deviate from the training distribution.
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Data availbilit: 1/40
Data availability 1/20
Data availability 1/5
Data avai wwility 1/1
5.75
12.5
0.50
Weut Distance Awarenes, With Distance Awareness
6.00
Wiot Distance Awareneso Distance Awareness
Wjout Distance Awarcness
5.50
With stance Awareness
5.75
12.0
5.25
8.00
3.50
11.5
ECE
1.75
ECC
5.00
11.0
7.50
5.00
7.25
4.50
10.5
Wiout Distance Awarencss With Distanze Awareness
7,00
4.75
4.25
4.50
none
low
medium
high
nome
loW
medium
high
none
IDW
medium
high
none
low
medium
high
Notse
Nolse
Nolse
Noise
Figure 5: Calibration of expert correct models with and without density awareness. Mean ECE with 95% confidence intervals across different noise levels and data availability settings. Data availability denotes the fraction of training instances labeled by each expert (1/1 = full coverage; 1/40- = sparse labeling).
Epistemic uncertainty and calibration in the conformal prediction approach. In our conformal prediction approach (Section 4 empty-set predictions are used as proxy for high epistemic uncertainty, controlled by the coverage level a: higher a yiclds more empty sets. These instances are handled via ReL strategy, while non-emply predictions are assigned through L2D. Ideally, classifiers should exhibit low ECE on non-empty predictions (in-distribution instances, where probability estimates should be reliable) and higher ECE on empty-set predictions (OOD instances, which are deferred to human experts). To examine this, Figure d shows the ECE of instances predicted as empty sets across coverage levels a. The right plot averages results across expert models with 95% confidence intervals for the mean. ECE is initially high small and decreases as a increases across all noise settings. This pattern is consistent with the empirical behavior of density-based conformal prediction: OOD instances tend to receive low density scores and are therefore classified as empty sets, enabling deferral in shifted regimes.
These rcsults highlight the need to choose an optimal coverage level a to balance OOD detection against errors on in-distribution data. In practice, this means optimizing the use of L2D on in-distribution instances and deferring OOD cases to human experts. Consequently, jointly optimizing a and the assignment matrix (Equation 11 is necessary. Results on tuning a are presented in Section D of the Appendix.
Importantly, conformal prediction guarantees coverage only under exchangeabilityy and its behavior under distribution shift is not theoretically guaranteed. In settings where shift corresponds to movement into low-density regions, this mechanism performs well in practice, as observed here. However, in more complex or multimodal distributions, or under conditional shifts that preserve density while altering label structure, this correspondence may break down and requires empirical validation.
Classifier h ECE on Empty Set Preds
Expert Models ECE on Empty Preds
20
low notse medium noise
14
low noise medium
high noise
85
ECE
ECE
1.0
10
0.1
0.2
Alpha
Alpha
Figure 6: Calibration behavior on instances predicted as emply sets by conformal prediction. Left: classifier ECE on empty-set instances across coverage levels a. Right: average ECE of expert correctness models on empty-set instances (shaded regions denote 95% confidence intervals). Smaller a values identify only extreme OOD cases (higher ECE), while increasing a includes more moderately shifted instances, redueing ECE.
Misclassification cost analysis. We evaluate the misclassification cost across different deferral stratogies and experimental settings. Table compares five strategies (Density-Softmi Softmax (DS), Conformal Prediction (CP), L2D, ReL, and random assignment) showing representative settings from the 300 test cases described
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in Section 6 covering three noise levels (low, medium, high), two deferral rates (20% 40%), 1, or 5 experts, and two data availability scenarios (full data and one-fifth). Each setting is run five times with distinct seeds for data sampling and noise generation, and results are reported with 95% confidence intervals for the mean. Tables with the remaining 300 settings are available at lhttps:/ htttss///mooymmooo..ooo.occccce /unnnrrrinnnyyy
Table 1: Misclassification cost for the representative settings. The best result is in bold and the second best is underlined.
Setting
Deferral Strategy
Noise
NE
DR
DA
CP
DS
L,2
ReL.
Random
low
1
20
1/1
4.81
0.11
4.81 + 0.17
5.09 + 0.18
5.11 + 0.07
5.20 + 0.15
low
1
20
1/5
4.85
i 0.18
4.83 + 0.22
5.18
t: 0.16
5.11
i 0.07
5.23 i 0.11
low
1
40
1/1
4.42
= 0.09
4.48 - 0.11
5.00
+ 0.18
4.77 - 0.07
4.97 = 0.13
low
1
40
1/5
4.40
+ 0.18
4.41 1 0.09
4.89 1 0.15
4.77 1 0.07
4.99 1 0.09
low
3
20
1/1
4.78
+ 0.13
4.72 + 0.11
5.20 + 0.13
5.14 + 0.10
5.25 0.12
low
3
20
1/5
4.91
0.10
4.90 + 0.18
5.23 1 0.11
5.14 + 0.11
5.28 0.18
low
3
40
1/1
4.40
- 0.07
4.35 + 0.09
5.11 + 0.13
4.77 + 0.07
5.12 - 0.16
low
3
40
1/5
4.53
+ 0.28
4.45 + 0.28
5.03 + 0.16
4.76 + 0.08
5.16 + 0.15
low
5
20
1/1
4.76
0.15
4.70 + 0.09
5.20
0.13
5.09 + 0.06
low
5
20
1/5
4.85 1: 0.10
4.84 + 0.16
5.19 1 0.14
5.12 1 0.04
5.25 1 0.12
low
5
40
1/1
4.46
4.44 + 0.09
4.71 0.13
4.79 + 0.09
5.11 - 0.11
low
5
40
1/5
1.481.011
4.42 + 0.16
4.80 0.10
4.79 1 0.11
5.07 1 0.18
medium
1
20
1/1
4.82
+ 0.07
4.96 + 0.09
5.32 1 0.08
4.85 1 0.06
5.39 1 0.03
medium
1
20
1/5
4.82 = 0.09
4.97 + 0.15
5.37 + 0.06
4.85 + 0.06
5.46 + 0.15
medium
1
40
1/1
4.41 1 0.05
4.61 0.10
5.20 1 0.08
4.49 + 0.09
6.13
medium
40
1/5
4.46 + 0.12
4.60 + 0.12
5.08 + 0.11
4.49 + 0.09
5.17 0.24
medium
3
20
1/1
4.85 = 0.09
4.91 = 0.08
5.42 0.06
5.01 = 0.13
5.47
medium
3
20
1/5
5.00 1
5.08 1 0.19
5.39 1 0.08
4.99 + 0.14
5.50 0.14
medium
3
40
1/1
4.41 + 0.08
4.52 1 0.08
5.29 1 0.08
4.55 1 0.11
5.39
0.13 0.13
medium
3
40
1/5
4.56 1.56=000 0.19
4.70 - 0.28
5.20 + 0.15
4.50 = 0.09
5.40 0.12
medium
5
20
1/1
4.86 1 0.07
4.94 + 0.13
5.41 + 0.08
4.86 + 0.05
5.51 0.08 0.08
medium
5
20
1/5
4.86 +
5.00 + 0.09
5.36 + 0.14
4.87 + 0.07
5.47 + 0.11
medium
5
40
1/1
4.37 = 0.08
4.51 - 0.07
5.03 + 0.08
4.54 + 0.11
5.35 0.14
medium
5
40
1/5
4.47 = 0.12
4.60 = 0.16
5.06 + 0.16
4.53 + 0.12
5.27 0.13
high
1
20
1/1 4.62 + 0.07
5.00 1 0.09
5.44 0.13
4.86 1 0.07
5.50 0.14
high high 1
1
20
1/5
4.65 = 0.14
4.97 = 0.19
5.49 0.13
0.13
4.86 + 0.07
5.48 0.10
40
1/1
4.21 = 0.08
4.53 1 0.08
5.23 1 0.13
4.39 1 0.04
5.25 1 0.22
high
1
40
1/5
4.22 - 0.10
4.56 + 0.13
5.15 + 0.15
4.39 + 0.04
5.25 0.17
0.17
high
3
20
1/1
4.74
= 0.18
5.50 1 0.13
5.09 + 0.19
5.53 1 0.16
high
3
20
1/5
4.81
-
5,15
-
5.49 1 0.16
5.09 + 0.15
5.56 - 0.15
high
3
40
1/1
4.29
+ 0.09
4.53
+ 0.09
5.41 + 0.13
4.46 + 0.09
5.40 1 0.17
high
3
40
1/5
4.29
0.14
4.65
= 0.28
5.32 0.23
4.47 + 0.06
5.42 = 0.08
high
5
20
1/1
4.72
+ 0.15
5.04
1 011
5.54 1 0.18
4.85 1 0.09
5.61 1 0.13
high
5
20
1/5
4.75
0.17
0.17
5.49
+ 0.11
4.86 + 0.10
5.59 = 0.17
high
5
40
1/1
4.25
0.10
4.57
1 0.14
5.01
1 0.13
4.42 1 0.07
5.37 1 0.19
high
5
40
1/5
4.25
+ 0.10
4.56
- 0.13
5.10 1 0.17
4.44 + 0.06
5.41 1: 0.17
Across all noise levels, both DS and CP outperform the baselines on average. In low-noise scenarios, DS consistently achieves the lowest misclassification cost, benefiting from its gradual adjustment of probability estimates: by slightly adjusting overconfident predictions in uncertain regions, DS produces more accurate estimates of expert correctness and thus better assignment decisions. Under medium and high noise, CP becomes the strongest strategy. Its hard cutoff mechanism deferring all instances deemed OOD to ex- protiiees clear advantage when noisy data is easier to identify, while DS may still allow some OOD instances to be handled by the classifier. The most informative baseline is ReL. Both ReL and CP use density-based conformal prediction to flag empty-set (OOD) cases, but differ in how the coverage level a is set. ReL fixes a to match expert capacity, rejecting as many instances as possible up to that limit. CP instead optimizes a to balance assignments between L2D and ReL: more OOD data pushes assignments toward ReL, while more in-distribution data favors L.2.. This optimization enables CP to interpolate be- tween the two strategies depending on the data distribution, and the CP-Red performance gap therefore quantifies the added value of assignment and coverage intimiztiion. On the other hand, standard T.2D lacks
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density information to assign instances correctly, highlighting the importance of having calibrated estimates of correctness in T.2D. The DS vs. T.2D comparison shows that incorporating density scores improves expert assignment in the presence of OOD data.
Sensitivity and robustness. Although the two systems rely on different mechanisms, they share the same structural principle: combining an uncertainty signal with deferral policies. Their consistent improvement over L2D and ReL suggests that performance gains stem from uncertainty-guided policy selection rather than any single implementation detail. Regarding hyperparameters, the conformal approach is primarily sensitive to the coverage level a, which controls the balance between routing strategies. However, across roughly 300 experimental settings, the optimization procedure consistently identifies appropriate values (sce Appendix DJ. For density-soflmaxx, there are no dedicated hyperparameters beyond those of the underlying ML models. The only additional design choice is the weighting between predicted and average expert correctness, but this varies naturally across settings since each condition assumes different labeled data subsets per expert. Performance therefore does not hinge on a fixed weighting configuration.
Computational considerations. Both approaches introduce moderate additional training cost due to density estimation, while maintaining lightweight test-time overhead. In the uncertainty-aware L2D system, density-softmax augments each OvA correctness model with a density estimator, requiring one additional density model per expert (trained on the subset of data labeled by that expert). At inference time, the added cost is limited to computing a density score and applying a simple logit scaling, and overall complexity scales linearly with the number of experts, as in standard OvA L2D. In the conformal prediction approach, the additional component is density- based conformal prediction, which requires training class-conditen conditional density models and computing empirical quantiles with the number of classes, as each class requires its own density estimator and threshold. At inference, computation consists of evaluating density scores and comparing them to class-specific thresholds.
calibration set. In multiclass settings, the cost scales linearly
8 Conclusions and Future Work
We showed that in dynamic environments, human-Al collaboration (HAIC) systems must adapt their rout- ing policy based on epistemic uncertainty, rather than rely on a single deferral strategy. We introduced two uncortainty-aware approaches that outperform traditional learning-to-defer (L2D) and rejection Icarn- ing (ReL) methods. Both approaches incorporate uncertainty estimation to improve robustness under dis- tribution shift while accounting for cost sensitivity, limited expert data, and human capacity constraints. Empirical results demonstrate that uucertainty-drivee routing enables the system to select, for each instance, the appropriate deferral policy according to its estimated epistemic uncertainty.
Although our experiments focus on frand detection, the proposed framework is domain-agnostic in the sense that it combines an uncertainty signal, deferral policies, and capscity-constrained assigmment. These components are generalizable in other high-stakes settings such as healthcare triage and risk assessment. Adapting the approach to a new domain mainly requires selecting an appropriate uncertainty proxy for the data modality, and defining domain-specifie costs and capacity constraints. We scope our empirical claims to the tabular alert-review selting, and validating performance in other domains remains future work.
Beyond this, several extensions merit further investigation. Incorporating dynamic expert feedback, for ex- ample by retraining on newly labeled cases to account for evolving expert strengths, would better reflect real-world human AI collaboration. Moreover, uncertainty-driven deferral policies directly affect workload distribution and responsibility allocation. If low-density regions correlate with specific subpopulations, sys- tematic deferral may concentrate human scrutiny or delays on those groups. Future rescarch should therefore analyze deferral patterns and explore fairness-awer aware constraints in deployed HAIC systems.
Acknowledgments
M. Figueiredo was partially supported by FCT (Fundação para a Ciência a Tecnologia). under project CTD/50008/225 1200008/20250222 Instituto de Instiuttt Telecomunicações, with DOT hattps://doi..o http:///...rrr/000454/////000000
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A Training details
A.1 Learning Defer
For the MI classifier h, we employ a LightGBM classifier (Ke et al. 2017), trained on the alorts raised from months four six and validated on month 7. We perform hyperparameter optimization using TPE (Akiba et al.j 2019), running the optimization process for 300 trials with 200 start-up trials, using the hyperparameter search space in Table 2 As described in Section 5 the goal of this search is to minimize the weighted log-loss
1 Ch (i N
Σ
yi log サ (o((a))))))
:::) log (1-
(13)
where g is the scoring function we are training to predict yi, Φ is a well-defined inverse link function, and & the instance-specific cost. Note that although in our experiments o can only have two possible values (CFP or CFN), this formulation can be applied to any misclassification cost structure.
Since false negatives carry higher cost, we explore whether introducing bias towards predicting frand is beneficial for our model. This is done by testing different initial probability estimates for the base predictor in the boosting model. During model training, we perform an independent hyperparameter search over a range of values for the initial prediction value Iinitial, from to ga + 2, in increments of 0.2, where Pa is the default initial prediction value
Eicon Σ,er
Id = logit
(14)
In the first hyperparameter search, LightGBM classifiers with a maximum tree depth of 2 achieved the best performance. Therefore, we conducted a sccond search consisting of a total of 1700 trials, with 1500 startup trials, where we used the same hyperparameter search space detailed in Table but fixing the maximum depth parameter at 2.
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Table
ML classifier: LightGBM hyperparameter search space.
Hyperparameter
Values
Distribution
"dart"
enable
enable_bundll bundle
False, True]
d_sstimators
[50, 250]
Uniform
depth
[2, 5]
Uniform
num leaves
[100, 1000]
Uniform
min min_child sss_slessssssssssse
[5, 200]
Uniform
learning rate
[0.001, 1]
Uniform
reg regha
[0.0001,
Uniform
reg lambda
[0.0001,
Uniform
For the expert correctness models, we also use LightGBM classifiers (Ke et al. 2017). These models are trained on alerts raised during months four to six and validated on alerts from month seven. The objective is to predict the correctness of the experts' predictions, using only data for which human labels are available. Consequently, the amount of training data depends on the data availability scenario under consideration. Hyperparameter optimization is performed using TPE (Akiba et al. 2019 with total of 120 trials, inchuding 100 start-up trials. The hyperparameter search space is detailed in Table 3 The objective is to minimize the
weighted log-loss, adapted to predict expert correctness instead of fraud labels. The loss function is defined
as
N
Cj (IS.)
Σe N 1=1
I[m. = y/ log (0_)())) 1[mi, * yl log (1_
115)
where S. f yi. Ci, mayhi and my represents a prediction from expert on instance I,,
Table 3: Expert models:
lightGBM hyperparameter search space.
Hyperparameter
Values
Distribution
"dart"
enable bundle
False, True]
esstimatooss
[50, 250]
Uniform
depth
[2, 20]
Uniform
leaves
[100, 1000]
Log
min _hild_hiihhhe _ampless
[5, 100]
Log
learning rate
[0.005, 0.5]
Log
reg alpha
[0.0001, 0.1]
Log
reg lambda
[0.0001, 0.1]
Log
A.2 Density Estimation
Both our systems incorporate a density estimation step. For this, we train an MLP and use penultimate dense layer as feature extractor to map inputs into a continuous latent space. The MLP is trained alerts from months 4 to 6 and validated month 7. It is optimized to minimize the weighted log-loss described in Equation 13 Hyperparaneter optimization is performed using TPE (Akiba et al. 2019), running for 100 trials with 10 startup trials. The hyperparameter search space and the selected parameters are shown in Table
In our density-basod conformal prediction method, we apply KDE (Rosenblatt 1956) with a bandwidth of 0.2 the feature vectors extracted from the MLP. These density scores are subsequently used compute prediction sets, outlined in Section B of the Appendix.
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Table 4: Feature extraction MLP: hyperparameter search space.
Hyperparameter
Values
Distribution Selected
optimizer
Adam
Adam
{[128/ /200
hidden
layer sizes
20/50/ 128,
1288 50]
50]}
[1c-5,
learning rate
Log
3.096e-5
1e-3]
[1e-5,
weight decay
Log
3.84e-4
le-3]
dropout_ras rate
[0.0, 0.5]
Uniform
0.056
num _pmc_es
[20, 200
Uniform
73
batch size
[10, 128
Log
30
In the densstt--sfttaax approach, we use RealNVP normalizing flows (Dinh et al. 2017 to estimate data likelihoods from the extracted features. Hyperparameter optimization for RealNVP is performed using TPE (Akiba et al., 2019) over 100 trials (10 startup trials) to minimize the negative log-likelihood on validation data. Training data spans alerts from months to 6, with validation on month 7. The search space for hyperparameters is detailed in Table A separate RealNVP model is then trained for each expert and data availability scenario, producing unique density scores for each expert based their labeled subsets.
Table RealNVP: hyperparameter search space.
Hyperparameter
Values
Distribution
num coupling layers
[2, 10]
Uniform
hidden ddie
[64, 256]
Uniform (step 32)
learning rate
1e-5, 1e-3]
Log
mum epochs
500 300]
Uniform
B Density-Based Conformal Prediction
The training and prediction algorithms for density-based conformal prediction are defined in Algorithms
and 2
Algorithm 1: Training algorithm
Input: Training data Z (Jii, ve), n, Class list. y, Confidence level a, Ratio p
Output: Plist Qlst
Initialize: Pist = list, qust = list
for
E y do
tr X + SutastDDta(Z,)) (Z,V.p)
p + LearnDensity Estimmattyt (X!")
G + Quantile fo (xca)), a)
Plit append(())
qist. aamaad
end for
return Prist quet
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Algorithm 2: Prediction algorithm
Input: Input 2, Trained Plist qist, Class list Output: C
Initialize: C= list
for ) do
if (x) 2 dy then Cappend(y)
end if end for return C
C Downweighing model prediction in the conformal prediction approach
The dowuweighting factor 1 in Equation 11 determined by the conformal coverage level a and the an proportion of empty set predictions in the batch. For each new instance, compute two density scores p(s;ly) (one for each class in binary setting). If neither score exceeds the quantile by defined during calibration, the instance is classified into the empty set. These quantiles are selected to meet the desired coverage level a. Lower values represent a more conservative approach to detecting OOD) data, prioritizing accuracy and reducing empty set predictions, while higher a allows for more empty set predictions with a higher error rate (Figure 7 For each instance, we can find the smallest alpha ogg for which the instance is predicted the empty set a by gradually increasing the coverage level a. This process requires minimal additional computation since the density scores are already available; we simply need to find the quantile. The smaller ag. the more OOD the instance is considered, and one approach is to set w, cg.
It's important to differentiate between instances classified as empty sets duc to the desired coverage level and those classified as empty sets due to data drift. In the absence of data drift, the proportion of emply set predictions should approximate a but should not exceed it. If the proportion of empty set predictions does exccod a, this suggests that accuracy has fallen below 1 a, indicating lack of data exchangcability and confirming the presence of drift (as illustrated in Figure 7 Consequently, we should only downweigh instances classified emply sets due to data drift, rather than those classified emply sets to meet the coverage level.
To build on this reasoning, we can detect OOD data by monitoring the ratio Pa.ng where PM.og represents the proportion of empty set predictions at a specific coverage level og- This ratio compares the actual proportion of empty set predictions with the expected proportion based on ag. A high ratio suggests that the proportion of empty set predictions is higher than what is anticipated under normal circumstances, indicating potential data drift. By calculating this ratio for each instance, we distinguish empty set predictions due to OOD data from those due to the desired coverage level ag-
Train CP regions (alpha=0.02)
Test CP regions (alpha=0.00 0.00)
Conformal Coverage
2.0
2.0
Class
Class
1.-
Clasification Accuracy (Triir)
Class
Class 1
Propartion null (Train)
1.0
1.0
Clasification Accuracy (Tast)
Y c.corr
Proportion
0.6
Proportion null set (last)
0.0
0.0
Y
1.0
1.0
0.2
15-
-2.0
-2.0
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Xoord
X_coord
Alpha
Figure 7: Example of how density-based conformal prodiction is affected by data drift. At test time the distribution changes significantly, increasing the number empty set predictions.
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For example, in Figure 7 consider instances predicted empty sets at ap = 0. Since Po 0.2, the ratio becomes 0.2 xx, leading to these instances being fully downweighted with 1 = 0. For instances with og = 0.2, the ratio is 0.4 0.2 = 2, resulting in a downweighing factor of 1.2
0
One challenge here is that an instance predicted as an empty set at a particular ag will also remain an empty set for all higher a values. This inflates the empty set proportion P0.as: not specifically due to the amount of empty sets at cg. but due previously identified empty sets at lower a levels. For instance, in the previous example, all OOD data is detected for a low as 0.02; however, the instance that is predicted the empty set for = 0.2 is still downweighed by 0.5.
To address this, rather than directly comparing PO.ag with ogg, we fit a line between the points (ag-s, (.g-5.PD.as and (1, 1), where s is the slep size between successive values of a. This approach is based on the assumption that at a = 1, we expect 100% of instances to be classified as empty sets. The value of this line provides a hcuristic for the expected proportion of empty sets, assuming no additional OOD data identified as a increases. Therefore, this adjustmentt allows determining if additional OOD data is identified al ag- The resulting weight W; for an instance 2; is then calculated as:
P0.0a -s)
P0.0a
w1,, Rbstch Clas)az))
(16)
P8.00-2 (a
Pa.
where Po [Cog (1hsscn)==0 represents the proportion of empty set predictions at ag, based on the instance 24 and the batch Nbatch- The denominator provides the expected proportion of empty sets, derived from fitting the line as described, where is the step size between successive values of a. If ag = 0, the denominator is set to O, ensuring that fully OOD instances are appropriately downweighted.
[Khaschl]
By applying this approach to the example in Figure 7 the first point in the conformal coverage plot (corre- sponding to 0g = 0) would still be significantly downweighed, as the high proportion of empty set predictions indicates a clear detection of OOD data. However, the second point, which corresponds to a higher ogg would not be downweighed at all, since all OOD data had already been identified at lower a levels. This behavior is exactly what we want, as it prevents the system from penalizing in-distribution data that comes after OOD data has been detected at lower Cry.
D Optimizing the conformal coverage level
In our conformall prediction framework, an emply set prediction indicates high epistemic uncertainly, con- trolled by the coverage level a: a higher a leads to more empty set predictions overall. Figure g illustrates two complementary views of this behavior. The left plot shows, for noisy (OOD) instances only, the propor- tion predicted as the empty set as a increases. The right plot shows the proportion of empty set predictions corresponding to noisy instances. Note that when a = 1, all instances are predicted as the empty set, which explains why, in the right plot, the y-axis lower bound 0.2 (the fraction of noisy data we introduced) and why in the left plot all noisy data, is eventually identified.
The key question is how easily (i.e., at low a values, where only a few empty sets are allowed overall) noisy data can be detected. In the high-noise setting, even for very low a, nearly all noisy instances are already identified as empty sets, with the right plot showing that these empty set predictions almost exclusively originate from noisy data. By contrast, in the low-noise setting, noisy data is harder to separate: the proportion of noisy instances predicted as empty sets lower, with a substantial fraction of empty set predictions coming from in-distribution data. This is expected, as in this setting the noisy data is more similar to the original distribution. Nevertheless, even under low noise, at very small a values, roughly 60% of empty set predictions still correspond to noisy data, meaning the method identifies the most evident OOD instances. These results confirm the method's ability to identify noisy instances and defer such cases via ReL, especially in high noise scenarios.
In Table 6 we present the proportion of empty set predictions (with 95% confidence intervals) for cach experimental setting. These results are averaged over five runs, each using a different random seed for noise injection.
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Iddettfied
Noisy Data Identified
Null Predictions from Noisy Data
3.0
Proportion of Null Predictions
0.9
from Nolsy Oela
0.8
Hig h noise
Progertion
02
noise High noise
0.3-
0.0
0.6
0.8
1.0
0.2
0.2
1.0
Alpha
Alpha
Figure 8: Conformal prediction for OOD detection. Left: proportion of noisy (OOD) instances predicted
empty sets. Right: proportion of empty set predictions originating from noisy data.
Our optimization process (Equation Ii] is highly dependent on both the noise setting and the deferral rate. The noise setting controls the degree of distributional shift in the test higher noise levels lead more empty set predictions at lower coverage levels. For instance, in the low-noise scenario, fewer than 4% of instances on average are predicted as the empty set; in contrast, under high noise, this proportion can rise to 20%, reflecting the fact that around 20% of the test instances are corrupted.
The deferral rate further influences the optimization process. As the deferral rate increases, the solver selects coverage level that typically yields a higher fraction of empty sets, ensuring that the number of cases referred human experts remains within their workload constraints. Consistently across all settings, we observe rising percentage of emply set predictions with increasing deferral rates.
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Table 6: Conformal Coverage Optimization for the representative settings.
Setting
Empty set predictions
Noise
NE
DR
DA
0 %
Alpha
low
1
20
1/1
4.29%
+ 0.66
0.03 + 0.0068
low
1
20
1/5
3.08%
+ 0.67
0.02 + 0.0054
low
1
40
1/1
8.23%
+ 0.63
0.07 + 0.0064
low
1
40
1/5
4.61%
+ 0.88
0.03 + 0,0090
low
3
20
1/1
2.57%
+ 0.32
0.01 = 0,0026
low
3
20
1/5
2.38%
+ 0.42
0.01 = 0.0024
low
3
40
1/1
4.11%
-1 0.44
0.03 1 0.0055
low
3
40
1/5
3.55%
0.67
0.02 1 0.0059
low
20
1/1
2.58%
0.23
0.01 0.0018
low
1/5
2.37%
0.45
0.0032
low
1/1
3.65%
0.59
+ 0.0054
low
1/5
3.25%
0.51
medium
1
20
1/1
9.93%
0.42
1 0.0034
medium
20
1/5
9.03%
0.44
0.03 + 0.0022
medium
40
1/1
13.04%
0.58
0.08 + 0.0067
medium
40
1/5
10.94%
1.14
0.04 + 0.0085
medium
3
20
1/1
8.47%
+ 0.13
0.02 F 0.0013
medium
3
20
1/5
8.35%
+ 0.25
0.02 # 0.0023
medium
3
40
1/1
9.77%
+ 0.43
0.03 # 0.0015
medium
3
40
1/5
9.56% + 0.53
0.03 + 0.0019
medium
5
20
1/1
8.55% + 0.06
0.02 + 0.0014
medium
5
20
1/5
8.28%
+ 0.11
0.02 + 0.0019
medium
5
40
1/1
9.69%
+ 0.51
0.03 = 0.0022
medium
5
40
1/5
9.44%
1 0.43
0.03 1 0.0027
high
20
1/1
17.03%
1 0.59
0.02 1 0.0020
high 20
1/5
16.62%
0.95
0.02 + 0.0023
high
1/1
20.19%
0.61
0.05 0.0073
high
1/5
18.33%
+ 0.0034
high
1/1
15.12%
+ 0.0023
high
1/5
14.93%
1.00
1
high
3
40
1/1
17.90%
0.17
0.02 + 0.0012
high
3
40
1/5
17.75%
0.25
0.02 + 0.0008
high
5
20
1/1
16.25%
0.95
0.02 + 0.0028
high
5
20
1/5
13.96%
4 0.88
0.02 + 0.0022
high
5
40
1/1
17.79%
+ 0.19
0.02
# 0.0009
high
5
40
1/5
17.72%
+ 0.24
0.02 + 0.0020
24


Reviews:
[{"review_id": "iBItkxVLY4", "reviewer": "Reviewer_d3bB", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper studies the problem of collaborative decision-making using both an AI system and human experts. The task is to decide how to allocate decisions between the AI system and the different experts to minimize the expected misclassification cost while respecting expert capacity constraints.\n\nThe authors describe two improvements to current methods for this problem that both focus on improving robustness to OOD data:\n* They incorporate out-of-distribution uncertainty into learning to defer (L2D) by scaling logits according to a normalizing flow likelihood.\n* They propose using conformal prediction to decide when to defer to experts, which also leverages OOD detection.", "claims_and_evidence_yn": "Yes", "claims_explanation": "In general the results suggest that the two proposed methods reduce misclassification cost compared to baselines. The methods are well-motivated and seem reasonable.", "audience_yn": "Yes", "audience_explanation": "I am not an expert in this particular problem, but it seems important and there is a community around it. I am convinced that incorporating OOD detection addresses an important limitation of previous methods (assuming that the authors have represented the previous literature well—I did not carefully check for novelty).", "requested_changes": "I think the main weakness of the paper is the organization/writing. I found that reading through the paper, there was not enough signposting to clearly understand what the main content of each section was going to be; the authors often dive right into technical details without first introducing what they are going to discuss. It was difficult at times to tell which parts of each section were describing previous methods from the literature and which parts were describing the authors' novel contributions. I also found it a bit confusing that the authors propose two methods—at first I thought these were going to be combined, but my understanding is that they are just separate ideas and are evaluated separately. Overall, I think improving the organization and clarity would help the paper have more impact.", "broader_impact_concerns": "No concerns.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "Uh3iTPMByq", "reviewer": "Reviewer_LN8K", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper studies human–AI decision pipelines under distribution shift with limited human capacity and asymmetric costs. It proposes two uncertainty-aware routing methods: (i) a density-based logit scaling (“density-softmax”) to reduce overconfident predictions in low-density regions of a learned representation, and (ii) a density-based conformal-style set predictor coupled with a capacity-constrained assignment optimizer to decide when to defer to humans. Experiments on a fraud-alert dataset with simulated shift suggest improved calibration and allocation relative to uncertainty-agnostic baselines.", "claims_and_evidence_yn": "Yes", "claims_explanation": "I am not an expert in learning-to-defer and I may miss relevant related work; my comments focus on correctness and statistical clarity.\n\nMy main concern is an apparent error in the stated Bayes-optimal deferral rule. The paper compares terms involving $\\max _y \\mathbb{P}\\left(h^\\*(x)=y \\mid x\\right)$ where $h^\\*(x)$ is defined as an argmax classifier. As written, $h^\\*(x)$ is deterministic given $x$, so this probability is 0 or 1 and the maximum is identically 1 , making the criterion degenerate. I believe the intended quantity is the model's probability of being correct, such as $\\max _y \\mathbb{P}(Y=y \\mid x)$, and similarly for experts $\\mathbb{P}\\left(Y=m_j(x) \\mid x\\right.$ ), or a calibrated correctness estimate used in standard L2D formulations. This needs correction or a careful re-derivation.\n\nThat being said, the paper’s main strengths are its clear focus on a realistic deployment constraint and its attempt to build uncertainty-awareness directly into the routing mechanism rather than treating calibration as an afterthought. The proposed implementations are also fairly concrete, making the ideas easy to reproduce and potentially useful beyond the specific fraud-alert setting.", "audience_yn": "Yes", "audience_explanation": "Yes. The operational focus on capacity constraints and cost-sensitive routing is practically relevant.", "requested_changes": "Correct and clearly explain the Bayes-optimal deferral rule (what random variable the probability is taken over, and what quantity is being compared).", "broader_impact_concerns": "NA", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "ISjHwAOqzt", "reviewer": "Reviewer_bDyr", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "In my view, the paper elevates uncertainty from a model-level diagnostic to a system-level decision variable in human-AI collaboration under distribution shift. It demonstrates that robust human-AI collaboration under shift is fundamentally a policy selection problem, not merely a better prediction problem, and uncertainty is the correct control signal for that selection. \n\nUncertainty is explicitly operationalized to decide which decision policy to trust—fine-grained learning-to-defer versus conservative rejection—depending on epistemic conditions.\nThis resolves a long-standing tension in HAIC between expressiveness (L2D) and robustness (ReL) under distribution shift. The work shows that the distribution shift should not be handled by a single monolithic policy. Instead, it proposes a principled policy switching mechanism driven by uncertainty via density-aware calibration or conformal emptiness, which is both interpretable and deployable.\n\nI think the paper is impactful beyond fraud detection or the specific architectures used.", "claims_and_evidence_yn": "Yes", "claims_explanation": "- The experiments clearly demonstrate that uncertainty-aware routing improves robustness under distribution shift compared to standard Learning-to-Defer and pure Rejection Learning baselines.\n- The controlled noise-injection setup shows consistent trends: density-aware calibration improves probability calibration (ECE), and conformal-based rejection becomes increasingly effective as shift severity grows. \n- The ablation-style comparisons (DS vs. CP vs. L2D vs. ReL) convincingly support the claim that no single policy dominates across all shift regimes, motivating uncertainty-driven policy selection.", "audience_yn": "Yes", "audience_explanation": "1. This paper directly addresses how uncertainty should be used, not merely estimated, in the presence of distribution shift. \n\n2. The paper goes beyond standard classification or uncertainty benchmarking and studies decision-making systems that combine models, humans, and constraints. \n\n3. Although evaluated in a fraud detection setting, the core findings—such as uncertainty-driven policy switching and the tradeoff between expressive routing and conservative rejection—generalize to many high-stakes domains.", "requested_changes": "- The paper frequently equates low density estimates or conformal empty prediction sets with epistemic uncertainty, but this identification is largely empirical and not formally justified. In complex or multimodal distributions, low likelihood does not necessarily imply epistemic uncertainty, and conformal emptiness under distribution shift does not come with theoretical guarantees. Clarify that density and conformal emptiness are used as proxies for epistemic uncertainty rather than exact characterizations. Please add a short discussion on when this assumption may break (e.g., conditional shift or sparse in-distribution regions).\n\n- The paper’s most valuable insight—that robust human–AI collaboration under distribution shift requires uncertainty-driven policy switching rather than a single deferral strategy—is not clearly highlighted as a central contribution. As a result, the work may appear as a collection of techniques rather than a coherent conceptual advance. I suggest providing a conceptual illustration of different regimes of distribution shift and the corresponding optimal policies. \n\n- The use of conformal prediction set emptiness as a trigger for conservative deferral implicitly treats emptiness as a reliable indicator of epistemic shift. However, conformal prediction guarantees coverage only under exchangeability, and its behavior under distribution shift is not theoretically grounded. \n\n- The joint optimization over routing decisions, expert capacity, and conformal thresholds is a strong systems contribution, but the objective function is presented in an engineering-centric manner without a clear decision-theoretic interpretation.\n\n- The combination of density estimation, conformal prediction, learning-to-defer, and constrained optimization can give the impression of a method stack rather than a unified framework, potentially obscuring the paper’s central message. \n\n- Provide an interpretive justification for density-softmax, for example by framing it as a data-dependent temperature scaling mechanism or as an approximation to epistemic variance shrinkage, even a qualitative theoretical interpretation would help distinguish it from an ad-hoc engineering choice.", "broader_impact_concerns": "The proposed methods implicitly determine when decisions are automated and when they are deferred to human experts, thereby influencing human workload, responsibility allocation, and accountability. Systematic deferral of certain subpopulations—particularly those associated with low-density or out-of-distribution regions—could lead to uneven human scrutiny or delays, potentially introducing fairness concerns if such regions correlate with sensitive attributes.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "cr1dvL5vWA", "reviewer": "Reviewer_5ow4", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper addresses a central limitation of learning-to-defer (L2D) systems for human–AI collaboration: their brittleness under distribution shift due to unreliable confidence and correctness estimates. The authors propose two uncertainty-aware HAIC frameworks that explicitly incorporate epistemic uncertainty into the decision-allocation process.\n\nFirst, the paper introduces an uncertainty-aware L2D system that augments the OvA L2D framework with density-softmax models based on normalizing flows. By adjusting classifier and expert-correctness logits using density estimates in latent space, the method reduces overconfidence on out-of-distribution (OOD) instances and improves calibration. The approach further blends instance-level predictions with experts’ historical average performance under high epistemic uncertainty, enabling more robust expert assignment when data is scarce or shifted.\n\nSecond, the paper proposes a hybrid conformal prediction–based HAIC system that dynamically switches between L2D and rejection learning (ReL). Density-based conformal prediction is used to identify OOD instances (empty prediction sets), which are directly deferred to human experts, while in-distribution instances are handled via L2D. The coverage level is optimized jointly with expert assignment under cost-sensitive objectives and human capacity constraints.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The submission provides clear and convincing evidence supporting its claims. The proposed methods are well motivated, grounded in established uncertainty estimation techniques, and evaluated through extensive experiments across diverse and realistic settings (e.g., distribution shift, cost sensitivity, limited expert data, and capacity constraints). The empirical results consistently demonstrate improved calibration and reduced misclassification cost compared to strong baselines, and the analyses (e.g., calibration error, OOD behavior) directly support the paper’s main claims. While the evaluation relies on synthetic experts and a single application domain, these limitations are acknowledged and do not undermine the validity of the presented evidence.", "audience_yn": "Yes", "audience_explanation": "The paper would be of clear interest to segments of TMLR’s audience working on learning to defer, uncertainty estimation, human–AI collaboration, selective prediction, and decision-making under distribution shift. It addresses a well-known limitation of existing L2D methods and proposes principled, uncertainty-aware extensions with practical relevance, including cost sensitivity and capacity constraints. The combination of methodological contributions and a thorough empirical study makes the findings valuable to researchers interested in robust ML systems deployed in real-world, high-stakes settings.", "requested_changes": "## Requested Changes\n\n### Critical Changes (required for acceptance)\n\n1. **Clarify generalization beyond the fraud detection domain**\n   While the fraud detection setting is realistic and well motivated, all empirical evidence is drawn from a single application domain. The paper should more clearly justify why the proposed uncertainty-aware HAIC approaches are expected to generalize to other domains (e.g., healthcare, moderation, risk assessment), or explicitly scope the claims to similar tabular, alert-review settings. This clarification is important to properly contextualize the contribution.\n\n2. **Stronger justification of the synthetic expert assumptions**\n   Although the FiFAR/OpenL2D framework is more realistic than prior synthetic expert simulations, the paper should more clearly discuss which aspects of real human behavior are captured and which are not. In particular, limitations related to expert adaptation over time, correlated expert errors, and feedback loops should be discussed more explicitly, as these factors are central to human–AI collaboration.\n\n3. **Sensitivity analysis of key hyperparameters**\n   The performance of both proposed methods depends on important design choices (e.g., density model configuration, conformal coverage level optimization, weighting between predicted and average expert correctness). While some tuning details are relegated to the appendix, a clearer sensitivity analysis or robustness discussion in the main paper would strengthen confidence that improvements are not narrowly dependent on specific parameter settings.\n\n---\n\n### Non-Critical Changes (would strengthen the paper)\n\n4. **Improve conceptual clarity between the two proposed approaches**\n   While the paper presents Uncertainty-Aware L2D and Conformal Prediction for HAIC as complementary, the high-level guidance on *when* a practitioner should prefer one over the other could be made more explicit earlier in the paper. A short summary table or decision guideline would improve accessibility.\n\n5. **Reduce technical overhead in the main exposition**\n   Some sections (e.g., density-softmax integration and assignment optimization) are mathematically dense. Light restructuring, additional intuition, or a simplified running example could help readers less familiar with L2D or uncertainty estimation follow the core ideas without relying heavily on the appendix.\n\n6. **Discuss computational and deployment costs more explicitly**\n   Although the paper notes that density-softmax has low test-time overhead, the overall system includes normalizing flows, conformal prediction, and integer optimization. A brief discussion of training and inference cost trade-offs, and how these scale with problem size and number of experts, would improve practical relevance.\n\n7. **Minor presentation improvements**\n\n   * Add clearer captions or annotations to figures illustrating calibration and OOD behavior to make them more self-contained.\n   * Ensure consistent terminology when referring to epistemic uncertainty, OOD data, and empty-set predictions across sections.", "broader_impact_concerns": "NA`", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)