We study post-hoc Learning to Defer (L2D) through the lens of ideal distributions: divergence-regularized reweightings of the data distribution under which a model attains low loss. We define deferral via the density-ratio between a model's and an expert's ideals. Using the reduction from density-ratio estimation to class-probability estimation, we derive the DR CPE losses for post-hoc L2D scorers. Deferral decisions are then made by thresholding the scorer, allowing deferral rates to be adjusted without retraining. For KL-based ideal distributions, our deferral rules recovers Chow's rule under the original distribution and a connection to an expert-tilted Bayes posterior -- which incorporates the expert's performance -- depending on if the ideal distributions are joint or marginal distributions. Experimentally, our approach is competitive compared to common baselines and more robust across dataset settings. More broadly, our results cast post-hoc L2D as density-ratio learning between ideal distributions, bridging Chow-style rules, expert comparison, and elucidating connections to related learning settings including anomaly detection.

Large language models (LLMs) have achieved remarkable performance but face critical challenges: hallucinations and high inference costs. Leveraging multiple experts offers a solution: deferring uncertain inputs to more capable experts improves reliability, while routing simpler queries to smaller, distilled models enhances efficiency. This motivates the problem of learning with multiple-expert deferral. This thesis presents a comprehensive study of this problem and the related problem of learning with abstention, supported by strong consistency guarantees. First, for learning with abstention (a special case of deferral), we analyze score-based and predictor-rejector formulations in multi-class classification. We introduce new families of surrogate losses and prove strong non-asymptotic, hypothesis set-specific consistency guarantees, resolving two existing open questions. We analyze both single-stage and practical two-stage settings, with experiments on CIFAR-10, CIFAR-100, and SVHN demonstrating the superior performance of our algorithms. Second, we address general multi-expert deferral in classification. We design new surrogate losses for both single-stage and two-stage scenarios and prove they benefit from strong $H$-consistency bounds. For the two-stage scenario, we show that our surrogate losses are realizable $H$-consistent for constant cost functions, leading to effective new algorithms. Finally, we introduce a novel framework for regression with deferral to address continuous label spaces. Our versatile framework accommodates multiple experts and various cost structures, supporting both single-stage and two-stage methods. It subsumes recent work on regression with abstention. We propose new surrogate losses with proven $H$-consistency and demonstrate the empirical effectiveness of the resulting algorithms.

AI based mental health diagnosis is often judged by benchmark accuracy, yet in practice its value depends on how psychologists respond whether they accept, adjust, or reject AI suggestions. Mental health makes this especially challenging: decisions are continuous and shaped by cues in tone, pauses, word choice, and nonverbal behaviors of patients. Current research rarely examines how AI diagnosis interface design influences these choices, leaving little basis for reliable testing before live studies. We present SimClinician, an interactive simulation platform, to transform patient data into psychologist AI collaborative diagnosis. Contributions include: (1) a dashboard integrating audio, text, and gaze-expression patterns; (2) an avatar module rendering de-identified dynamics for analysis; (3) a decision layer that maps AI outputs to multimodal evidence, letting psychologists review AI reasoning, and enter a diagnosis. Tested on the E-DAIC corpus (276 clinical interviews, expanded to 480,000 simulations), SimClinician shows that a confirmation step raises acceptance by 23%, keeping escalations below 9%, and maintaining smooth interaction flow.

Modern artificial intelligence systems make critical decisions yet often fail silently when uncertain -- even well-calibrated models provide no mechanism to identify \textit{which specific predictions} are unreliable. We develop a geometric framework addressing both calibration and instance-level uncertainty quantification for neural network probability outputs. Treating probability vectors as points on the $(c-1)$-dimensional probability simplex equipped with the Fisher--Rao metric, we construct: (i) Additive Log-Ratio (ALR) calibration maps that reduce exactly to Platt scaling for binary problems while extending naturally to multi-class settings, and (ii) geometric reliability scores that translate calibrated probabilities into actionable uncertainty measures, enabling principled deferral of ambiguous predictions to human review. Theoretical contributions include: consistency of the calibration estimator at rate $O_p(n^{-1/2})$ via M-estimation theory (Theorem~1), and tight concentration bounds for reliability scores with explicit sub-Gaussian parameters enabling sample size calculations for validation set design (Theorem~2). We conjecture Neyman--Pearson optimality of our neutral zone construction based on connections to Bhattacharyya coefficients. Empirical validation on Adeno-Associated Virus classification demonstrates that the two-stage framework captures 72.5\% of errors while deferring 34.5\% of samples, reducing automated decision error rates from 16.8\% to 6.9\%. Notably, calibration alone yields marginal accuracy gains; the operational benefit arises primarily from the reliability scoring mechanism, which applies to any well-calibrated probability output. This work bridges information geometry and statistical learning, offering formal guarantees for uncertainty-aware classification in applications requiring rigorous validation.

Model Cascading, recently applied successfully to LLMs, is a simple but powerful technique that improves the efficiency of inference by selectively applying models of varying sizes. Models are used in sequence from smallest to largest, only deferring samples to large, costly models when smaller models are not sufficiently confident. Existing approaches to deferral use only limited small model confidence estimates because of the inaccessibility of the large model, although large model confidence is known to be important. We therefore propose a bi-directional approach to deferral that considers the confidence of small and large models in the cascade simultaneously through the use of a proxy for the large model. This requires a richer representation of model confidence to enable comparative calibration: we use an analysis of hidden states to improve post-invocation confidence of the small model, which in itself improves cascading results over prior approaches. We then combine this with a tiny proxy model to estimate pre-invocation confidence of the large model. We examine the proposed cascading system over challenging, multiple-choice datasets, finding improvements over standard cascading baselines reflected in reductions in deferrals to more costly models.

We consider the task of learning how to act in collaboration with a human expert based on observational data. The task is motivated by high-stake scenarios such as healthcare and welfare where algorithmic action recommendations are made to a human expert, opening the option of deferring making a recommendation in cases where the human might act better on their own. This task is especially challenging when dealing with observational data, as using such data runs the risk of hidden confounders whose existence can lead to biased and harmful policies. However, unlike standard policy learning, the presence of a human expert can mitigate some of these risks. We build on the work of Mozannar and Sontag (2020) on consistent surrogate loss for learning with the option of deferral to an expert, where they solve a cost-sensitive supervised classification problem. Since we are solving a causal problem, where labels don't exist, we use a causal model to learn costs which are robust to a bounded degree of hidden confounding.

In human-AI collaboration, a central challenge is deciding whether the AI should handle a task, be deferred to a human expert, or be addressed through collaborative effort. Existing Learning to Defer approaches typically make binary choices between AI and humans, neglecting their complementary strengths. They also lack interpretability, a critical property in high-stakes scenarios where users must understand and, if necessary, correct the model's reasoning. To overcome these limitations, we propose Defer-and-Complement Decision-Making via Decoupled Concept Bottleneck Models (DeCoDe), a concept-driven framework for human-AI collaboration. DeCoDe makes strategy decisions based on human-interpretable concept representations, enhancing transparency throughout the decision process. It supports three flexible modes: autonomous AI prediction, deferral to humans, and human-AI collaborative complementarity, selected via a gating network that takes concept-level inputs and is trained using a novel surrogate loss that balances accuracy and human effort. This approach enables instance-specific, interpretable, and adaptive human-AI collaboration. Experiments on real-world datasets demonstrate that DeCoDe significantly outperforms AI-only, human-only, and traditional deferral baselines, while maintaining strong robustness and interpretability even under noisy expert annotations.

We introduce the first one-stage Top-$k$ Learning-to-Defer framework, which unifies prediction and deferral by learning a shared score-based model that selects the $k$ most cost-effective entities-labels or experts-per input. While existing one-stage L2D methods are limited to deferring to a single expert, our approach jointly optimizes prediction and deferral across multiple entities through a single end-to-end objective. We define a cost-sensitive loss and derive a novel convex surrogate that is independent of the cardinality parameter $k$, enabling generalization across Top-$k$ regimes without retraining. Our formulation recovers the Top-1 deferral policy of prior score-based methods as a special case, and we prove that our surrogate is both Bayes-consistent and $\mathcal{H}$-consistent under mild assumptions. We further introduce an adaptive variant, Top-$k(x)$, which dynamically selects the number of consulted entities per input to balance predictive accuracy and consultation cost. Experiments on CIFAR-10 and SVHN confirm that our one-stage Top-$k$ method strictly outperforms Top-1 deferral, while Top-$k(x)$ achieves superior accuracy-cost trade-offs by tailoring allocations to input complexity.

Larger models often outperform smaller ones but come with high computational costs. Cascading offers a potential solution. By default, it uses smaller models and defers only some instances to larger, more powerful models. However, designing effective deferral rules remains a challenge. In this paper, we propose a simple yet effective approach for machine translation, using existing quality estimation (QE) metrics as deferral rules. We show that QE-based deferral allows a cascaded system to match the performance of a larger model while invoking it for a small fraction (30% to 50%) of the examples, significantly reducing computational costs. We validate this approach through both automatic and human evaluation.

In the Learning to Defer (L2D) framework, a prediction model can either make a prediction or defer it to an expert, as determined by a rejector. Current L2D methods train the rejector to decide whether to reject the entire prediction, which is not desirable when the model predicts long sequences. We present an L2D setting for sequence outputs where the system can defer specific outputs of the whole model prediction to an expert in an effort to interleave the expert and machine throughout the prediction. We propose two types of model-based post-hoc rejectors for pre-trained predictors: a token-level rejector, which defers specific token predictions to experts with next token prediction capabilities, and a one-time rejector for experts without such abilities, which defers the remaining sequence from a specific point onward. In the experiments, we also empirically demonstrate that such granular deferrals achieve better cost-accuracy tradeoffs than whole deferrals on Traveling salesman solvers and News summarization models.