Discrete Choice Modeling

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3 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

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Latest papers 25

Oct 4, 2026cs.LG

Logic-Logit: A Logic-Based Approach to Choice Modeling

In this study, we propose a novel rule-based interpretable choice model, Logic-Logit, designed to effectively learn and explain human choices. Choice models have been widely applied across various domains---such as commercial demand forecasting, recommendation systems, and consumer behavior analysis---typically categorized as parametric, nonparametric, or deep network-based. While recent innovations have favored neural network approaches for their computational power, these flexible models often involve large parameter sets and lack interpretability, limiting their effectiveness in contexts where transparency is essential. Previous empirical evidence shows that individuals usually use heuristic decision rules to form their consideration sets, from which they then choose. These rules are often represented as disjunctions of conjunctions (i.e., OR-of-ANDs). These rules-driven, consider-then-choose decision processes enable people to quickly screen numerous alternatives while reducing cognitive and search costs. Motivated by this insight, our approach leverages logic rules to elucidate human choices, providing a fresh perspective on preference modeling. We introduce a unique combination of column generation techniques and the Frank-Wolfe algorithm to facilitate efficient rule extraction for preference modeling---a process recognized as NP-hard. Our empirical evaluation, conducted on both synthetic datasets and real-world data from commercial and healthcare domains, demonstrates that Logic-Logit significantly outperforms baseline models in terms of interpretability and accuracy.

Shuhan Zhang, Wendi Ren, Shuang Li

CUHK-Shenzhen

Human Preference Modeling Interpretable ML Discrete Choice Modeling

Oct 2, 2026cs.LG

Consideration Circuits: Depth Separation and Universality Beyond a Single Softmax

Most feature-based choice models, classical and deep, score items and apply a single softmax. We introduce consideration circuits (CC), feature-based models of multi-stage choice defined by directed acyclic graphs of multinomial logit (MNL) units. Source units assign probabilities to menu items, and internal units combine predecessor distributions using MNL weights computed from their probability-weighted feature summaries. On a three-item compromise task with fixed non-collinear features, menu-independent random-utility models (RUM), including a single MNL unit, suffer an error bounded away from zero. For CC, in contrast, we establish a sharp depth--norm separation: increasing depth from

2

to

3

reduces the optimal maximum taste-vector norm for error

ε

from

Θ(\log(1/ε)/ε)

to

Θ(\log(1/ε))

. The depth-

2

lower bound holds for arbitrary width and menu-independent routing biases, while a five-node depth-

3

circuit with zero routing biases attains the logarithmic rate. More generally, we characterize two geometric conditions that are necessary and sufficient for approximating arbitrary deterministic choice tables on finite menu families. Under these conditions, depth

3

suffices, while depth

4

achieves optimal logarithmic norm scaling whenever the family contains a non-singleton menu. In experiments, standalone tree circuits with fewer than

600

parameters attain the lowest mean test negative log-likelihood (NLL) among the evaluated models on four fixed-pool benchmarks and the Expedia temporal split. As output heads, CC generalize the linear MNL readout and lower mean test NLL for every tested encoder on Expedia and Trivago.

Junjie Xiao, Huiwen Jia

Department of Mathematics, Peking University · Department of Industrial Engineering and Operations Research, University of California, Berkeley

Discrete Choice Modeling

Sep 16, 2026econ.GN

Multitask Reinforcement Learning for Assisting Choice Model Specification

Discrete choice model specification is a time-consuming task in which modellers often specify and estimate multiple models while balancing goodness-of-fit, parsimony, and behavioural plausibility. We present Delphos, a multitask reinforcement learning framework that learns transferable specification strategies across transport choice datasets. Delphos frames model specification as a sequential decision-making problem in which it applies a sequence of modelling actions and receives feedback from an estimation environment based on model performance and convergence. To transfer modelling decisions across datasets with different sets of variables, Delphos represents utility specifications as sets of modelling terms using a DeepSet-Q architecture, allowing a shared specification policy to learn across multiple datasets. Trained on nine transport choice datasets, Delphos consistently outperforms independently trained single-task agents, indicating that sharing modelling experience improves learning efficiency and helps identify promising sequences of modelling decisions with fewer unsuccessful estimation attempts. When applied without further training to the unseen Swissmetro and Decisions datasets, the same agent identifies competitive specifications in less than 20 minutes on a standard CPU. It achieves a higher log-likelihood per observation than the VNS metaheuristic on Swissmetro and performance comparable to a published MNL specification developed by expert modellers on Decisions. These findings show that accumulating and reusing modelling experience enables Delphos to function as an intelligent assistant for discrete choice model specification. It reduces manual trial-and-error while allowing modellers to retain control over model diagnosis, refinement, and final selection.

Gabriel Nova, Stephane Hess, Sander Van Cranenburgh

CityAI Lab, Transport and Logistics Group, Delft University of Technology, The Netherlands · Institute for Transport Studies and Choice Modelling Centre, University of Leeds, UK

Discrete Choice Modeling Deep Sets Multi-Task RL

Aug 25, 2026cs.LG

MoPLEx: Estimating Plackett-Luce Mixture Models for Multi-Objective Alignment

We study learning a mixture of

k

Plackett-Luce models from multi-way ranking responses from annotators that may represent heterogeneous underlying preferences. This problem has many applications in AI alignment and preference optimization. Prior work has studied mixtures of Bradley-Terry models from pairwise comparisons. However, estimating a mixture of multi-way ranking models can become theoretically unidentifiable when

k

exceeds

m/2

, where

m

is the ranking length. We design an efficient algorithm to address this issue by first augmenting the rankings to a larger size (e.g., generating comparisons from a base model), followed by a gradient-based estimation to reduce inference cost (in the input embedding space). With this procedure in mind, we then fit a mixture of Plackett-Luce (PL) models via an expectation-maximization-style iteration, or MoPLEx in short. We conduct extensive experiments to verify this algorithm. First, we find that the gradient-based approximation estimates true probabilities with less than 5% error on models with up to 34 billion parameters. Second, MoPLEx improves clustering and ranking accuracy by an average of 43.7% and 15.2% over baselines using a single PL model or a mixture of Bradley-Terry models, on UltraFeedback and PERSONA datasets. These results demonstrate the effectiveness of MoPLEx for tackling multi-way rankings following heterogeneous preferences through measuring alignment via gradients.

Dongyue Li, Ziniu Zhang, Lu Wang +1

Northeastern University, Boston, MA · University of Michigan, Ann Arbor, MI

Learning to Rank Discrete Choice Modeling Multi-Objective Language Model Alignment User Preference Modeling

Aug 13, 2026cs.LG

Demand Transfer Estimation at Scale via Restricted Logit Modeling

Item demand forecasting is an integral component of store assortment optimization. Existing literature focuses on learning a suitable customer choice model and using this model to determine the value of an objective function (i.e. expected demand) with respect to an assortment proposal. However, for large item universe with many categories, this approach can prove inefficient, needing a separate demand forecast for every possible item assortment. An alternate approach exists whereby we combine the efficiency of forecasting item demand independently, while at the same time applying adjustments to the independent forecasts that account for the relations between item demand and the availability of other similar items on the shelf. Central to this approach is the estimation of Demand Transfer (DT) coefficients. These DT coefficients represent the percent of a particular target item's (item that the customer walked in the store to buy) demand that is redirected to each other item in the universe should the target item be removed from the shelf. We introduce an approach that allows us to compute these DT coefficients on large item universes (assortments having 1 million+ items). Experiments on data as well as historical transaction data for multiple locations within categories demonstrate that when certain reasonable assumptions about substitution behavior are satisfied, our procedure is able to accurately estimate underlying DT coefficients and lead to improvements in demand forecasting.

Lakshya Garg, Deep Narayan Mishra, Swapnil Yadav +4

Walmart Global Tech, Sunnyvale, CA, USA

Discrete Choice Modeling

Jul 30, 2026cs.LG

An analysis of machine learning approaches for enhancing decision-making in complex discrete choice tasks

Discrete choice modeling is a common tool used for preference elicitation during policy-making, but this is typically done through parametric models. Machine learning can push the boundaries of discrete choice modeling for policy-based preference elicitation by adopting a data-driven approach or learning individual preferences. However, there is limited knowledge of how well machine learning methods can estimate individual discrete choice rules under individual heterogeneity, especially in the context of challenges often experienced during preference elicitation. This study evaluates four machine learning models (multinomial logistic regression, generalized additive model, twinned neural network, and Gaussian process) with respect to their capacity to learn and predict five choice rules that are important in the behavioral and social sciences (linear strong utility, monotonic strong utility, ideal point, lexicographic semiorder, and multiattribute linear ballistic accumulator). Monte Carlo experiments were performed to assess model performance when increasing a) the number of attributes in the choice alternatives, b) the number of training choice sets, and c) the choice rule's determinism. The simulation results demonstrated that semi-parametric and non-parametric models generally outperform parametric models across all choice rules and experimental contexts. Model performance also generally improves by 6% to 96% and 0% to 55%, respectively, with an increase in training choice sets and choice rule determinism. A case study using real energy policy preference data was also conducted, where TNN performed best with a BIC of 13.351. This work demonstrated the viability and limitations of semi-parametric and non-parametric models in the context of policy-centric discrete choice modeling and showed how the choice task context should drive model selection.

Sheng Lun Christine Cao, Destenie Nock, Alex Davis

Department of Electrical and Software Engineering, University of Calgary, Calgary, AB, Canada · Department of Engineering and Public Policy, Carnegie Mellon University, Pittsburgh, PA, USA · Department of Civil Engineering, Carnegie Mellon University, Pittsburgh, PA, USA +1

Discrete Choice Modeling User Preference Modeling Preference Elicitation

Jul 14, 2026cs.LG

Tabular Foundation Models for Discrete Choice Estimation

Tabular foundation models (TFMs) generate predictions on structured data via in-context learning, without task-specific estimation. We ask whether TFMs can be effectively applied to discrete choice, a central demand estimation framework in marketing and operations, and find that directly applying TFMs yields limited performance. The gap is structural: TFMs assume row-independent observations, whereas discrete choice is inherently set-valued and subject to persistent consumer preference heterogeneity. We propose a reformulation that encodes both choice-set dependence and individual heterogeneity within a row-based learning framework. Evaluated on a yogurt scanner panel, individual-level heterogeneity encoding is the dominant driver of predictive accuracy. The best reformulation outperforms hierarchical Bayesian estimation by 8% in holdout log-likelihood and 3.6% in hit rate, running 16 times faster, a practical advantage for large-scale demand estimation. The advantage is largest in the medium-data regime (10--40 purchase occasions per consumer), where parametric Bayesian shrinkage most distorts estimates for atypical consumers. Fine-tuning on population choice data provides additional gains for consumers with shallow purchase histories, where in-context learning has limited individual-specific signal to condition on. These results establish a principled approach for applying foundation models to consumer choice problems more broadly.

Liu Liu, Dan Zhang

Leeds School of Business, University of Colorado Boulder

Tabular Foundation Models Discrete Choice Modeling Tabular ICL

Jul 13, 2026stat.ML

Diversified Multinomial Logit Contextual Bandits

Existing contextual multinomial logit (MNL) bandits model relevance-driven choice but ignore the potential benefits of within-assortment diversity, while submodular/combinatorial bandits encode diversity in rewards but lack structured choice probabilities. We bridge this gap with the

\textit{diversified multinomial logit}

(DMNL) contextual bandit, which augments MNL choice probabilities with a generally submodular diversity function, thereby formalizing the relevance--diversity trade-off within a single model. Incorporating diversity renders exact MNL assortment optimization intractable. We propose a

\textit{white-box}

UCB-based algorithm,

\texttt{OFU-DMNL}

, that constructs assortments item-wise by maximizing optimistic marginal gains, avoids black-box optimization oracles. We show that

\texttt{OFU-DMNL}

achieves at least a

(1-\frac{1}{e+1})

-

\textit{approximate}

regret bound

\tilde{O}\left(d \sqrt{T/K}\right)

, where

d

is the context dimension,

K

the maximum assortment size, and

T

the horizon, and attains an improved approximation factor over standard submodular baselines. Experiments demonstrate consistent gains and, relative to exhaustive enumeration, comparable regret with substantially lower runtime. Overall, DMNL bandits provide a practical foundation for diversity-aware assortment optimization under uncertainty, and

\texttt{OFU-DMNL}

offers a statistically and computationally efficient solution.

Heesang Ann, Taehyun Hwang, Min-hwan Oh

Seoul National University

Multi-Armed Bandits Discrete Choice Modeling Contextual Bandits Assortment Optimization

Jul 10, 2026cs.LG

Estimation, Prediction, and Assortment Optimization for Markov Chain Choice Models with Panel Data

We propose a framework for the Markov chain (MC) choice model with panel data, including parameter estimation, personalized choice prediction, and personalized assortment optimization. In contrast to the traditional setting, which assumes that each transaction is independently drawn from a random utility model, our framework accounts for dependencies among transactions for the same customer in historical data, captured by partial-ordering preference information. To the best of our knowledge, our framework initiates the study of choice modeling with panel data under MC. As our primary result, we propose novel expectation-maximization (EM) algorithms for MC parameter estimation by incorporating partial-ordering-based customer preference information. On synthetic datasets and the sushi dataset, our EM algorithms outperform the traditional EM algorithm of Simsek and Topaloglu (Operations Research, 66, 2018) and multinomial-logit-based partial-order benchmarks adapted from Jagabathula and Vulcano (Management Science, 64, 2018). As our secondary contribution, we present hardness and computational results for conditional choice prediction and assortment optimization problems. These results complement our estimation framework and clarify the computational landscape of conditional choice and assortment optimization, which may be of independent interest.

Yalcin Akcay, Gerardo Berbeglia, Young-San Lin

Melbourne Business School

Expectation-Maximization Discrete Choice Modeling Assortment Optimization

Jul 8, 2026econ.EM

Sensitivity to Subjective Expected Utility Maximization: A Methodological Study, with an Illustrative Application to LLM Decision-Making

Evaluating decisions made under uncertainty is hard when labeled outcomes are scarce, costly, or confounded with luck. We treat subjective expected utility (SEU) maximization as a stated standard and define a graded measure -- SEU sensitivity -- of an agent's conformity to it. The vehicle is a softmax choice model with a sensitivity parameter

α

on SEU-valued alternatives; the contribution is a sequence of identifiability results for

α

and for belief and utility parameters

(β, δ)

, validated in Stan via prior predictive checks, parameter recovery, and simulation-based calibration (SBC), with finite-sample caveats intact. In the uncertain-choice-only model

m_0

,

α

is identifiable given the expected-utility vector

η

and sharply recovered, while

(β, δ)

are only weakly informed: the posterior barely contracts and concentrates on a

β

-

δ

trade-off. In the extended model

m_1

,

δ

becomes identifiable in principle via a

β

-free risky block, but its practical recovery gain at realistic sample sizes is negligible (matched-count CI-width reduction under 1%), and that block yields no detected

α

-precision gain at matched choice count. These are two distinct phenomena: for

δ

, identifiability does not imply precise estimability at realistic

n

; for

α

, identifiability is silent about what governs finite-

n

precision. Marginal SBC passes for both models even where the joint posterior is weakly informed -- a demarcation we make precise. A two-by-two application (GPT-4o and Claude 3.5 Sonnet, each on insurance-claims triage and Ellsberg-style urns, with sampling temperature as the lever) runs end-to-end on real LLM choice data, detecting a structured comparative

α

effect in two of four cells.

Jeff Helzner

Parameter Estimation Parameter Identifiability Discrete Choice Modeling Decision-Making under Uncertainty

Jul 3, 2026cs.LG

OpFlow: Learning Opportunity-Conditioned Choice Potentials for Robust OD Flow Prediction

Origin-destination (OD) flow prediction is central to urban analytics, yet deep models trained on raw counts remain vulnerable to distribution shift. The core problem is that raw count supervision cannot distinguish transferable choice mechanisms from environment-specific shortcuts. Raw OD count mixes two objects: how much demand an origin produces and how that demand is allocated across destinations. We argue that the transferable object is the exposure-to-choice law that maps spatial conditions to relative destination preferences. We propose OpFlow, a mechanism-constrained framework that learns row-centered choice potentials and reconstructs flows by combining the induced allocation with a separately calibrated origin scale. Under distribution shift, spatial exposures and the induced allocations are allowed to vary; what transfers is the conditional map from exposure states to relative choice potentials. Theoretically, we characterize the identifiable row-centered potential and show that classical spatial interaction laws are restricted log-potential cases. Controlled synthetic shifts and a real-world experiment show OpFlow improves robustness under environment shifts.

Changjian Liu, Yong Gao, Yuqing Wang +5

School of Earth and Space Sciences Peking University China, CN 100871 · College of Artificial Intelligence Zhejiang University China, CN 310027

Distribution Shift Robustness Discrete Choice Modeling Traffic Forecasting

Jun 24, 2026cs.LG

Embedding Foundation Model Predictions in Discrete-Choice Models with Structural Guarantees

Tabular foundation models achieve strong accuracy on choice prediction tasks, but their predictions often violate the economic logic those tasks require: raising a price can increase predicted demand, implied willingness-to-pay estimates are frequently negative or implausible, and unavailable alternatives receive nonzero probability. We propose a two-stage adapter that takes a foundation model's predicted choice probabilities as a precomputed feature and embeds them inside a multinomial logit's utility. In Stage 1, we fit the multinomial logit's structural coefficients by maximum likelihood with sign constraints; in Stage 2, we freeze those coefficients and fit a small neural correction operating on the foundation model's predictions. We prove that this composition exactly preserves the multinomial logit's marginal rate of substitution, so analytically computable value-of-time becomes a mathematical guarantee rather than an empirical accident. Across three datasets and two foundation models, the adapter gains 6.4 percentage points (pp) of test accuracy on average over the multinomial logit and up to 12.8 pp, maintains 100% cost monotonicity, and produces values of time within the published transportation-economics range on the transportation datasets. Performance degrades gracefully under foundation-model context restriction, retaining at least 6 pp of accuracy gain even at 10% of the original foundation-model context.

Yingshuo Wang, Xian Sun, Yanhang Li +2

University of California, Berkeley, CA, USA. · Duke University, Durham, NC, USA. · Northeastern University, Boston, MA, USA. +2

Tabular Foundation Models Discrete Choice Modeling

Jun 11, 2026cs.AI

A Minimal Model of Bounded Trade-Off Screening in Multi-Attribute Choice

Human decision-making often involves choosing between multi-attribute alternatives, yet classical models assume fully compensatory utility aggregation despite evidence that people reject options with poor performance on critical attributes. We propose a bounded trade-off reasoning framework in which decisions are governed by a screening process that evaluates the balance between gains and losses across attributes. The model introduces a trade-off tolerance parameter that controls acceptable imbalance and can vary across contexts. Through simulation, we show that this mechanism produces preference patterns that differ from standard utility-based models and captures context-dependent variation in trade-off behavior. These results establish bounded trade-off screening as a plausible computational mechanism for multi-attribute choice and generate testable predictions for future behavioral studies.

Manisha Dubey, Anirban Sarkar, Subramanian Ramamoorthy

School of Informatics, University of Edinburgh, UK · Cold Spring Harbor Laboratory, USA

Computational Cognitive Modeling Multi-Criteria Decision Analysis Discrete Choice Modeling

Jun 3, 2026cs.LG

Worker Utility as Hysteresis: A Preisach Model of Transaction Acceptance in Gig Labour Markets

Worker utility is not observed -- only its consequence is. Each gig transaction produces a single bit: accepted or rejected. We argue this structure points directly to the Preisach hysteresis model as the natural representation of latent worker preferences. The Preisach operator models aggregate output as an integral over a population of binary threshold elements -- precisely the structure that emerges when heterogeneous workers each carry a private acceptance wage. We estimate two latent utility surfaces: acceptance utility U_1(X) and rejection utility U_0(X), via a dual-output neural network (shared layers 256->128, margin loss enforcing U_1 >= U_0). Classification reduces to the Preisach gap U_1(X) - U_0(X), passed into an XGBoost classifier alongside clip-stabilised price-to-threshold encodings. On 36,891 gig transactions, this pipeline achieves Jaccard = 0.827 and ROC AUC = 0.799. The price-to-threshold encoding accounts for +11.0 pp AUC over raw utility features. The model confirms the directional asymmetry hysteresis predicts: price decreases depress completion rates more than equivalent increases raise them. Applied to the full dataset, the model's recommendations simultaneously reduce the total wage bill by 21.3% and increase expected fill rate by 9.7 pp. For 74.2% of transactions, P(accept) already exceeds 0.80; reducing the wage keeps it above threshold (mean post-cut P = 0.972), releasing cost savings (median 31%). For the remaining 25.4%, a median 7% wage increase recovers +43 pp acceptance. A model without an explicit indifference zone cannot execute both moves simultaneously.

Piotr Frydrych

Metrology and Biomedical Engineering Institute, Faculty of Mechatronics, Warsaw University of Technology, 00-661 Warsaw, Poland

Discrete Choice Modeling AI and Labor

May 26, 2026cs.LG

Auditing and Fixing Economic Validity in Tabular Foundation Models for Discrete Choice

Tabular foundation models achieve strong accuracy on choice prediction tasks, but their predictions often violate the economic logic those tasks require: raising a price sometimes increases predicted demand, and implied willingness-to-pay estimates are frequently negative or implausible. We propose a two-stage adapter that embeds foundation model predictions within a utility-maximization framework. In the first stage, we estimate a standard choice model whose parameters are constrained to obey economic theory. In the second stage, we freeze those parameters and train a correction term that incorporates the foundation model's predictions as additional information. The result is a model that inherits the foundation model's accuracy gains while guaranteeing monotonic price-demand relationships under policy perturbation and producing analytically computable trade-off measures. On two transportation datasets, the adapter recovers up to 13 percentage points of accuracy over a standard logit model while maintaining perfect economic consistency, something neither the raw foundation models nor conventional distillation achieve.

Yingshuo Wang, Xian Sun, Yanhang Li +2

University of California, Berkeley, CA, USA · Duke University, Durham, NC, USA · Northeastern University, Boston, MA, USA +2

Tabular Foundation Models Discrete Choice Modeling Black-Box Model Auditing

May 25, 2026stat.ML

Optimal Design for Multinomial Logit Model with Applications to Best Assortment Identification

We study optimal experimental design for multinomial logit (MNL) bandits, where an agent repeatedly selects a subset of

K

items from a ground set of size

N

and observes single-choice feedback. Unlike linear or generalized linear bandits, MNL bandits have a combinatorial action space, which makes classical optimal design approaches and naive optimization over all subsets computationally intractable. We propose a computationally efficient optimal design framework for MNL models that achieves both statistical efficiency and scalability through two complementary approaches: (i) an exact or certified-approximate reformulation of the design oracle as a

0

-

1

mixed-integer linear program (MILP) with solver-certified early stopping, and (ii) a fully polynomial-time lifted design that replaces the nonlinear objective with a tractable surrogate. Using the Kiefer-Wolfowitz equivalence theorem, we establish near G-optimality guarantees and characterize the induced statistical-computational trade-offs. As an application, we develop a best assortment identification algorithm for MNL bandits with linear utilities and non-uniform revenues, and prove an instance-dependent sample complexity of

\tilde{O}\big(\frac{d \log N}{Δ^2}\big)

, where

d

is the feature dimension,

N

is the number of arms, and

Δ

is the minimum revenue gap.

Joongkyu Lee, Min-hwan Oh

Seoul National University, Seoul, Korea.

Multi-Armed Bandits Discrete Choice Modeling Assortment Optimization

May 17, 2026cs.LG

Learning in Position-Aware Multinomial Logit Bandits: From Multiplicative to General Position Effects

We study the dynamic joint assortment selection and positioning problem, where the attraction of each product depends on both its intrinsic appeal and its display position under a Multinomial Logit (MNL) choice framework. Our study ranges from the multiplicative position effects model, in which each product's attraction is scaled by a position-specific factor, to a general position effects model assigning independent attraction parameters to every product--position pair to capture heterogeneous synergies. For both models, we design round-based learning algorithms that update decisions after every single feedback, and establish the first regret-optimal characterization. Besides, our round-based algorithms provide the prompt operations needed by modern platforms. For the multiplicative model, we develop a cross-position pairwise maximum likelihood estimator with a clipping mechanism, and prove that our algorithm P2MLE-UCB attains a regret of

\tilde{O}(\sqrt{NT})

, matching the lower bound and closing the

\sqrt{K}

gap left by prior epoch-based analyses. For the general model, we establish a minimax lower bound and propose GP2-UCB with a matching upper bound. Moreover, we design an efficient subroutine for the per-round joint assortment and positioning optimization based on Dinkelbach's method and maximum-weight bipartite matching. Numerical experiments on synthetic data and the Expedia dataset show that our algorithms consistently outperform state-of-the-art benchmarks.

Xi Chen, Shibo Dai, Jiameng Lyu +1

Leonard N. Stern School of Business, New York University, New York, NY 10012, USA · Qiuzhen College, Tsinghua University, Beijing 100084, China · Department of Management Science, School of Management, Fudan University, Shanghai, 200433, China +1

Multi-Armed Bandits Discrete Choice Modeling Assortment Optimization

May 15, 2026cs.LG

Boundedly Rational Meta-Learning in Sequential Consumer Choice

Many consumer decisions are repeated choices under uncertainty. Standard models capture these decisions using Bayesian learning and dynamic programming: consumers update beliefs from feedback and use those beliefs to guide future choices. In many markets, however, learning does not restart when consumers enter a new context: prior experience with a brand, product, or provider can shape beliefs in later, related decisions. We study this cross-context knowledge transfer, or meta-learning, in sequential choice. We design a hierarchical laboratory task in which participants repeatedly choose among airlines across routes and observe noisy binary outcomes. Reduced-form evidence shows that participants improve not only within routes, but also across routes: they choose better airlines earlier in later routes and reduce pseudo-regret. To identify the mechanism behind this transfer, we compare human choices to a no-transfer benchmark and a fully integrated Bayesian meta-learning benchmark. In particular, we introduce a class of boundedly rational meta dynamic programming policies, BRMDP(D), that approximate full integration using a limited number of hyper-posterior draws, denoted by D. Trial-by-trial likelihood comparisons show that low-D boundedly rational meta-learning, especially BRMDP(1), fits participant behavior better than both no transfer and fully integrated Bayesian transfer. Consumers, therefore, transfer brand-level regularities across contexts, but through coarse representations of prior uncertainty. The findings imply that models of consumer learning should allow for approximate cross-context transfer, and that managerial counterfactuals based on either no-transfer or fully integrated learning can be misleading.

Mehrzad Khosravi, Max Kleiman-Weiner, Hema Yoganarasimhan

University of Washington

Meta-Learning Sequential Decision Making Discrete Choice Modeling Bayesian Decision Theory Bounded Rationality Decision-Making under Uncertainty

May 9, 2026cs.LG

Contextual Plackett-Luce: An Efficient Neural Model for Probabilistic Sequence Selection under Ambiguity

Selecting a coherent sequence or subset of elements is a fundamental problem in structured prediction, arising in tasks such as detection, trajectory forecasting, and representative subset selection. In many such settings, the target is inherently ambiguous: each input admits multiple valid outputs, while supervision provides only a single sampled instance. This induces a mismatch between the underlying multi-modal target distribution and the observed training signal. We propose Contextual Plackett-Luce (CPL), a structured probabilistic model for sequence selection that extends the classical Plackett-Luce model to a context-dependent setting following an Ising-style parameterization with unary and pairwise interaction terms. CPL can be viewed as a hybrid between fully autoregressive prediction and parallel sequence selection: autoregressive models effectively capture uncertainty but are computationally expensive on modern parallel hardware such as GPUs, while parallel methods are efficient but struggle to represent multi-modal dependencies. CPL combines the strengths of both by constructing the parameters of a probabilistic selection model in a fully parallel manner, followed by a lightweight autoregressive selection process in which each step applies incremental updates to contextual logits. This decoupling of parallel scoring and sequential selection enables efficient computation without sacrificing expressivity. We evaluate CPL on two structured selection tasks: multi-modal path prediction and representative subset selection. CPL achieves improved structural consistency and robustness under ambiguous supervision compared to strong parallel baselines.

Noam Mizrachi, Nadav Har-Tuv, Shai Shalev-Shwartz

Mobileye

Discrete Choice Modeling Structured Prediction

May 7, 2026cs.LG

Causal-Aware Foundation-Model for Bilevel Optimization in Discrete Choice Settings

We introduce a causal aware foundation-model framework for real time optimal decision making in discrete choice environments. We propose a constrained triple-head price optimization (C3PO) network to solve a bilevel decision problem in which a service provider selects an optimal assortment while heterogeneous users make personalized acceptance or rejection choices optimizing their own personalized preferences. C3PO integrates imitation learning of prices, multi-task learning of revenue responses, and in context learning of price elasticity to generate pricing recommendations while adhering to business constraints. During inference, frontier model prompting retrieves an enhanced elasticity prior for new products from behavioral economics literature, improving pricing effectiveness. We demonstrate strong in context learning performance using simulated, synthetic, and real-world datasets. C3PO is trained on simulated data generated from multiple classical discrete choice models in economics. The model is trained on data comprising simulated customer segments and counterfactual action and outcome pairs and evaluated on randomly generated choice environments with no access to the underlying preference structure. The trained model consistently improves the pricing KPIs, with gains increasing as customer price sensitivity increases. We also deploy the tuned foundation model for optimal pricing in real-world applications such as healthcare, tender pricing, airline ancillary pricing, and other domains, achieving substantial gains across multiple products, markets, and divisions.

Shivaram Subramanian, Zhengliang Xue, Markus Ettl +2

IBM T.J. Watson Research Center Yorktown Heights, New York, 10598, U.S.A.

Large Language Model-Guided Optimization Discrete Choice Modeling Bilevel Optimization Dynamic Pricing

Mar 25, 2026stat.ME

Amortized Inference for Correlated Discrete Choice Models via Equivariant Neural Networks

Discrete choice models are fundamental tools in management science, economics, and marketing for understanding and predicting decision-making. Logit-based models are dominant in applied work, largely due to their convenient closed-form expressions for choice probabilities. However, they impose restrictive assumptions on the stochastic utility component, constraining our ability to capture realistic substitution patterns. We propose an amortized inference approach that relies on a neural network emulator to approximate choice probabilities for general error distributions, including those with correlated errors. We develop a specialized neural network architecture designed to respect the invariance properties of discrete choice models. We provide group-theoretic foundations for the architecture, including a proof of universal approximation given a minimal set of invariant features. Once trained, the emulator enables rapid likelihood evaluation and gradient computation. We use Sobolev training, augmenting the likelihood loss with a gradient-matching penalty, so that the emulator learns both choice probabilities and their derivatives. We show that emulator-based maximum likelihood estimators are consistent and asymptotically normal under mild approximation conditions, and we provide sandwich standard errors that remain valid for a psuedo-true parameter even with imperfect likelihood approximation. Simulations show significant gains over the GHK simulator in accuracy and speed.

Easton Huch, Michael Keane

Postdoctoral Fellow, Johns Hopkins Carey Business School · Carey Distinguished Professor, Johns Hopkins Carey Business School

Neural Surrogate Modeling Amortized Inference Equivariant Neural Networks Discrete Choice Modeling

Sep 8, 2025stat.ML

Alternative Graph Neural Networks: Synergizing GEV Models and Deep Learning for Travel Mode Choice Modeling

Generalized extreme value models capture dependence among choice alternatives in discrete choice modeling, but require this dependence to be predefined, symmetric, and shared uniformly across individuals. Recent efforts to synergize discrete choice models with deep neural networks have improved predictive performance but still cannot explicitly represent alternative dependence within neural architectures. To address these gaps, we introduce the alternative graph -- a graph in which nodes represent choice alternatives and edges encode their dependence -- and propose Alternative Graph Neural Networks (Alt-GNNs), a family of GNN-based discrete choice models that embed alternative dependence within a unified framework. Theoretically, Alt-GNNs incorporate multinomial logit, nested logit, and ASU-DNN as special cases and enable innovative model designs, including Nested Alt-GNN, Complete Alt-GNN, and Attention Alt-GNN. Alt-GNNs are consistent with random utility maximization theory, enforce behavioral constraints through alternative graphs, and offer a novel graph-based interpretation of utility functions. Empirically, on two travel mode choice datasets from London and Chicago, Alt-GNNs significantly improve predictive performance over all benchmark models in mode choice modeling because of their flexible alternative graph design and vast hyperparameter space. Even the simplest Alt-GNN variant -- Nested Alt-GNN -- generalizes the nested logit model while preserving its unique two-layer substitution properties, enabling graph-based behavioral constraints over otherwise unconstrained behavioral patterns from deep neural networks.

Yuqi Zhou, Zhanhong Cheng, Dingyi Zhuang +3

aDepartment of Urban and Regional Planning, University of Florida · dDepartment of Civil and Environmental Engineering, Massachusetts Institute of Technology · bCollege of Architecture, Texas A&M University +1

Graph Neural Networks Discrete Choice Modeling

May 23, 2025stat.ML

Bayesian Deep Learning for Discrete Choice

Discrete choice models (DCMs) are used to analyze individual decision-making in contexts such as transportation choices, political elections, and consumer preferences. DCMs play a central role in applied econometrics by enabling inference on key economic variables, such as marginal rates of substitution, rather than focusing solely on predicting choices on new unlabeled data. However, while traditional DCMs offer high interpretability and support for point and interval estimation of economic quantities, these models often underperform in predictive tasks compared to deep learning (DL) models. Despite their predictive advantages, DL models remain largely underutilized in discrete choice due to concerns about their lack of interpretability, unstable parameter estimates, and the absence of established methods for uncertainty quantification. Here, we introduce a deep learning model architecture specifically designed to integrate with approximate Bayesian inference methods, such as Stochastic Gradient Langevin Dynamics (SGLD). Our proposed model collapses to behaviorally informed hypotheses when data is limited, mitigating overfitting and instability in underspecified settings while retaining the flexibility to capture complex nonlinear relationships when sufficient data is available. We demonstrate our approach using SGLD through a Monte Carlo simulation study, evaluating both predictive metrics--such as out-of-sample balanced accuracy--and inferential metrics--such as empirical coverage for marginal rates of substitution interval estimates. Additionally, we present results from two empirical case studies: one using revealed mode choice data in NYC, and the other based on the widely used Swiss train choice stated preference data.

Daniel F. Villarraga, Ricardo A. Daziano

School of Civil and Environmental Engineering, Cornell University, 220 Hollister Hall, Ithaca, NY 14853, USA

Bayesian Neural Networks Bayesian Inference Discrete Choice Modeling

Jan 13, 2025stat.ML

Pairwise Comparisons without Stochastic Transitivity: Model, Theory and Applications

Most statistical models for pairwise comparisons, including the Bradley-Terry (BT) and Thurstone models and many extensions, make a relatively strong assumption of stochastic transitivity. This assumption imposes the existence of an unobserved global ranking among all the players/teams/items and monotone constraints on the comparison probabilities implied by the global ranking. However, the stochastic transitivity assumption does not hold in many real-world scenarios of pairwise comparisons, especially games involving multiple skills or strategies. As a result, models relying on this assumption can have suboptimal predictive performance. In this paper, we propose a general family of statistical models for pairwise comparison data without a stochastic transitivity assumption, substantially extending the BT and Thurstone models. In this model, the pairwise probabilities are determined by a (approximately) low-dimensional skew-symmetric matrix. Likelihood-based estimation methods and computational algorithms are developed, which allow for sparse data with only a small proportion of observed pairs. Theoretical analysis shows that the proposed estimator achieves minimax-rate optimality, which adapts effectively to the sparsity level of the data. The spectral theory for skew-symmetric matrices plays a crucial role in the implementation and theoretical analysis. The proposed method's superiority against the BT model, along with its broad applicability across diverse scenarios, is further supported by simulations and real data analysis.

Sze Ming Lee, Yunxiao Chen

Department of Statistics · London School of Economics and Political Science · London WC2A 2AE, United Kingdom

Pairwise Comparison Pairwise Preference Evaluation Learning to Rank Pairwise Ranking Discrete Choice Modeling

Sep 16, 2024stat.ML

The EM-algorithm and the Method of Moments in Softmax Mixture Models

Softmax Mixture Models (SMMs) are discrete

K

-component mixture models for the probabilities of selecting one of

p

candidate feature vectors

X_1,\ldots,X_p\in\mathbb{R}^L

in heterogeneous populations and are widely used in econometrics and scientific applications. Related softmax mixture mechanisms also appear in modern LLM architectures. We provide a theoretical and methodological study of SMMs, focusing on the Expectation-Maximization (EM) algorithm and the Method of Moments (MoM). We show that EM recovers the mixture atoms at the parametric rate, up to logarithmic factors, after

\mathcal{O}(\log N)

iterations, provided atom separation is at least of order

\log K

. This improves on separation conditions in existing analyses of EM for high-dimensional Gaussian mixtures. We also develop MoM procedures for parameter and subspace estimation. Although MoM parameter estimates converge more slowly than EM and can deteriorate with

K

, they provide provable warm starts for EM and are useful for small

K

. For general

K

, we estimate the atom subspace via MoM and recommend running EM from multiple random initializations within this subspace. Finally, as

p\to\infty

, we show that SMMs approximate mixtures of exponential tilts of the feature distribution, yielding asymptotic identifiability.

Xin Bing, Florentina Bunea, Jonathan Niles-Weed +1

Department of Statistical Sciences, University of Toronto · Department of Statistics and Data Science, Cornell University · Courant Institute of Mathematical Sciences and Center for Data Science, New York University +1

Expectation-Maximization Discrete Choice Modeling Statistical Learning Theory