Equilibrium-Constrained Estimation of Recursive Logit Choice Models

2025-10-19

AI Summary

Recursive logit (RL) models flexibly capture sequential choice behavior but suffer from computationally expensive and numerically unstable estimation via the traditional nested fixed-point (NFXP) algorithm. This paper proposes a novel estimation framework that reformulates the RL maximum likelihood problem as a constrained optimization task with equilibrium constraints, jointly estimating structural parameters and value functions. Crucially, we introduce exponential cone modeling to recast the problem as a convex optimization program solvable efficiently by modern conic solvers (e.g., MOSEK). Unlike NFXP, our approach avoids iterative fixed-point computation and associated convergence failures. Empirical evaluation on both synthetic and real-world datasets demonstrates that the method preserves estimation accuracy while substantially improving computational efficiency and numerical robustness. This work establishes a scalable, stable, and tractable paradigm for large-scale dynamic discrete choice modeling.

Technology Category

• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

Abstract

The recursive logit (RL) model provides a flexible framework for modeling sequential decision-making in transportation and choice networks, with important applications in route choice analysis, multiple discrete choice problems, and activity-based travel demand modeling. Despite its versatility, estimation of the RL model typically relies on nested fixed-point (NFXP) algorithms that are computationally expensive and prone to numerical instability. We propose a new approach that reformulates the maximum likelihood estimation problem as an optimization problem with equilibrium constraints, where both the structural parameters and the value functions are treated as decision variables. We further show that this formulation can be equivalently transformed into a conic optimization problem with exponential cones, enabling efficient solution using modern conic solvers such as MOSEK. Experiments on synthetic and real-world datasets demonstrate that our convex reformulation achieves accuracy comparable to traditional methods while offering significant improvements in computational stability and efficiency, thereby providing a practical and scalable alternative for recursive logit model estimation.

Problem

• Reformulating recursive logit estimation as equilibrium-constrained optimization
• Converting maximum likelihood estimation into conic optimization problem
• Improving computational stability and efficiency for sequential choice modeling

Innovation

• Reformulates estimation as equilibrium-constrained optimization
• Transforms problem into conic optimization with exponential cones
• Uses modern conic solvers for computational stability