Undiscounted Recursive Path Choice Models: Convergence Properties and Algorithms
Bibliographic record
Abstract
Traffic flow predictions are central to a wealth of problems in transportation. Path choice models can be used for this purpose, and in state-of-the-art models—so-called recursive path choice (RPC) models—the choice of a path is formulated as a sequential arc choice process using undiscounted Markov decision process (MDP) with an absorbing state. The MDP has a utility maximization objective with unknown parameters that are estimated based on data. The estimation and prediction using RPC models require repeatedly solving value functions that are solutions to the Bellman equation. Although there are several examples of successful applications of RPC models in the literature, the convergence of the value iteration method has not been studied. We aim to address this gap. For the two closed-form models in the literature—recursive logit (RL) and nested recursive logit (NRL)—we study the convergence properties of the value iteration method. In the case of the RL model, we show that the operator associated with the Bellman equation is a contraction under certain assumptions on the parameter values. On the contrary, the operator in the NRL case is not a contraction. Focusing on the latter, we study two algorithms designed to improve upon the basic value iteration method. Extensive numerical results based on two real data sets show that the least squares approach we propose outperforms two value iteration methods.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.010 | 0.046 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".