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Preference-Centric Route Recommendation: Equilibrium, Learning, and Provable Efficiency

Ya-Ting Yang, Yunian Pan, Quanyan Zhu

TL;DR

This paper addresses the limitations of Wardrop Equilibrium for capturing diverse, context-dependent user preferences in route recommendation. It introduces a preference-centric framework built on Borda Coarse Correlated Equilibrium (BCCE) and a Dueling-Adaptive Recommendation (DR) algorithm that learns from binary, pairwise feedback to drive the system toward BCCE. The authors prove an expected regret bound of $\mathcal{O}(\max_u (|\mathcal{S}_u|\log|\mathcal{S}_u|)^{1/3} T^{2/3})$ under carefully chosen learning and exploration parameters and illustrate practical efficacy via a case study. The work offers a scalable, parameter-free approach with provable efficiency for preference-guided route recommendation, highlighting its potential to better model bounded rationality and real-time user feedback in navigation platforms.

Abstract

Traditional approaches to modeling and predicting traffic behavior often rely on Wardrop Equilibrium (WE), assuming non-atomic traffic demand and neglecting correlations in individual decisions. However, the growing role of real-time human feedback and adaptive recommendation systems calls for more expressive equilibrium concepts that better capture user preferences and the stochastic nature of routing behavior. In this paper, we introduce a preference-centric route recommendation framework grounded in the concept of Borda Coarse Correlated Equilibrium (BCCE), wherein users have no incentive to deviate from recommended strategies when evaluated by Borda scores-pairwise comparisons encoding user preferences. We develop an adaptive algorithm that learns from dueling feedback and show that it achieves $\mathcal{O}(T^{\frac{2}{3}})$ regret, implying convergence to the BCCE under mild assumptions. We conduct empirical evaluations using a case study to illustrate and justify our theoretical analysis. The results demonstrate the efficacy and practical relevance of our approach.

Preference-Centric Route Recommendation: Equilibrium, Learning, and Provable Efficiency

TL;DR

This paper addresses the limitations of Wardrop Equilibrium for capturing diverse, context-dependent user preferences in route recommendation. It introduces a preference-centric framework built on Borda Coarse Correlated Equilibrium (BCCE) and a Dueling-Adaptive Recommendation (DR) algorithm that learns from binary, pairwise feedback to drive the system toward BCCE. The authors prove an expected regret bound of under carefully chosen learning and exploration parameters and illustrate practical efficacy via a case study. The work offers a scalable, parameter-free approach with provable efficiency for preference-guided route recommendation, highlighting its potential to better model bounded rationality and real-time user feedback in navigation platforms.

Abstract

Traditional approaches to modeling and predicting traffic behavior often rely on Wardrop Equilibrium (WE), assuming non-atomic traffic demand and neglecting correlations in individual decisions. However, the growing role of real-time human feedback and adaptive recommendation systems calls for more expressive equilibrium concepts that better capture user preferences and the stochastic nature of routing behavior. In this paper, we introduce a preference-centric route recommendation framework grounded in the concept of Borda Coarse Correlated Equilibrium (BCCE), wherein users have no incentive to deviate from recommended strategies when evaluated by Borda scores-pairwise comparisons encoding user preferences. We develop an adaptive algorithm that learns from dueling feedback and show that it achieves regret, implying convergence to the BCCE under mild assumptions. We conduct empirical evaluations using a case study to illustrate and justify our theoretical analysis. The results demonstrate the efficacy and practical relevance of our approach.

Paper Structure

This paper contains 11 sections, 6 theorems, 33 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Formulation
  4. Repeated Route Recommendation
  5. Equilibrium Concept and Learning
  6. Algorithm and Regret Analysis
  7. The Dueling-Adaptive Recommendation
  8. Provable Efficiency
  9. Case Study
  10. Conclusion and Future Work
  11. Proofs

Key Result

Lemma 1

Suppose for a sufficiently small $\varepsilon > 0$, there is a sequence of flows and recommendations $\{ x^{t-1}, (i^t_u, j^t_u)_{u \in \mathcal{U}}\}_{t=1}^T$ such that $\mathcal{R}_u (T) \leq T \varepsilon$ for every user $u \in \mathcal{U}$, then the empirical distribution of flows and route reco is an $\varepsilon$-BCCE, i.e., for all $u \in \mathcal{U}$ and $s^{\prime}_u \in \mathcal{S}_u$.

Figures (2)

  • Figure 1: In this example network, there are three O-D pairs (1-7), (1-9), and (3-9). The edge values represent the free-flow travel time of the corresponding road segment.
  • Figure 2: The regret plot of different user population configurations, where we plot the mean regret with standard deviations for different OD populations.

Theorems & Definitions (8)

  • Definition 1: Borda Coarse Correlated Equilibrium (BCCE)
  • Lemma 1
  • Theorem 1
  • Remark 1
  • Lemma 2: Bounded Magnitude of Borda Estimator
  • Lemma 3: Unbiasedness
  • Lemma 4: Expected Borda score
  • Lemma 5: Bounded second moment