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Distributed Learning for Dynamic Congestion Games

Hongbo Li, Lingjie Duan

TL;DR

This work studies distributed learning in dynamic congestion games where user routing decisions alter future congestion and information evolves endogenously. It shows that myopic routing leads to under-exploration of stochastic paths and a PoA exceeding $2$, motivating an information-design solution. The authors propose the CHAR mechanism, combining hiding and probabilistic, state-dependent recommendations to achieve a near-optimal long-run performance with PoA below $5/4$ and guaranteed learning convergence, significantly improving over benchmark information-design approaches. Real-world data experiments using Baidu Map confirm CHAR’s strong average performance, with only minor efficiency loss relative to the social optimum. Practically, CHAR provides a robust, incentive-compatible way to coordinate distributed learning and routing in crowdsourced traffic systems.

Abstract

Today mobile users learn and share their traffic observations via crowdsourcing platforms (e.g., Google Maps and Waze). Yet such platforms myopically recommend the currently shortest path to users, and selfish users are unwilling to travel to longer paths of varying traffic conditions to explore. Prior studies focus on one-shot congestion games without information learning, while our work studies how users learn and alter traffic conditions on stochastic paths in a distributed manner. Our analysis shows that, as compared to the social optimum in minimizing the long-term social cost via optimal exploration-exploitation tradeoff, the myopic routing policy leads to severe under-exploration of stochastic paths with the price of anarchy (PoA) greater than \(2\). Besides, it fails to ensure the correct learning convergence about users' traffic hazard beliefs. To mitigate the efficiency loss, we first show that existing information-hiding mechanisms and deterministic path-recommendation mechanisms in Bayesian persuasion literature do not work with even \(\text{PoA}=\infty\). Accordingly, we propose a new combined hiding and probabilistic recommendation (CHAR) mechanism to hide all information from a selected user group and provide state-dependent probabilistic recommendations to the other user group. Our CHAR successfully ensures PoA less than \(\frac{5}{4}\), which cannot be further reduced by any other informational mechanism. Additionally, we experiment with real-world data to verify our CHAR's good average performance.

Distributed Learning for Dynamic Congestion Games

TL;DR

This work studies distributed learning in dynamic congestion games where user routing decisions alter future congestion and information evolves endogenously. It shows that myopic routing leads to under-exploration of stochastic paths and a PoA exceeding , motivating an information-design solution. The authors propose the CHAR mechanism, combining hiding and probabilistic, state-dependent recommendations to achieve a near-optimal long-run performance with PoA below and guaranteed learning convergence, significantly improving over benchmark information-design approaches. Real-world data experiments using Baidu Map confirm CHAR’s strong average performance, with only minor efficiency loss relative to the social optimum. Practically, CHAR provides a robust, incentive-compatible way to coordinate distributed learning and routing in crowdsourced traffic systems.

Abstract

Today mobile users learn and share their traffic observations via crowdsourcing platforms (e.g., Google Maps and Waze). Yet such platforms myopically recommend the currently shortest path to users, and selfish users are unwilling to travel to longer paths of varying traffic conditions to explore. Prior studies focus on one-shot congestion games without information learning, while our work studies how users learn and alter traffic conditions on stochastic paths in a distributed manner. Our analysis shows that, as compared to the social optimum in minimizing the long-term social cost via optimal exploration-exploitation tradeoff, the myopic routing policy leads to severe under-exploration of stochastic paths with the price of anarchy (PoA) greater than . Besides, it fails to ensure the correct learning convergence about users' traffic hazard beliefs. To mitigate the efficiency loss, we first show that existing information-hiding mechanisms and deterministic path-recommendation mechanisms in Bayesian persuasion literature do not work with even . Accordingly, we propose a new combined hiding and probabilistic recommendation (CHAR) mechanism to hide all information from a selected user group and provide state-dependent probabilistic recommendations to the other user group. Our CHAR successfully ensures PoA less than , which cannot be further reduced by any other informational mechanism. Additionally, we experiment with real-world data to verify our CHAR's good average performance.
Paper Structure (27 sections, 8 theorems, 53 equations, 3 figures)

This paper contains 27 sections, 8 theorems, 53 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Dynamic Congestion Model
  4. Distributed Learning Model
  5. Problem Formulations and Policies Comparison
  6. Problem Formulation for Myopic Policy
  7. Problem Formulation for Socially Optimal Policy
  8. Policies Comparison via PoA Analysis
  9. CHAR Mechanism with Learning Convergence
  10. Benchmark Informational Mechanisms Comparison
  11. New CHAR Mechanism Design and Analysis
  12. Experiment Validation Using Real Datasets
  13. Proof of Lemma 1
  14. Proof of Lemma 2
  15. Monotonicity of Exploration Numbers
  16. ...and 12 more sections

Key Result

Lemma 1

Under the myopic policy, given $\hbox{$\mathbb{E}[\ell_1(t)|x_1'(t-1)]$}$ and $\hbox{$x_1(t)$}$ of stochastic path 1, the exploration number is:

Figures (3)

  • Figure 1: Dynamic congestion model: within each time slot $t$, a random number $\hbox{$N(t)$}$ of users arrive at O to decide routings to D.
  • Figure 2: A popular hybrid road network consisting of three path choices from the Palace Museum to the National Stadium.
  • Figure 3: Average long-term costs (in minutes) under myopic, information hiding and socially optimal policies, and our CHAR mechanism versus $T$.

Theorems & Definitions (9)

  • Lemma 1
  • Lemma 2
  • Proposition 1
  • Theorem 1
  • Proposition 2
  • Lemma 3
  • Lemma 4
  • Definition 1: CHAR mechanism
  • Theorem 2