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Provably Stable Multi-Agent Routing with Bounded-Delay Adversaries in the Decision Loop

Roee M. Francos, Daniel Garces, Stephanie Gil

TL;DR

This work investigates stability in multi-agent routing when a subset of agents behave adversarially with bounded delays in a centralized decision loop. It analyzes instantaneous and random assignment policies, deriving a threshold on the adversarial fraction $F$ that leads to instability for random assignment and a new fleet-size bound $N \ge \mathbb{E}[\eta] D_{\max} + 2 \Delta \mathbb{E}[\eta] F_{\max}$ that guarantees stability under bounded delays; the same bound extends to instantaneous assignment since it yields lower expected service times. The authors validate the theory with a case study using real San Francisco taxi data, estimating demand and travel-time distributions to compute the bound and demonstrate stability restoration with modest increases in cooperative agents. The results offer practical guidelines for fleet design under potential internal adversaries and pave the way for broader attack models and monitoring strategies in routing systems.

Abstract

In this work, we are interested in studying multi-agent routing settings, where adversarial agents are part of the assignment and decision loop, degrading the performance of the fleet by incurring bounded delays while servicing pickup-and-delivery requests. Specifically, we are interested in characterizing conditions on the fleet size and the proportion of adversarial agents for which a routing policy remains stable, where stability for a routing policy is achieved if the number of outstanding requests is uniformly bounded over time. To obtain this characterization, we first establish a threshold on the proportion of adversarial agents above which previously stable routing policies for fully cooperative fleets are provably unstable. We then derive a sufficient condition on the fleet size to recover stability given a maximum proportion of adversarial agents. We empirically validate our theoretical results on a case study on autonomous taxi routing, where we consider transportation requests from real San Francisco taxicab data.

Provably Stable Multi-Agent Routing with Bounded-Delay Adversaries in the Decision Loop

TL;DR

This work investigates stability in multi-agent routing when a subset of agents behave adversarially with bounded delays in a centralized decision loop. It analyzes instantaneous and random assignment policies, deriving a threshold on the adversarial fraction that leads to instability for random assignment and a new fleet-size bound that guarantees stability under bounded delays; the same bound extends to instantaneous assignment since it yields lower expected service times. The authors validate the theory with a case study using real San Francisco taxi data, estimating demand and travel-time distributions to compute the bound and demonstrate stability restoration with modest increases in cooperative agents. The results offer practical guidelines for fleet design under potential internal adversaries and pave the way for broader attack models and monitoring strategies in routing systems.

Abstract

In this work, we are interested in studying multi-agent routing settings, where adversarial agents are part of the assignment and decision loop, degrading the performance of the fleet by incurring bounded delays while servicing pickup-and-delivery requests. Specifically, we are interested in characterizing conditions on the fleet size and the proportion of adversarial agents for which a routing policy remains stable, where stability for a routing policy is achieved if the number of outstanding requests is uniformly bounded over time. To obtain this characterization, we first establish a threshold on the proportion of adversarial agents above which previously stable routing policies for fully cooperative fleets are provably unstable. We then derive a sufficient condition on the fleet size to recover stability given a maximum proportion of adversarial agents. We empirically validate our theoretical results on a case study on autonomous taxi routing, where we consider transportation requests from real San Francisco taxicab data.

Paper Structure

This paper contains 18 sections, 6 theorems, 38 equations, 4 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Environment and Control Space
  4. Request Model
  5. Adversarial Influence Model
  6. Stability of a Policy
  7. Policy of Interest
  8. Background: Necessary and Sufficient Conditions for Stability of a Policy with Only Cooperative Agents
  9. Theoretical Results
  10. Characterizing the Proportion of Adversarial Agents That Results in Instability of Random Assignment
  11. New Sufficient Condition on the Fleet Size for Stability of a Routing Policy in the Presence of Adversarial Agents
  12. Case Study and Empirical Results: Autonomous Taxicab Routing in San Francisco
  13. Implementation Details
  14. Estimating Probability Distributions
  15. Proportion of Adversarial Agents That Provably Results in Instability
  16. ...and 3 more sections

Key Result

Theorem 1

(Lemma 1 in garces2024approximate) Let the random variable $v_{\text{rand}}$ with support $\mathds{V}$ represent the location of a random agent that gets assigned to a request after that agent has previously served a different request. Define $D_{\text{max}} \triangleq \max\{E[d(\xi, \rho)], E[d(v_{

Figures (4)

  • Figure 1: Map of the environment used for numerical simulations.
  • Figure 2: Number of outstanding requests for random assignment (RA) and Instantaneous Assignment (IA) policies with a fleet size of $35$ agents and different proportions of adversarial agents $F$.
  • Figure 3: Number of outstanding requests for Random Assignment (RA) policy with different proportions of adversarial agents $F$ and different fleet sizes $N$.
  • Figure 4: Number of outstanding requests for instantaneous assignment (IA) policy with different proportions of adversarial agents $F$ and different fleet sizes $N$. Note that the vertical axis scale is different for all three sub-figures, and the vertical axis scale is smaller than the one for Fig. \ref{['ref:rand_stability_results']}

Theorems & Definitions (12)

  • Definition 1
  • Definition 2
  • Theorem 1
  • Theorem 2
  • Corollary 1
  • proof
  • Theorem 3
  • proof
  • Theorem 4
  • proof
  • ...and 2 more