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Who Moved My Distribution? Conformal Prediction for Interactive Multi-Agent Systems

Allen Emmanuel Binny, Anushri Dixit

TL;DR

This work introduces an iterative conformal prediction framework that systematically adapts the uncertainty-aware ego-agent controller to the endogenous distribution shift, and provides probabilistic safety guarantees while adapting to the evolving behavior of reactive, non-ego agents.

Abstract

Uncertainty-aware prediction is essential for safe motion planning, especially when using learned models to forecast the behavior of surrounding agents. Conformal prediction is a statistical tool often used to produce uncertainty-aware prediction regions for machine learning models. Most existing frameworks utilizing conformal prediction-based uncertainty predictions assume that the surrounding agents are non-interactive. This is because in closed-loop, as uncertainty-aware agents change their behavior to account for prediction uncertainty, the surrounding agents respond to this change, leading to a distribution shift which we call endogenous distribution shift. To address this challenge, we introduce an iterative conformal prediction framework that systematically adapts the uncertainty-aware ego-agent controller to the endogenous distribution shift. The proposed method provides probabilistic safety guarantees while adapting to the evolving behavior of reactive, non-ego agents. We establish a model for the endogenous distribution shift and provide the conditions for the iterative conformal prediction pipeline to converge under such a distribution shift. We validate our framework in simulation for 2- and 3- agent interaction scenarios, demonstrating collision avoidance without resulting in overly conservative behavior and an overall improvement in success rates of up to 9.6% compared to other conformal prediction-based baselines.

Who Moved My Distribution? Conformal Prediction for Interactive Multi-Agent Systems

TL;DR

This work introduces an iterative conformal prediction framework that systematically adapts the uncertainty-aware ego-agent controller to the endogenous distribution shift, and provides probabilistic safety guarantees while adapting to the evolving behavior of reactive, non-ego agents.

Abstract

Uncertainty-aware prediction is essential for safe motion planning, especially when using learned models to forecast the behavior of surrounding agents. Conformal prediction is a statistical tool often used to produce uncertainty-aware prediction regions for machine learning models. Most existing frameworks utilizing conformal prediction-based uncertainty predictions assume that the surrounding agents are non-interactive. This is because in closed-loop, as uncertainty-aware agents change their behavior to account for prediction uncertainty, the surrounding agents respond to this change, leading to a distribution shift which we call endogenous distribution shift. To address this challenge, we introduce an iterative conformal prediction framework that systematically adapts the uncertainty-aware ego-agent controller to the endogenous distribution shift. The proposed method provides probabilistic safety guarantees while adapting to the evolving behavior of reactive, non-ego agents. We establish a model for the endogenous distribution shift and provide the conditions for the iterative conformal prediction pipeline to converge under such a distribution shift. We validate our framework in simulation for 2- and 3- agent interaction scenarios, demonstrating collision avoidance without resulting in overly conservative behavior and an overall improvement in success rates of up to 9.6% compared to other conformal prediction-based baselines.

Paper Structure

This paper contains 18 sections, 1 theorem, 19 equations, 16 figures, 10 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Statement
  4. System Dynamics and Environment
  5. Endogenous Distribution Shifts
  6. Conformal Prediction under Endogenous Distribution Shift
  7. Modeling Endogenous Distribution Shift
  8. Prediction Region Construction
  9. Smoothing Filter for Prediction Set
  10. Results
  11. Two Agent Simulations
  12. Three Agent Simulations
  13. Conclusion and Future Work
  14. Experimental Details
  15. Additional Details on System Dynamics and Environment
  16. ...and 3 more sections

Key Result

theorem 3

If Assumptions ass:cp_lipschitz and ass:mpc_lipschitz hold and the combined Lipschitz constant satisfies $\delta = L_{\text{MPC}} \cdot L_{\text{CP}} < 1$, then the operator $\mathcal{T} = F \circ \textit{CP}$ is a contraction mapping on the space of trajectory distributions equipped with the Wasser

Figures (16)

  • Figure 1: Iterative Conformal Prediction Framework Overview: The process alternates between calibration using collected agent trajectories, updating and smoothing the conformal prediction sets, and deploying an uncertainty-aware controller, with iterative adaptation until convergence is reached under endogenous distribution shift.
  • Figure 2: Comparison for $2$ agents across test cases: Our iterative methods produce trajectories closely matching those without conformal prediction. In Case I, the baseline conformal prediction (BCP) method leads to a deadlock, while in Case II, BCP exhibits significant trajectory deviation.
  • Figure 3: ISCP: $\boldsymbol{q}^{(r)}$ over H
  • Figure 4: ICP: $\boldsymbol{q}^{(r)}$ over H
  • Figure 6: Agent 0
  • ...and 11 more figures

Theorems & Definitions (4)

  • remark 1: Justification of Assumption \ref{['ass:cp_lipschitz']}
  • remark 2: Justification of Assumption \ref{['ass:mpc_lipschitz']}
  • theorem 3: Convergence to the fixed-point of the endogenous distribution shift map
  • proof