On Learning the Tail Quantiles of Driving Behavior Distributions via Quantile Regression and Flows

TL;DR

This work adapts two flexible quantile learning frameworks for this setting that avoid strong distributional assumptions: quantile regression (based on the titled absolute loss), and autoregressive quantile flows (a version of normalizing flows).

Abstract

Towards safe autonomous driving (AD), we consider the problem of learning models that accurately capture the diversity and tail quantiles of human driver behavior probability distributions, in interaction with an AD vehicle. Such models, which predict drivers' continuous actions from their states, are particularly relevant for closing the gap between AD agent simulations and reality. To this end, we adapt two flexible quantile learning frameworks for this setting that avoid strong distributional assumptions: (1) quantile regression (based on the titled absolute loss), and (2) autoregressive quantile flows (a version of normalizing flows). Training happens in a behavior cloning-fashion. We use the highD dataset consisting of driver trajectories on several highways. We evaluate our approach in a one-step acceleration prediction task, and in multi-step driver simulation rollouts. We report quantitative results using the tilted absolute loss as metric, give qualitative examples showing that realistic extremal behavior can be learned, and discuss the main insights.

Figures (7)

• Figure 1: For the green AD agent to assess how hard it can brake without causing a collision, it needs a detailed prediction that captures the diversity of the red modeled agent's realistic responses.
• Figure 2: Quantile loss (Eq. \ref{['eq:tiltedabsoluteloss']}) for quantile level $\alpha$koenker_quantile_2001.
• Figure 3: Structure of a conditional (generative direction).
• Figure 4: Quantile loss at different quantile levels for 1d case.
• Figure 5: Quantile loss at different quantile levels for 2d case.