AK: Attentive Kernel for Information Gathering

Authors: Weizhe Chen, Roni Khardon, Lantao Liu · RSS 2022

Licences

Open Access
Paper: CC BY 4.0

Everything below draws on the full paper under its CC BY 4.0 licence; its figure is credited to the authors.

TL;DR

A nonstationary GP kernel that blends fixed lengthscales and masks correlations across sharp changes, so map uncertainty follows real error and the robot samples where it matters.

Why it matters

When a sampling robot's model gives high uncertainty where its error is high, the planner spends the sampling budget on complex regions rather than covering space uniformly. Because the kernel wraps any existing base kernel, it can be dropped into existing GP-based mapping and informative-planning pipelines, and the field test shows it running on a surface vehicle doing bathymetric mapping.

Problem

Robotic information gathering chooses where a robot samples next from the uncertainty of a probabilistic model, usually a Gaussian process with a stationary kernel such as RBF. Real terrain is not stationary: some areas vary much more than others, so a stationary model over-smooths and assigns high uncertainty simply to unvisited areas regardless of error. Existing nonstationary kernels are often too flexible to train reliably.

Proposed solution

The Attentive Kernel combines two learned, input-dependent selections. Lengthscale selection mixes a fixed set of base kernels with preset lengthscales using softmax weights from a small neural network, instead of learning a lengthscale function. Instance selection gives each input a soft membership vector whose dot product masks correlations between points on opposite sides of sharp transitions; all parameters are fitted by maximizing the GP marginal likelihood, and the resulting uncertainty drives an entropy-minus-distance waypoint planner.

Key insights

Choosing among preset lengthscales, rather than learning a free lengthscale function, makes a nonstationary kernel easier to train and compatible with any base kernel.
Masking correlations with soft membership vectors handles abrupt changes that a small lengthscale alone cannot model well.
Better-calibrated uncertainty, not a better planner, was enough to improve informative planning: with the same simple planner, AK concentrated samples in high-error regions while RBF covered the space uniformly.
Ablation showed lengthscale selection is necessary; instance selection gave no significant gain in the aggregated metrics with the current training scheme, though the authors expect it to help at sharp transitions.
Performance changed little with the number of base kernels (5 to 10 recommended), hidden units and lengthscale bounds after input normalization.

Main results

Across four elevation-map environments and 10 random seeds, AK had the lowest SMSE and MSLL in the informative-planning experiments against RBF, Gibbs and Deep Kernel Learning (metrics averaged over the sampling curve).
Informative planning on N17E073: SMSE 0.114 for AK vs 0.145 RBF, 0.143 Gibbs and 0.138 DKL; MSLL −1.27 vs −0.97, −1.16 and −1.01.
Active sampling on N43W080: SMSE 0.051 for AK vs 0.078 for RBF; MSLL −1.72 vs −1.41.
Random sampling on N17E073: SMSE 0.111 for AK vs 0.133 for RBF; MSLL −1.24 vs −0.99.
In the field test, an autonomous surface vehicle with a downward single-beam sonar collected most samples in regions with drastic elevation changes and reduced prediction uncertainty across the workspace (qualitative result).

Limitations

The authors note that the marginal likelihood's Occam's-razor effect does not prevent overfitting when nonstationary kernels are trained for many iterations; they use a rule-of-thumb early-stopping scheme and call principled training an open problem.
Outliers and heteroscedastic noise are not handled and are named as future work.
Instance selection did not give a measurable improvement in aggregated metrics with the current training scheme, and a two-network variant degraded uncertainty in one environment.
Benchmarks use 2D elevation maps only, and the field experiment is a single qualitative run without numeric error reported.
Kernel cost grows with the number of base kernels (O(N²M) for the kernel matrices), on top of standard GP scaling.

Field impact

The paper won the RSS 2022 Best Student Paper Award and has 22 citations. It releases the code for reproducibility and PyPolo, a software library for robotic information gathering research.

Abstract

Robotic Information Gathering (RIG) relies on the uncertainty of a probabilistic model to identify critical areas for efficient data collection. Gaussian processes (GPs) with stationary kernels have been widely adopted for spatial modeling. However, real-world spatial data typically does not satisfy the assumption of stationarity, where different locations are assumed to have the same degree of variability. As a result, the prediction uncertainty does not accurately capture prediction error, limiting the success of RIG algorithms. We propose a novel family of nonstationary kernels, named the Attentive Kernel (AK), which is simple, robust, and can extend any existing kernel to a nonstationary one. We evaluate the new kernel in elevation mapping tasks, where AK provides better accuracy and uncertainty quantification over the commonly used RBF kernel and other popular nonstationary kernels. The improved uncertainty quantification guides the downstream RIG planner to collect more valuable data around the high-error area, further increasing prediction accuracy. A field experiment demonstrates that the proposed method can guide an Autonomous Surface Vehicle (ASV) to prioritize data collection in locations with high spatial variations, enabling the model to characterize the salient environmental features.

Open Source Robotics