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Decentralized Gaussian Process Classification and an Application in Subsea Robotics

Yifei Gao, Hans J. He, Daniel J. Stilwell, James McMahon

TL;DR

This work tackles real-time, decentralized learning of a map for the probability of successful underwater communication between AUVs, formulating it as a decentralized GP binary classifier with a latent function $f$ drawn from a GP $ ext{GP}(oldsymbol{ mu}, k)$. It leverages Pólya-Gamma augmentation to render the logistic likelihood conjugate, enabling tractable GP updates when combined with a sparse GP framework that uses inducing points. A KL-divergence upper bound guides a data-sharing policy: each agent selects inducing points to minimize $ rac{1}{2} ext{tr}( ilde{ extbf{K}})oldsymbol{ ontstrut ext}{ ext{λ}}_{ ext{max}}(oldsymbol{ ext{Ω}}) + rac{1}{2oldsymbol{ ext{λ}}_{ ext{min}}(oldsymbol{ ext{Ω}})}ig Vertoldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{old{old }}}}}}}}}}}}}}ig Vert^2$ to decide which local inducing points to share, constructing a decentralized posterior $q( extbf{f}_{M}|oldsymbol{w})$. Experiments on real field data from Virginia Tech AUVs show that sharing good inducing points yields higher predictive accuracy and lower negative log-likelihood (NLL) than random or bad inducer selections, validating the approach under bandwidth constraints. The method enables real-time cooperative learning of underwater communication maps and has potential applicability to other decentralized GP classification tasks in resource-constrained multi-robot systems.

Abstract

Teams of cooperating autonomous underwater vehicles (AUVs) rely on acoustic communication for coordination, yet this communication medium is constrained by limited range, multi-path effects, and low bandwidth. One way to address the uncertainty associated with acoustic communication is to learn the communication environment in real-time. We address the challenge of a team of robots building a map of the probability of communication success from one location to another in real-time. This is a decentralized classification problem -- communication events are either successful or unsuccessful -- where AUVs share a subset of their communication measurements to build the map. The main contribution of this work is a rigorously derived data sharing policy that selects measurements to be shared among AUVs. We experimentally validate our proposed sharing policy using real acoustic communication data collected from teams of Virginia Tech 690 AUVs, demonstrating its effectiveness in underwater environments.

Decentralized Gaussian Process Classification and an Application in Subsea Robotics

TL;DR

This work tackles real-time, decentralized learning of a map for the probability of successful underwater communication between AUVs, formulating it as a decentralized GP binary classifier with a latent function drawn from a GP . It leverages Pólya-Gamma augmentation to render the logistic likelihood conjugate, enabling tractable GP updates when combined with a sparse GP framework that uses inducing points. A KL-divergence upper bound guides a data-sharing policy: each agent selects inducing points to minimize to decide which local inducing points to share, constructing a decentralized posterior . Experiments on real field data from Virginia Tech AUVs show that sharing good inducing points yields higher predictive accuracy and lower negative log-likelihood (NLL) than random or bad inducer selections, validating the approach under bandwidth constraints. The method enables real-time cooperative learning of underwater communication maps and has potential applicability to other decentralized GP classification tasks in resource-constrained multi-robot systems.

Abstract

Teams of cooperating autonomous underwater vehicles (AUVs) rely on acoustic communication for coordination, yet this communication medium is constrained by limited range, multi-path effects, and low bandwidth. One way to address the uncertainty associated with acoustic communication is to learn the communication environment in real-time. We address the challenge of a team of robots building a map of the probability of communication success from one location to another in real-time. This is a decentralized classification problem -- communication events are either successful or unsuccessful -- where AUVs share a subset of their communication measurements to build the map. The main contribution of this work is a rigorously derived data sharing policy that selects measurements to be shared among AUVs. We experimentally validate our proposed sharing policy using real acoustic communication data collected from teams of Virginia Tech 690 AUVs, demonstrating its effectiveness in underwater environments.

Paper Structure

This paper contains 12 sections, 25 equations, 4 figures, 6 tables.

Table of Contents

  1. INTRODUCTION
  2. Preliminaries
  3. Gaussian Process Binary Classification
  4. Gaussian process classification with Pólya-Gamma (PG) random variable
  5. Sparse Gaussian process with Pólya-Gamma Variables
  6. Selection of inducing points
  7. Lower and Upper bound for Log Marginal likelihood
  8. KL Divergence Upper bound
  9. Communication Among Multiple agents
  10. Prediction
  11. Numerical Results
  12. Concluding Remarks

Figures (4)

  • Figure 1: Virginia Tech 690 AUVs
  • Figure 2: Partial trajectories of two AUVs.
  • Figure 3: Two AUVs trajectories (upper figure), Good(red arrows), random (yellow arrows)and bad (blue arrows )inducing points chosen by local agent inside a locality region.
  • Figure 4: Two agents decentralized prediction on test points from two different locality regions using good (upper figure)/random (middle figure)/bad (bottom figure)inducing points shared among each agent