Optimal Transport for Distribution Adaptation in Bayesian Hilbert Maps

Parameters are one of the most critical components of machine learning models. As datasets and learning domains change, it is often necessary and time-consuming to re-learn entire models. Rather than re-learning the parameters from scratch, replacing learning with optimization, we propose a framework building upon the theory of \emph{optimal transport} to adapt model parameters by discovering correspondences between models and data, significantly amortizing the training cost. We demonstrate our idea on the challenging problem of creating probabilistic spatial representations for autonomous robots. Although recent mapping techniques have facilitated robust occupancy mapping, learning all spatially-diverse parameters in such approximate Bayesian models demand considerable computational time, discouraging them to be used in real-world robotic mapping. Considering the fact that the geometric features a robot would observe with its sensors are similar across various environments, in this paper, we demonstrate how to re-use parameters and hyperparameters learned in different domains. This adaptation is computationally more efficient than variational inference and Monte Carlo techniques. A series of experiments conducted on realistic settings verified the possibility of transferring thousands of such parameters with a negligible time and memory cost, enabling large-scale mapping in urban environments.