Learning and Planning with Hierarchical Stochastic Models for Robot Navigation

ICML Workshop on Machine Learning of Spatial Knowledge, July 2, 2000, Stanford University
Learning and Planning with Hierarchical Stochastic Models for Robot Navigation
Georgios Theocharous, Khashayar Rohanimanesh, Sridhar Mahadevan, Georgios Theocharous, Khashayar Rohanimanesh, Sridhar Mahadevan
Abstract

We propose and investigate a method for hierarchical learning and planning in partially observable environments using the framework of Hierarchical Hidden Markov Models (HHMMs).

Our main goal is to use hierarchical modeling as a basis for exploring more efficient learning and planning algorithms. As a case study we focus on indoor robot navigation problem and will show how this framework can be used to learn a hierarchy of maps of the environment at different levels of spatial abstraction.

We train different families of HHMMs for a real corridor environment and compare them with the standard HMM representation of the same environment. We find significant bene ts to using HHMMs in terms of the fit of the model to the training data, localization of the robot, and the ability to infer the structure of the environment. We also introduce the idea of model reuse that can be used to combine already learned models into a larger model

Another publication from the same category: Machine Learning and Data Science

IEEE Computing Conference 2018, London, UK

Regularization of the Kernel Matrix via Covariance Matrix Shrinkage Estimation

The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix of the data requires outer products. Therefore, their spectral properties are tightly connected. This allows us to examine the kernel matrix through the sample covariance matrix in the feature space and vice versa. The use of kernels often involves a large number of features, compared to the number of observations. In this scenario, the sample covariance matrix is not well-conditioned nor is it necessarily invertible, mandating a solution to the problem of estimating high-dimensional covariance matrices under small sample size conditions. We tackle this problem through the use of a shrinkage estimator that offers a compromise between the sample covariance matrix and a well-conditioned matrix (also known as the "target") with the aim of minimizing the mean-squared error (MSE). We propose a distribution-free kernel matrix regularization approach that is tuned directly from the kernel matrix, avoiding the need to address the feature space explicitly. Numerical simulations demonstrate that the proposed regularization is effective in classification tasks.

Keywords