Machine Learning for Efficient Sampling-Based Algorithms in Robust Multi-Agent Planning Under Uncertainty

Abstract

Robust multi-agent planning algorithms have been developed to assign tasks to cooperative teams of robots operating under various uncertainties. Often, it is difficult to evaluate the robustness of potential task assignments analytically, so sampling-based approximations are used instead. In many applications, not only are sampling-based approximations the only solution, but these samples are computationally-burdensome to obtain. This paper presents a machine learning procedure for sampling-based approximations that actively selects samples in order to maximize the accuracy of the approximation with a limited number of samples. Gaussian process regression models are constructed from a small set of training samples and used to approximate the robustness evaluation. Active learning is then used to iteratively select samples that most improve this evaluation. Three example problems demonstrate that the new procedure achieves a similar level of accuracy as the existing sample-inefficient procedures, but with a significant reduction in the number of samples.

An Efficient Sampling-Based Algorithms Using Active Learning and Manifold Learning for Multiple Unmanned Aerial Vehicle Task Allocation under Uncertainty

“…The disadvantage of using the Monte Carlo sampling method is that there are too many sampling points and the sampling cost is too high. The GPAL algorithm [ 20 ] can perform the sampling of uncertain parameters of the robust allocation method, achieving a reduction in the number of samples without degrading the evaluation accuracy.…”

“…The most important application of gaussian process is to solve regression problem [ 21 ]. In particular, Gaussian process (GP) regression models return mean and covariance functions that both predict the unknown true function’s response and quantify the confidence in those predictions [ 20 ].…”

“…The underlying mapping from uncertain parameters to score is usually unknown and can be highly nonlinear. In those cases, approximate scores can be more easily computed using sampling-based procedures with the Monte-Carlo method, and the weighted score can be obtained from various realizations of the uncertain parameters, but using Monte Carlo sampling methods requires too many samples [ 20 ].…”

“…Machine learning approaches offer the potential to more efficiently sample the uncertainty space with fewer number of samples, but simultaneously minimize the impact on the accuracy of the robust score metrics associated with fewer samples [ 21 , 22 , 23 , 24 , 25 , 26 , 27 ]. Quindlen [ 20 ] used Gaussian process regression (GPR) and machine learning active learning algorithms (AL) to replace Monte-Carlo-based evaluation methods, and this effectively reduces the computational time complexity and sampling costs. However, the iterative training selection process of active learning requires a large amount of calculation, so we need to further improve the sample selection mechanism.…”

Risk-Based Human-Aware Multi-Robot Coordination in Dynamic Environments Shared with Humans

“…Such MRTA problems are commonly modeled as Markov Decision Processes (MDPs) [11], or as pure or mixed stochastic integer programs [12]. In a different approach, approximation of the parametric uncertainties captured by the underlying system model has been investigated in [13] by means of active learning.…”