Optimal Approximation of Random Variables for Estimating the Probability of Meeting a Plan Deadline

Authors

  • Liat Cohen Ben-Gurion University of the Negev
  • Tal Grinshpoun Ariel University
  • Gera Weiss Ben-Gurion University of the Negev

Keywords:

deadline, approximation of random variables, Kolmogorov, decision making under uncertainty

Abstract

In planning algorithms and in other domains, there is often a need to run long computations that involve summations, maximizations and other operations on random variables, and to store intermediate results. In this paper, as a main motivating example, we elaborate on the case of estimating probabilities of meeting deadlines in hierarchical plans. A source of computational complexity, often neglected in the analysis of such algorithms, is that the support of the variables needed as intermediate results may grow exponentially along the computation. Therefore, to avoid exponential memory and time complexities, we need to trim these variables. This is similar, in a sense, to rounding intermediate results in numerical computations. Of course, to maintain the quality of algorithms, the trimming procedure should be efficient and it must maintain accuracy as much as possible. In this paper, we propose an optimal trimming algorithm with polynomial time and memory complexities for the purpose of estimating probabilities of deadlines in plans. More specifically, we show that our algorithm, given the needed size of the representation of the variable, provides the best possible approximation, where approximation accuracy is considered with a measure that fits the goal of estimating deadline meeting probabilities.

Downloads

Published

2018-04-26

How to Cite

Cohen, L., Grinshpoun, T., & Weiss, G. (2018). Optimal Approximation of Random Variables for Estimating the Probability of Meeting a Plan Deadline. Proceedings of the AAAI Conference on Artificial Intelligence, 32(1). Retrieved from https://ojs.aaai.org/index.php/AAAI/article/view/12114

Issue

Section

AAAI Technical Track: Reasoning under Uncertainty