Publication Type
Conference Proceeding Article
Version
publishedVersion
Publication Date
7-2020
Abstract
Learning models from observations of a system is a powerful tool with many applications. In this paper, we consider learning Discrete Time Markov Chains (DTMC), with different methods such as frequency estimation or Laplace smoothing. While models learnt with such methods converge asymptotically towards the exact system, a more practical question in the realm of trusted machine learning is how accurate a model learnt with a limited time budget is. Existing approaches provide bounds on how close the model is to the original system, in terms of bounds on local (transition) probabilities, which has unclear implication on the global behavior. In this work, we provide global bounds on the error made by such a learning process, in terms of global behaviors formalized using temporal logic. More precisely, we propose a learning process ensuring a bound on the error in the probabilities of these properties. While such learning process cannot exist for the full LTL logic, we provide one ensuring a bound that is uniform over all the formulas of CTL. Further, given one timeto-failure property, we provide an improved learning algorithm. Interestingly, frequency estimation is sufficient for the latter, while Laplace smoothing is needed to ensure non-trivial uniform bounds for the full CTL logic.
Discipline
Software Engineering
Research Areas
Software and Cyber-Physical Systems
Publication
Proceedings of the 32nd International Conference on Computer-Aided Verification, Virtual Conference, 2020 July 21-24
First Page
304
Last Page
326
ISBN
9783030532901
Identifier
10.1007/978-3-030-53291-8_17
Publisher
Springer
City or Country
Virtual Conference
Citation
1
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.