Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Learning Robust Markov Models for Safe Runtime Monitoring

Antonina Skurka, Luko van der Maas, Sebastian Junges, Hazem Torfah

TL;DR

The paper provides a formalization of the problem of learning robust runtime monitors, introduces a novel framework that uses conformance-testing-based refinement for learning robust iHMMs with convergence guarantees, and presents an efficient monitoring algorithm for computing risk estimates over iHMMs.

Abstract

We present a model-based approach to learning robust runtime monitors for autonomous systems. Runtime monitors play a crucial role in raising the level of assurance by observing system behavior and predicting potential safety violations. In our approach, we propose to capture a system's (stochastic) behavior using interval Hidden Markov Models (iHMMs). The monitor then uses this learned iHMM to derive risk estimates for potential safety violations. The paper makes three key contributions: (1) it provides a formalization of the problem of learning robust runtime monitors, (2) introduces a novel framework that uses conformance-testing-based refinement for learning robust iHMMs with convergence guarantees, and (3) presents an efficient monitoring algorithm for computing risk estimates over iHMMs. Our empirical results demonstrate the efficacy of monitors learned using our approach, particularly when compared to model-free monitoring approaches that rely solely on collected data without access to a system model.

Learning Robust Markov Models for Safe Runtime Monitoring

TL;DR

The paper provides a formalization of the problem of learning robust runtime monitors, introduces a novel framework that uses conformance-testing-based refinement for learning robust iHMMs with convergence guarantees, and presents an efficient monitoring algorithm for computing risk estimates over iHMMs.

Abstract

We present a model-based approach to learning robust runtime monitors for autonomous systems. Runtime monitors play a crucial role in raising the level of assurance by observing system behavior and predicting potential safety violations. In our approach, we propose to capture a system's (stochastic) behavior using interval Hidden Markov Models (iHMMs). The monitor then uses this learned iHMM to derive risk estimates for potential safety violations. The paper makes three key contributions: (1) it provides a formalization of the problem of learning robust runtime monitors, (2) introduces a novel framework that uses conformance-testing-based refinement for learning robust iHMMs with convergence guarantees, and (3) presents an efficient monitoring algorithm for computing risk estimates over iHMMs. Our empirical results demonstrate the efficacy of monitors learned using our approach, particularly when compared to model-free monitoring approaches that rely solely on collected data without access to a system model.
Paper Structure (33 sections, 6 theorems, 6 equations, 101 figures)

This paper contains 33 sections, 6 theorems, 6 equations, 101 figures.

Table of Contents

  1. Introduction
  2. Problem statement
  3. Monitors for iHMMs
  4. (Interval) Hidden Markov Models
  5. Monitors for HMMs
  6. Monitors for iHMMs
  7. Relation to cautious monitors
  8. Learning Ideal Monitor Models
  9. Learning interval HMMs
  10. Conformance-testing-based refinement
  11. Experimental Evaluation
  12. Experimental Setup
  13. Terminology.
  14. Implementation.
  15. Benchmarks.
  16. ...and 18 more sections

Key Result

Lemma 1

Given an HMM ${\textsf{H}}$, modeling a SuO $\mathcal{S}$, a specification $\varphi$, and horizon $h$, the ideal monitor for $L^{\varphi,h,{\textsf{H}}}$ is $M^{*}_{\textsf{H}}$.

Figures (101)

  • Figure 1: Learning and integrating robust monitors in CPS
  • Figure 2: Transformation for monitoring an iHMM
  • Figure 3: iHMM refinement-based learning.
  • Figure 4: Comparing FNR and FPR between model-based and model-free methods.
  • Figure 5: Comparison between iHMM and HMM-based monitors, in terms of risk estimation (a-c) and FNR and FPR (d). Scatterplots (a-c) plot the values from all 10 runs for each method.
  • ...and 96 more figures

Theorems & Definitions (14)

  • Definition 1: System under Observation (SuO)
  • Definition 2: Specification
  • Definition 3: Risk Function
  • Definition 4: Ideal Monitor
  • Definition 5: Cautious Monitors
  • Definition 6: Hidden Markov Model (HMM)
  • Definition 7: Interval Hidden Markov Model (iHMM)
  • Lemma 1
  • Definition 8: iHMM Monitor
  • Lemma 2
  • ...and 4 more