Multi-armed Bandits for Boolean Connectives in Hybrid System Falsification

Abstract

Hybrid system falsification is an actively studied topic, as a scalable quality assurance methodology for real-world cyber-physical systems. In falsification, one employs stochastic hill-climbing optimization to quickly find a counterexample input to a black-box system model. Quantitative robust semantics is the technical key that enables use of such optimization. In this paper, we tackle the so-called scale problem regarding Boolean connectives that is widely recognized in the community: quantities of different scales (such as speed [km/h] vs. rpm, or worse, rph) can mask each other's contribution to robustness. Our solution consists of integration of the multi-armed bandit algorithms in hill climbing-guided falsification frameworks, with a technical novelty of a new reward notion that we call hill-climbing gain. Our experiments show our approach's robustness under the change of scales, and that it outperforms a state-of-the-art falsification tool.

Hybrid System Falsification Under (In)equality Constraints via Search Space Transformation

“…However, in the baseline approaches, the fitness landscape is given by the composition of the degree of violation of the constraints and of the robustness; in this way, the falsification task performed by hillclimbing is complicated. Moreover, note that the scales (i.e., orders of magnitude) of constraint violation and robustness may be very different, and this has been shown to affect the effectiveness of falsification algorithms [26]. In our approach, instead, hill-climbing operates over a fitness landscape that, although deformed, it is only given by robustness.…”

“…Although the All-Priorities approach guarantees to find the best priority (i.e., the one mapping to points with minimum robustness), it is computationally expensive, as it requires to simulate all the mapped points. In this section, we propose a method that tries to learn the best priority during execution: it is based on the multi-armed bandit problem, that has proven to be effective in other contexts for falsification [26].…”

“…. , AT14, regarding system's safety (see [12], [26], [27]). We consider 5 input constraints, covering both equalities and inequalities.…”

Effective Hybrid System Falsification Using Monte Carlo Tree Search Guided by QB-Robustness

“…However, since different signals may differ in magnitude, the comparison may be biased, such that one signal w may always (or often) mask the contribution of the others, and, therefore, the final robustness may be dominated by this signal w. Note that, although the scale problem affects connective operators, it is not only local to the place of their application, but it is always propagated to the robustness of the whole formula. The scale problem has been shown as a root cause of the failure of many falsification problems [21,40].…”

“…The scale problem is a recognized issue in optimization-based falsification [21,40], which could arise when multiple signals with different scales are present in the specification. Namely, it is due to the computation of robust semantics of Boolean connectives, i.e., the way in which the robustness values of different sub-formulas are compared and aggregated: such computation is problematic in the presence of signals that take values having different order of magnitudes.…”