Konstantin Kueffner
Publications
Shielding for Higher-Order Safety
Safety shields are runtime enforcement mechanisms that restrict the actions of a controller to guarantee safety. Classical shields are usually synthesised for state predicates: the current physical state is either safe or unsafe, and the shield disables precisely those actions that can force the system into an unsafe state in the future. In many cyber-physical applications this view is too coarse. A vehicle approaching an obstacle should not only avoid collision, but also respect speed regulations, force limits induced by acceleration, and jerk limits to prevent injuries. From a physical perspective, these requirements are predicated over the derivatives of the state. This paper develops a finite-state safety-game construction for such high-order smoothness constraints. We define differential safety properties using finite differences over a discretised state space, characterise their expressiveness, and reduce shield synthesis to an ordinary safety game over a history state space. We give a synthesis algorithm whose shields store exactly $k$ past states for properties of order $k$ and prove that this memory is necessary. We describe an iterative synthesis procedure for a maximally permissive shield that operates over hierarchies of derivative constraints. The algorithm solves constraints iteratively in increasing order and uses the solution at each iteration to prune the state space for the next constraint. This makes shield synthesis more efficient in practice, as the algorithm refrains from exploring large regions of the state space that are known to be unsafe.
Confidence Sequences for Online Statistical Model Checking of Markov Decision Processes
Markov decision processes (MDPs) are a classic model of decision making under uncertainty, exhibiting both non-deterministic choice as well as probabilistic uncertainty. Traditionally, exact knowledge of the underlying probabilities is assumed. However, this often is unrealistic, e.g.\ when modelling cyber-physical systems or biological processes. Here, statistical methods provide a way towards obtaining meaningful guarantees. The classical approach is to gather samples in the MDP, use these to draw statistical conclusions about the transition probabilities, and from there obtain bounds on the true value; then, if these bounds are too broad, repeat. However, existing implementations of this approach are either subtly incorrect or sub-optimal, and quite often both. We present several \emph{confidence sequences}, which are specifically designed for such \enquote{online} settings, implement all of them in an efficient tool, and show their practical applicability. In particular, we show that they outperform classical \enquote{union-bound} style approaches, and overall our implementation requires 50x less samples on average than previous state of the art.