Maximilian Weininger
Publications
Property-driven Causal Abstractions for Markov Decision Processes
Markov Decision Processes (MDPs) are widely used as decision-making models, commonly specified over factored state spaces through state variables and their valuations. The exponential blowup in the number of states renders many reasoning tasks in MDPs challenging. Abstractions are promising techniques to reduce MDPs and thus mitigate scalability issues. In this work, we introduce a notion of causality on factored MDPs and a novel property-driven causal abstraction technique that retains many characteristics of the original MDP model. For this, we rely on causal relations over state variable predicates and identify those states that share the same reasons for fulfilling or violating a given abstraction property. We theoretically and empirically compare various causal MDP abstractions using different model types such as MDPs, interval MDPs, or stochastic games. Our evaluation demonstrates the potential of our approach: For several standard benchmarks, we obtain small abstractions that allow us to compute near-optimal policies for the original MDP. Furthermore, our causal abstractions often generalize to related large-scale MDP models.
dtControl2+$\varepsilon$: Trading Optimality for Explainability in MDPs via Decision Trees
Over the past decade, decision trees have been used to represent controllers (a.k.a. policies) in an explainable way, with dtControl2 as a current state-of-the-art tool. However, for systems that are large or have many corner cases, even such representations tend to be too complex and not human-comprehensible. Unfortunately, reducing the size of the decision tree is not straightforward, as missing just a single crucial case might result in an incorrect controller. We tackle this issue in the setting of Markov decision processes, extending dtControl2 by "$\varepsilon$" functionality: Given an allowed imprecision $\varepsilon \geq 0$, we construct a smaller decision tree, distilling the essence of the controller, while still guaranteeing its $\varepsilon$-optimality. This enables us to provide tunably simpler explanations, omitting a controllable amount of detail. Our tool constructs decision trees that are orders of magnitude smaller than the state of the art.
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.