Multi-objective Robust Strategy Synthesis for Interval Markov Decision Processes
For researchers working on probabilistic systems with transition uncertainty, this work provides the first algorithm for multi-objective robust synthesis in IMDPs, though it is incremental as it extends existing techniques.
The paper addresses multi-objective robust strategy synthesis for interval Markov decision processes (IMDPs), proving PSPACE-hardness and providing a value iteration-based algorithm to approximate the Pareto set. The approach is demonstrated on case studies.
Interval Markov decision processes (IMDPs) generalise classical MDPs by having interval-valued transition probabilities. They provide a powerful modelling tool for probabilistic systems with an additional variation or uncertainty that prevents the knowledge of the exact transition probabilities. In this paper, we consider the problem of multi-objective robust strategy synthesis for interval MDPs, where the aim is to find a robust strategy that guarantees the satisfaction of multiple properties at the same time in face of the transition probability uncertainty. We first show that this problem is PSPACE-hard. Then, we provide a value iteration-based decision algorithm to approximate the Pareto set of achievable points. We finally demonstrate the practical effectiveness of our proposed approaches by applying them on several case studies using a prototypical tool.