Algorithmic Minimization of Uncertain Continuous-Time Markov Chains

• 成果类型: Article
• 署名作者: Cardelli, Luca; Grosu, Radu; Larsen, Kim Guldstrand; Tribastone, Mirco; Tschaikowski, Max; Vandin, Andrea
• 署名单位: University of Oxford; Technische Universitat Wien; Aalborg University; IMT School for Advanced Studies Lucca; Scuola Superiore Sant'Anna; Technical University of Denmark
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3244093
• 发表日期: 2023
• 页码: 6557-6572
• 关键词: Markov processes; Model/controller reduction; Modeling; optimal control; optimization algorithms.

摘要

The assumption of perfect knowledge of rate parameters in continuous-time Markov chains (CTMCs) is undermined when confronted with reality, where they may be uncertain due to lack of information or because of measurement noise. Here, we consider uncertain CTMCs (UCTMCs), where rates are assumed to vary nondeterministically with time from bounded continuous intervals. A UCTMC can be, therefore, seen as a specific type of Markov decision process for which the analysis is computationally difficult. To tackle this, we develop a theory of minimization, which generalizes the notion of lumpability for CTMCs. Our first result is a quantitative and logical characterization of minimization. Specifically, we show that the reduced UCTMC model has amacrostate for each block of a partition of the state space, which preserves value functions and logical formulae whenever rewards are equal within each block. The second result is an efficient minimization algorithm for UCTMCs by means of partition refinement. As an application, we show that reductions in a number of CTMC benchmark models are robust with respect to uncertainties in original rates.