Convex Optimization for Parameter Synthesis in MDPs

• 成果类型: Article
• 署名作者: Cubuktepe, Murat; Jansen, Nils; Junges, Sebastian; Katoen, Joost-Pieter; Topcu, Ufuk
• 署名单位: University of Texas System; University of Texas Austin; Radboud University Nijmegen; RWTH Aachen University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3133265
• 发表日期: 2022
• 页码: 6333-6348
• 关键词: Convex optimization; Markov processes

摘要

Probabilistic model-checking aims to prove whether a Markov decision process (MDP) satisfies a temporal logic specification. The underlying methods rely on an often unrealistic assumption that the MDP is precisely known. Consequently, parametric MDPs (pMDPs) extend MDPs with transition probabilities that are functions over unspecified parameters. The parameter synthesis problem is to compute an instantiation of these unspecified parameters such that the resulting MDP satisfies the temporal logic specification. We formulate the parameter synthesis problem as a quadratically constrained quadratic program, which is nonconvex and is NP-hard to solve in general. We develop two approaches that iteratively obtain locally optimal solutions. The first approach exploits the so-called convex-concave procedure (CCP), and the second approach utilizes a sequential convex programming (SCP) method. The techniques improve the runtime and scalability by multiple orders of magnitude compared to black-box CCP and SCP by merging ideas from convex optimization and probabilistic model-checking. We demonstrate the approaches on a satellite collision avoidance problem with hundreds of thousands of states and tens of thousands of parameters and their scalability on a wide range of commonly used benchmarks.