Evaluating probabilistic model checking tools for verification of robot control policies

Research literature on Probabilistic Model Checking (PMC) encompasses a well-established set of algorithmic techniques whereby probabilistic models can be analyzed. In the last decade, owing to the increasing availability of effective tools, PMC has found applications in many domains, including computer networks, computational biology and robotics. In this paper, we evaluate PMC tools – namely COMICS, MRMC and PRISM – to investigate safe reinforcement learning in robots, i.e., to establish safety of policies learned considering feedback signals received upon acting in partially unknown environments. Introduced in previous contributions of ours, this application is a challenging domain wherein PMC tools act as back-engines of an automated methodology aimed to verify and repair control policies. We present an evaluation of the current state-of-the-art PMC tools to assess their potential on various case studies, including both real and simulated robots accomplishing navigation, manipulation and reaching tasks.

[1]  Bengt Jonsson,et al.  A logic for reasoning about time and reliability , 1990, Formal Aspects of Computing.

[2]  Moshe Y. Vardi Automatic verification of probabilistic concurrent finite state programs , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[3]  Marta Z. Kwiatkowska,et al.  Probabilistic Model Checking of the IEEE 802.11 Wireless Local Area Network Protocol , 2002, PAPM-PROBMIV.

[4]  Nils Jansen,et al.  The COMICS Tool - Computing Minimal Counterexamples for DTMCs , 2012, ATVA.

[5]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[6]  Marta Z. Kwiatkowska,et al.  PRISM: Probabilistic Symbolic Model Checker , 2002, Computer Performance Evaluation / TOOLS.

[7]  Marta Z. Kwiatkowska,et al.  Using probabilistic model checking in systems biology , 2008, PERV.

[8]  Giulio Sandini,et al.  The iCub humanoid robot: An open-systems platform for research in cognitive development , 2010, Neural Networks.

[9]  Marco Bozzano,et al.  A Comprehensive Approach to On-board Autonomy Verification and Validation , 2011, IJCAI.

[10]  Peter Dayan,et al.  Q-learning , 1992, Machine Learning.

[11]  Nils Jansen,et al.  A Greedy Approach for the Efficient Repair of Stochastic Models , 2015, NFM.

[12]  Richard S. Sutton,et al.  Reinforcement Learning: An Introduction , 1998, IEEE Trans. Neural Networks.

[13]  Joost-Pieter Katoen,et al.  The Ins and Outs of the Probabilistic Model Checker MRMC , 2009, 2009 Sixth International Conference on the Quantitative Evaluation of Systems.

[14]  Peter Dayan,et al.  Technical Note: Q-Learning , 2004, Machine Learning.

[15]  Marta Z. Kwiatkowska,et al.  Stochastic Model Checking , 2007, SFM.

[16]  Giorgio Metta,et al.  Ensuring safety of policies learned by reinforcement: Reaching objects in the presence of obstacles with the iCub , 2013, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[17]  Stefan Schaal,et al.  Editorial: Special Issue on Machine Learning in Robotics , 2008, Int. J. Robotics Res..

[18]  Christel Baier,et al.  Preface to the special issue on Probabilistic Model Checking , 2013, Formal Methods in System Design.

[19]  Marco Wiering,et al.  Reinforcement Learning , 2014, Adaptation, Learning, and Optimization.

[20]  Peter Secretan Learning , 1965, Mental Health.

[21]  Andrew G. Barto,et al.  Reinforcement learning , 1998 .

[22]  Adnan Aziz,et al.  It Usually Works: The Temporal Logic of Stochastic Systems , 1995, CAV.

[23]  Luca Pulina,et al.  Testing a Learn-Verify-Repair Approach for Safe Human-Robot Interaction , 2015, AI*IA.

[24]  Ali Khalili,et al.  Engineering Approaches and Methods to Verify Software in Autonomous Systems , 2014, IAS.

[25]  Marta Z. Kwiatkowska,et al.  PRISM 4.0: Verification of Probabilistic Real-Time Systems , 2011, CAV.

[26]  Nils Jansen,et al.  DTMC Model Checking by SCC Reduction , 2010, 2010 Seventh International Conference on the Quantitative Evaluation of Systems.