Abstract
We investigate the use of probabilistic model checking to synthesise optimal strategies for autonomous systems that operate among uncontrollable agents such as humans. To formally assess such uncontrollable behaviour, we use models obtained from reinforcement learning. These behaviour models are, e.g., based on data collected in experiments in which humans execute dynamic tasks in a virtual environment. We first describe a method to translate such behaviour models into Markov decision processes (MDPs). The composition of these MDPs with models for (controllable) autonomous systems gives rise to stochastic games (SGs). MDPs and SGs are amenable to probabilistic model checking which enables the synthesis of strategies that provably adhere to formal specifications such as probabilistic temporal logic constraints. Experiments with a prototype provide (1) systematic insights on the credibility and the characteristics of behavioural models and (2) methods for automated synthesis of strategies satisfying guarantees on their required characteristics in the presence of humans.
Supported by the CDZ project CAP (GZ 1023), the DFG RTG 2236 “UnRAVeL”, and the NSF grants 1652113, 1651089, and 1550212.
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Notes
- 1.
We use the term movements to clarify the distinction from actions in MDPs.
- 2.
Available at https://github.com/moves-rwth/human_factor_models.
References
Brafman, R.I., Tennenholtz, M.: On partially controlled multi-agent systems. J. Artif. Intell. Res. 4, 477–507 (1996)
Dresner, K., Stone, P.: A multiagent approach to autonomous intersection management. J. Artif. Intell. Res. 31, 591–656 (2008)
Wellman, M.P., Wurman, P.R., O’Malley, K., Bangera, R., Reeves, D., Walsh, W.E.: Designing the market game for a trading agent competition. IEEE Internet Comput. 5(2), 43–51 (2001)
Khandelwal, P., et al.: Bwibots: a platform for bridging the gap between AI and human-robot interaction research. Int. J. Robot. Res. 36, 635–659 (2017)
Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, New York (1994)
Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. MIT Press, Cambridge (1998)
Kwiatkowska, M.Z.: Model checking for probability and time: from theory to practice. In: LICS, p. 351. IEEE Computer Society (2003)
Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22110-1_47
Dehnert, C., Junges, S., Katoen, J.-P., Volk, M.: A STORM is coming: a modern probabilistic model checker. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017. LNCS, vol. 10427, pp. 592–600. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63390-9_31
Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects Comput. 6(5), 512–535 (1994)
Condon, A.: The complexity of stochastic games. Inf. Comput. 96(2), 203–224 (1992)
Kwiatkowska, M., Parker, D., Wiltsche, C.: PRISM-Games 2.0: a tool for multi-objective strategy synthesis for stochastic games. In: Chechik, M., Raskin, J.-F. (eds.) TACAS 2016. LNCS, vol. 9636, pp. 560–566. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49674-9_35
Dean, T.L., Givan, R.: Model minimization in Markov decision processes. In: AAAI/IAAI, pp. 106–111. AAAI Press/The MIT Press (1997)
Tong, M.H., Zohar, O., Hayhoe, M.M.: Control of gaze while walking: task structure, reward, and uncertainty. J. Vis. 17(1), 28 (2017)
Rothkopf, C.A., Ballard, D.H.: Modular inverse reinforcement learning for visuomotor behaviour. Biol. Cybern. 107(4), 477–490 (2013)
Sprague, N., Ballard, D.: Multiple-goal reinforcement learning with modular sarsa (0). IJCA I, 1445–1447 (2003)
Ballard, D.H., Kit, D., Rothkopf, C.A., Sullivan, B.: A hierarchical modular architecture for embodied cognition. Multisens. Res. 26(1–2), 177–204 (2013)
Leong, Y.C., Radulescu, A., Daniel, R., DeWoskin, V., Niv, Y.: Dynamic interaction between reinforcement learning and attention in multidimensional environments. Neuron 93(2), 451–463 (2017)
Konur, S., Dixon, C., Fisher, M.: Analysing robot swarm behaviour via probabilistic model checking. Robot. Auton. Syst. 60(2), 199–213 (2012)
Johnson, B., Kress-Gazit, H.: Analyzing and revising synthesized controllers for robots with sensing and actuation errors. Int. J. Robot. Res. 34(6), 816–832 (2015)
Giaquinta, R., Hoffmann, R., Ireland, M., Miller, A., Norman, G.: Strategy synthesis for autonomous agents using PRISM. In: Dutle, A., Muñoz, C., Narkawicz, A. (eds.) NFM 2018. LNCS, vol. 10811, pp. 220–236. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-77935-5_16
Chen, T., Kwiatkowska, M., Simaitis, A., Wiltsche, C.: Synthesis for multi-objective stochastic games: an application to autonomous urban driving. In: Joshi, K., Siegle, M., Stoelinga, M., D’Argenio, P.R. (eds.) QEST 2013. LNCS, vol. 8054, pp. 322–337. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40196-1_28
Feng, L., Wiltsche, C., Humphrey, L., Topcu, U.: Synthesis of human-in-the-loop control protocols for autonomous systems. IEEE Trans. Autom. Sci. Eng. 13(2), 450–462 (2016)
Lacerda, B., Parker, D., Hawes, N.: Optimal policy generation for partially satisfiable co-safe LTL specifications. In: IJCAI, pp. 1587–1593. AAAI Press (2015)
Littman, M.L.: Markov games as a framework for multi-agent reinforcement learning. ICML 157, 157–163 (1994)
Bowling, M., Veloso, M.: Multiagent learning using a variable learning rate. Artif. Intell. 136(2), 215–250 (2002)
Bruni, R., Corradini, A., Gadducci, F., Lluch Lafuente, A., Vandin, A.: Modelling and analyzing adaptive self-assembly strategies with maude. In: Durán, F. (ed.) WRLA 2012. LNCS, vol. 7571, pp. 118–138. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34005-5_7
Katoen, J.P.: The probabilistic model checking landscape. In: LICS, pp. 31–45. ACM (2016)
Garcıa, J., Fernández, F.: A comprehensive survey on safe reinforcement learning. J. Mach. Learn. Res. 16(1), 1437–1480 (2015)
Sculley, D., Phillips, T., Ebner, D., Chaudhary, V., Young, M.: Machine learning: the high-interest credit card of technical debt (2014)
Winterer, L., et al.: Motion planning under partial observability using game-based abstraction. In: CDC, pp. 2201–2208. IEEE (2017)
Etessami, K., Kwiatkowska, M.Z., Vardi, M.Y., Yannakakis, M.: Multi-objective model checking of Markov decision processes. Log. Methods Comput. Sci. 4(4), 1–21 (2008)
Agha, G., Palmskog, K.: A survey of statistical model checking. ACM Trans. Model. Comput. Simul. 28(1), 6:1–6:39 (2018)
Wachter, B., Zhang, L., Hermanns, H.: Probabilistic model checking modulo theories. In: QEST, pp. 129–140. IEEE CS (2007)
Brázdil, T., et al.: Verification of Markov decision processes using learning algorithms. In: Cassez, F., Raskin, J.-F. (eds.) ATVA 2014. LNCS, vol. 8837, pp. 98–114. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11936-6_8
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Junges, S., Jansen, N., Katoen, JP., Topcu, U., Zhang, R., Hayhoe, M. (2018). Model Checking for Safe Navigation Among Humans. In: McIver, A., Horvath, A. (eds) Quantitative Evaluation of Systems. QEST 2018. Lecture Notes in Computer Science(), vol 11024. Springer, Cham. https://doi.org/10.1007/978-3-319-99154-2_13
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