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DSMC Evaluation Stages: Fostering Robust and Safe Behavior in Deep Reinforcement Learning

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Quantitative Evaluation of Systems (QEST 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12846))

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Abstract

Neural networks (NN) are gaining importance in sequential decision-making. Deep reinforcement learning (DRL), in particular, is extremely successful in learning action policies in complex and dynamic environments. Despite this success however, DRL technology is not without its failures, especially in safety-critical applications: (i) the training objective maximizes average rewards, which may disregard rare but critical situations and hence lack local robustness; (ii) optimization objectives targeting safety typically yield degenerated reward structures which for DRL to work must be replaced with proxy objectives. Here we introduce methodology that can help to address both deficiencies. We incorporate evaluation stages (ES) into DRL, leveraging recent work on deep statistical model checking (DSMC) which verifies NN policies in MDPs. Our ES apply DSMC at regular intervals to determine state space regions with weak performance. We adapt the subsequent DRL training priorities based on the outcome, (i) focusing DRL on critical situations, and (ii) allowing to foster arbitrary objectives. We run case studies in Racetrack, an abstraction of autonomous driving that requires navigating a map without crashing into a wall. Our results show that DSMC-based ES can significantly improve both (i) and (ii).

Authors are listed alphabetically. This work was partially supported by the German Research Foundation (DFG) under grant No. 389792660, as part of TRR 248, see https://perspicuous-computing.science, and by the European Regional Development Fund (ERDF).

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Change history

  • 19 August 2021

    In an older version of this paper, there was a mistake in line 12 of the algorithm on page 206. This was corrected.

Notes

  1. 1.

    One can combine such a proxy with the goal probability objective, though multiple objectives are difficult to achieve with a one-dimensional reward signal and standard backpropagation algorithms for neural nets [26]; anyway, training objective vs. ideal objective are still not identical here. Reward shaping is an alternative option that can in principle preserve the optimal policy [31], but this is not always possible, and manual work is needed for individual learning tasks (substantial work sometimes, see e.g. [46]).

  2. 2.

    The benefit of our proposed ES thus hinges, in particular, on how meaningful these representative states are for policy performance. While this is a limitation, partitioning by physical location like in Racetrack could be a canonical candidate in many scenarios.

  3. 3.

    In our Racetrack case studies, we use the map cells as the basis of \(\mathbb {P}\) – i.e., states sharing the same physical location. We believe that this partitioning method may work for many application scenarios involving physical space. Alternatively, one may, for example, partition state-variable ranges into intervals.

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Authors and Affiliations

  1. Saarland University, Saarland Informatics Campus, Saarbrücken, Germany

    Timo P. Gros, Daniel Höller, Jörg Hoffmann, Michaela Klauck, Hendrik Meerkamp & Verena Wolf

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  1. Timo P. Gros
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Correspondence to Timo P. Gros .

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  1. University of Oxford, Oxford, UK

    Alessandro Abate

  2. Ca’ Foscari University of Venice, Venice, Italy

    Andrea Marin

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Gros, T.P., Höller, D., Hoffmann, J., Klauck, M., Meerkamp, H., Wolf, V. (2021). DSMC Evaluation Stages: Fostering Robust and Safe Behavior in Deep Reinforcement Learning. In: Abate, A., Marin, A. (eds) Quantitative Evaluation of Systems. QEST 2021. Lecture Notes in Computer Science(), vol 12846. Springer, Cham. https://doi.org/10.1007/978-3-030-85172-9_11

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