Majumdar, Rupak; Kunčak, Viktor
Markov decision processes (MDPs) are standard models for probabilistic systems with non-deterministic behaviours. Long-run average rewards provide a mathematically elegant formalism for expressing long term performance. Value iteration (VI) is one of the simplest and most efficient algorithmic approaches to MDPs with other properties, such as reachability objectives. Unfortunately, a naive extension of VI does not work for MDPs with long-run average rewards, as there is no known stopping criterion. In this work our contributions are threefold. (1) We refute a conjecture related to stopping criteria for MDPs with long-run average rewards. (2) We present two practical algorithms for MDPs with long-run average rewards based on VI. First, we show that a combination of applying VI locally for each maximal end-component (MEC) and VI for reachability objectives can provide approximation guarantees. Second, extending the above approach with a simulation-guided on-demand variant of VI, we present an anytime algorithm that is able to deal with very large models. (3) Finally, we present experimental results showing that our methods significantly outperform the standard approaches on several benchmarks.
201 - 221
CAV: Computer Aided Verification
2017-07-24 – 2017-07-28
Ashok P, Chatterjee K, Daca P, Kretinsky J, Meggendorfer T. Value iteration for long run average reward in markov decision processes. In: Majumdar R, Kunčak V, eds. Vol 10426. Springer; 2017:201-221. doi:10.1007/978-3-319-63387-9_10
Ashok, P., Chatterjee, K., Daca, P., Kretinsky, J., & Meggendorfer, T. (2017). Value iteration for long run average reward in markov decision processes. In R. Majumdar & V. Kunčak (Eds.) (Vol. 10426, pp. 201–221). Presented at the CAV: Computer Aided Verification, Heidelberg, Germany: Springer. https://doi.org/10.1007/978-3-319-63387-9_10
Ashok, Pranav, Krishnendu Chatterjee, Przemyslaw Daca, Jan Kretinsky, and Tobias Meggendorfer. “Value Iteration for Long Run Average Reward in Markov Decision Processes.” edited by Rupak Majumdar and Viktor Kunčak, 10426:201–21. Springer, 2017. https://doi.org/10.1007/978-3-319-63387-9_10.
P. Ashok, K. Chatterjee, P. Daca, J. Kretinsky, and T. Meggendorfer, “Value iteration for long run average reward in markov decision processes,” presented at the CAV: Computer Aided Verification, Heidelberg, Germany, 2017, vol. 10426, pp. 201–221.
Ashok P, Chatterjee K, Daca P, Kretinsky J, Meggendorfer T. 2017. Value iteration for long run average reward in markov decision processes. CAV: Computer Aided Verification, LNCS, vol. 10426, 201–221.
Ashok, Pranav, et al. Value Iteration for Long Run Average Reward in Markov Decision Processes. Edited by Rupak Majumdar and Viktor Kunčak, vol. 10426, Springer, 2017, pp. 201–21, doi:10.1007/978-3-319-63387-9_10.