Interval Markov Decision Processes with Continuous Action-Spaces

Interval Markov Decision Processes with Continuous Action-Spaces

Delimpaltadakis, Giannis (Eindhoven University of Technology)
Lahijanian, Morteza (University of Colorado)
Mazo, M. (TU Delft Team Manuel Mazo Jr)
Laurenti, L. (TU Delft Team Luca Laurenti)

2023

Interval Markov Decision Processes (IMDPs) are finite-state uncertain Markov models, where the transition probabilities belong to intervals. Recently, there has been a surge of research on employing IMDPs as abstractions of stochastic systems for control synthesis. However, due to the absence of algorithms for synthesis over IMDPs with continuous action-spaces, the action-space is assumed discrete a-priori, which is a restrictive assumption for many applications. Motivated by this, we introduce continuous-action IMDPs (caIMDPs), where the bounds on transition probabilities are functions of the action variables, and study value iteration for maximizing expected cumulative rewards. Specifically, we decompose the max-min problem associated to value iteration to |Q| max problems, where |Q| is the number of states of the caIMDP. Then, exploiting the simple form of these max problems, we identify cases where value iteration over caIMDPs can be solved efficiently (e.g., with linear or convex programming). We also gain other interesting insights: e.g., in certain cases where the action set A is a polytope, synthesis over a discrete-action IMDP, where the actions are the vertices of A, is sufficient for optimality. We demonstrate our results on a numerical example. Finally, we include a short discussion on employing caIMDPs as abstractions for control synthesis.

bounded-parameter Markov decision processes
control synthesis
planning under uncertainty
uncertain Markov decision processes
value iteration

http://resolver.tudelft.nl/uuid:814b2ec0-11a1-4080-a782-c43d100ab130

https://doi.org/10.1145/3575870.3587117

Association for Computing Machinery (ACM)

979-8-4007-0033-0

HSCC 2023 - Proceedings of the 26th ACM International Conference on Hybrid Systems: Computation and Control, Part of CPS-IoT Week

26th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2023, Part of CPS-IoT Week 2023, 2023-05-10 → 2023-05-12, San Antonio, United States

Institutional Repository

conference paper

© 2023 Giannis Delimpaltadakis, Morteza Lahijanian, M. Mazo, L. Laurenti