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Simple Strategies in Multi-Objective MDPs

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12078)


We consider the verification of multiple expected reward objectives at once on Markov decision processes (MDPs). This enables a trade-off analysis among multiple objectives by obtaining a Pareto front. We focus on strategies that are easy to employ and implement. That is, strategies that are pure (no randomization) and have bounded memory. We show that checking whether a point is achievable by a pure stationary strategy is NP-complete, even for two objectives, and we provide an MILP encoding to solve the corresponding problem. The bounded memory case is treated by a product construction. Experimental results using Storm and Gurobi show the feasibility of our algorithms.

currently affiliated with Vrije Universiteit Brussel.

Research partially supported by F.R.S.-FNRS Grant n\(^{\circ }\) F.4520.18 (ManySynth). Mickael Randour is an F.R.S.-FNRS Research Associate.


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Delgrange, F., Katoen, JP., Quatmann, T., Randour, M. (2020). Simple Strategies in Multi-Objective MDPs. In: Biere, A., Parker, D. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2020. Lecture Notes in Computer Science(), vol 12078. Springer, Cham.

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