1-2-3-Go! Policy Synthesis for Parameterized Markov Decision Processes via Decision-Tree Learning and Generalization
This addresses the state-space explosion problem in probabilistic model checking for verification engineers, though it is an incremental improvement over existing methods.
The paper tackles the scalability issue in synthesizing policies for parameterized Markov decision processes (MDPs) by using decision-tree learning to generalize policies from small instances to larger ones, bypassing state-space exploration and achieving good performance on models orders of magnitude beyond current tools.
Despite the advances in probabilistic model checking, the scalability of the verification methods remains limited. In particular, the state space often becomes extremely large when instantiating parameterized Markov decision processes (MDPs) even with moderate values. Synthesizing policies for such \emph{huge} MDPs is beyond the reach of available tools. We propose a learning-based approach to obtain a reasonable policy for such huge MDPs. The idea is to generalize optimal policies obtained by model-checking small instances to larger ones using decision-tree learning. Consequently, our method bypasses the need for explicit state-space exploration of large models, providing a practical solution to the state-space explosion problem. We demonstrate the efficacy of our approach by performing extensive experimentation on the relevant models from the quantitative verification benchmark set. The experimental results indicate that our policies perform well, even when the size of the model is orders of magnitude beyond the reach of state-of-the-art analysis tools.