  We introduce Multi-Environment Markov Decision Processes (MEMDPs) which are
MDPs with a set of probabilistic transition functions. The goal in a MEMDP is
to synthesize a single controller with guaranteed performances against all
environments even though the environment is unknown a priori. While MEMDPs can
be seen as a special class of partially observable MDPs, we show that several
verification problems that are undecidable for partially observable MDPs, are
decidable for MEMDPs and sometimes have even efficient solutions.
