  In this paper we study a model-based approach to calculating approximately
optimal policies in Markovian Decision Processes. In particular, we derive
novel bounds on the loss of using a policy derived from a factored linear
model, a class of models which generalize numerous previous models out of those
that come with strong computational guarantees. For the first time in the
literature, we derive performance bounds for model-based techniques where the
model inaccuracy is measured in weighted norms. Moreover, our bounds show a
decreased sensitivity to the discount factor and, unlike similar bounds derived
for other approaches, they are insensitive to measure mismatch. Similarly to
previous works, our proofs are also based on contraction arguments, but with
the main differences that we use carefully constructed norms building on Banach
lattices, and the contraction property is only assumed for operators acting on
"compressed" spaces, thus weakening previous assumptions, while strengthening
previous results.
