  We consider POMDPs in which the weight of the stage payoff depends on the
past sequence of signals and actions occurring in the infinitely repeated
problem. We prove that for all epsilon>0, there exists a strategy that is
epsilon-optimal for any sequence of weights satisfying a property that
interprets as "the decision-maker is patient enough". This unifies and
generalizes several results of the literature, and applies notably to POMDPs
with limsup payoffs.
