  This paper describes a novel method to solve average-reward semi-Markov
decision processes, by reducing them to a minimal sequence of cumulative reward
problems. The usual solution methods for this type of problems update the gain
(optimal average reward) immediately after observing the result of taking an
action. The alternative introduced, optimal nudging, relies instead on setting
the gain to some fixed value, which transitorily makes the problem a
cumulative-reward task, solving it by any standard reinforcement learning
method, and only then updating the gain in a way that minimizes uncertainty in
a minmax sense. The rule for optimal gain update is derived by exploiting the
geometric features of the w-l space, a simple mapping of the space of policies.
The total number of cumulative reward tasks that need to be solved is shown to
be small. Some experiments are presented to explore the features of the
algorithm and to compare its performance with other approaches.
