Optimizing the Expected Mean Payoff in Energy Markov Decision Processes
  Energy Markov Decision Processes (EMDPs) are finite-state Markov decision processes where each transition is assigned an integer counter update and a rational payoff. An EMDP configuration is a pair s(n), where s is a control state and n is the current counter value. The configurations are changed by performing transitions in the standard way. We consider the problem of computing a safe strategy (i.e., a strategy that keeps the counter non-negative) which maximizes the expected mean payoff. 
Tom\'a\v{s} Br\'azdil, Anton\'in Ku\v{c}era, Petr Novotn\'y
cs.LO