We study Markov Decision Process (MDP) games with the usual ±1 reinforcement signal. We consider the scenario in which the goal of the game, rather than just winning, is to maximize the number of wins in an allotted period of time (or maximize the expected reward in the same period). In the reinforcement learning literature, this type of tradeoff is often handled by tuning the discount parameter in order to encourage the learning algorithm to find policies that take fewer steps on average, at the cost of a lower probability of winning. We show that this approach is not guaranteed to solve the tradeoff problem optimally, and hence a different strategy is needed when tackling this type of problems.
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