General discounting versus average reward
Consider an agent interacting with an environment in cycles. In every interaction cycle the agent is rewarded for its performance. We compare the average reward U from cycle 1 to m (average value) with the future discounted reward V from cycle k to ∞ (discounted value). We consider essentially arbitrary (non-geometric) discount sequences and arbitrary reward sequences (non-MDP environments). We show that asymptotically U for m→∞ and V for k→∞ are equal, provided both limits exist. Further, if...[Show more]
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