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I know that in a MDP there always exists a unique optimal deterministic policy. Does a statement like this also exist for optimal stochastic policies? Is there also always a unique optimal stochastic policy? Can it be better than the optimal deterministic policy?

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  • $\begingroup$ Hi. I've reformulated the title in a way that tries to summarise your actual main question based on the accepted answer too. Make sure that this reformulation is correct. $\endgroup$
    – nbro
    Commented May 28 at 15:06

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Sutton and Barto give an example of an MDP where the optimal stochastic policy strictly dominates the best deterministic one, should answer all your questions

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