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Oct 16, 2019 at 11:57 comment added Fabian Werner Although I have not worked it out explicitly I am still convinced that I either do not understand the equation you have written down or it is wrong. Reason: the Bellman equation ( see stats.stackexchange.com/questions/243384/…) tells us that $v(s) = const + \sum_{s‘} p(s‘|s) v(s‘)$ which does not seem to match the one you want... so let me ask: what is the context? Is the Bellman equation sufficient for your purpose or do you explicitly need the equation in your form?
Oct 15, 2019 at 18:58 comment added NeukirchLover Thank you very much for your fast answer Fabian! I am so sorry that I forgot to weight each term in the same with its distribution probability. Otherwise it would be kinda obvious :D Do you still think the upper equation is wrong?
Oct 14, 2019 at 17:21 history answered Fabian Werner CC BY-SA 4.0