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5.10 examples 83 POMDPs. POMDPs differ from MDPs in that the state st of the environment is not observed directly but, as in latent-variable time series models, only through stochastic observations ot, which depend on the latent states st via pE(ot | st). The policy there- fore has to be a function of the history of past observations πθ(at | o1 . . . ot). Applying Theorem 2, we obtain a gradient estimator: ∂T∂T ∂θL = Eτ∼pθ ∂θ logπθ(at |o1 ...ot)) r(st′,at′)−bt(o1 ...ot) . (45) t=1 t′=t Here, the baseline bt and the policy πθ can depend on the observation history through time t, and these functions can be parameterized as recurrent neural networks [Wie+10; Mni+14]. The stochastic computation graph is shown in Figure 14. θ s1 s2 ... sT a1 a2 ... aT r1 r2 ... rT s1 s2 o1 o2 m1 m2 a1 a2 r1 r2 θ ... sT ... oT ... mT ... aT ... rT Figure 14: Stochastic Computation Graphs for MDPs (left) and POMDPs (right)PDF Image | OPTIMIZING EXPECTATIONS: FROM DEEP REINFORCEMENT LEARNING TO STOCHASTIC COMPUTATION GRAPHS
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