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Additional resources for Reinforcement Learning and Approximate Dynamic Programming for Feedback Control (IEEE Press Series on Computational Intelligence, Volume 17)
14) i=1 This approximation is still governed, in principle, by Barron’s results on linear basis function approximators, but if the users supply basis functions suited to his particular problem, it might allow better performance in practice. ” It is also analogous to the use of user-defined “features,” like HOG or SIFT features, in traditional image processing. It also opens the door to many special cases of general-purpose ADP methods, and new specialpurpose methods for the linear case, such as the use of linear programming to estimate the weights W .
Besides approximating J ∗ (X) or λ(X), it is also possible to approximate: J (X(t), u(t)) = Q(X(t), u(t)) = U(X(t), u(t)) + Max J ∗ (X(t + 1))/(1 + r) . 12) Note that J and Q are the same thing. D. ” In the same year , independently, I proposed the use of universal approximators to approximate J , in action-dependent HDP. Actiondependent HDP was the method used by White and Sofge  in their breakthrough control for the continuous production of thermoplastic carbon–carbon parts, a technology which is now of enormous importance to the aircraft industry, as in the recent breakthrough commercial airplane, the Boeing 787.
8) 10 REINFORCEMENT LEARNING AND APPROXIMATE DYNAMIC PROGRAMMING This leads directly to the key equation derived by Richard Bellman (in updated notation): J ∗ (X(t)) = max U(X(t), u(t)) + J ∗ (X(t + 1))/(1 + r) . 5), and the set of allowed values which u(t) may be taken from. ) With that information, it is possible to solve for the function J ∗ which satisfies this equation. The original theorems of DP tell us that J ∗ exists, and that maximizing U + J ∗ /(1 + r) as shown in the Bellman equation gives us an optimal policy.
Reinforcement Learning and Approximate Dynamic Programming for Feedback Control (IEEE Press Series on Computational Intelligence, Volume 17)