Download Abstraction, Reformulation, and Approximation: 4th by Patrick Cousot (auth.), Berthe Y. Choueiry, Toby Walsh PDF

By Patrick Cousot (auth.), Berthe Y. Choueiry, Toby Walsh (eds.)

This quantity includes the lawsuits of SARA 2000, the fourth Symposium on Abstraction, Reformulations, and Approximation (SARA). The convention was once held at Horseshoe Bay lodge and convention membership, Lake LBJ, Texas, July 26– 29, 2000, simply sooner than the AAAI 2000 convention in Austin. prior SARA meetings happened at Jackson gap in Wyoming (1994), Ville d’Est´erel in Qu´ebec (1995), and Asilomar in California (1998). The symposium grewout of a chain of workshops on abstraction, approximation, and reformulation that had taken position along AAAI because 1989. This year’s symposium used to be truly scheduled to happen at Lago Vista golf equipment & lodge on Lake Travis yet, a result of resort’s failure to pay taxes, the convention needed to be moved overdue within the day. This mischance engendered eleventh-hour reformulations, abstractions, and source re-allocations of its personal. Such are the perils of organizing a convention. this is often the ?rst SARA for which the complaints were released within the LNAI sequence of Springer-Verlag. we are hoping that this can be a re?ection of the elevated adulthood of the ?eld and that the elevated visibility introduced by way of the ebook of this quantity may help the self-discipline develop even additional. Abstractions, reformulations, and approximations (AR&A) have discovered - plications in quite a few disciplines and difficulties together with automated progr- ming, constraint pride, layout, prognosis, desktop studying, making plans, qu- itative reasoning, scheduling, source allocation, and theorem proving. The - pers during this quantity catch a cross-section of those software domains.

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So if X Y then by Hyp. 6 and monotony, γ(X) ≤ γ(Y ) ≤ γ ◦ α(S) ≤ S and I ≤ γ ◦ α(I) ≤ γ(X) ≤ γ(Y ). So X Y implies γ(X) ≤ S & I ≤ γ(Y ) and the argument used in the proof of Th. 24 concludes the partial correctness proof of Alg. 8. Theorem 27. Under Hyps. 1, 4 & 6, the abstraction α, γ and α, γ is partially complete for Alg. 4 if and only if either α(L) contains an abstract value A such that γ(A) is an invariant for F , I, S or dually α(L) contains an abstract value A such that γ(A) is an invariant for F , I, S .

After each action in the real world, prioritized sweeping performs a fixed number of dynamic programming steps to update the Q values of those state-action pairs whose Q values are believed to be most inaccurate. Experimental tests show that prioritized sweeping can be dramatically more efficient than Q learning. We have implemented a prioritized sweeping algorithm for the MAXQ hierarchy. The algorithm learns a model for each subtask within the MAXQ task hierarchy. Unfortunately, the model for subtask p must remember the values of all state variables that are relevant to subtask p or to any of its descendants.

The basic idea would be to treat the completion function Q(p, s, a) as a “terminal state” reward for action a, which would then influence the value function inside subtask a. Although this would permit MAXQQ learning to discover a hierarchically optimal policy, it would also destroy many opportunities for state abstraction. Consider what happens if the goal location (in the right room) is a state variable that can change. Then the choice of hierarchically optimal policy inside the left room will depend on the location of the goal in the right room.

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