ON THE ASYMPTOTIC COST CONVERGENCE RATE OF THE MODIFIED METHOD OF SUCCESSIVE APPROXIMATIONS.
CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP
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The modified method of successive approximations of White, Schweitzer, MacQueen, and Odoni concentrates attention on cost differences either between successive stages, or relative to a base state in the same stage, rather than the total cost function itself. It is instructive to work out the actual asymptotic convergence rates of these constructs for the special case of a single fixed policy. Convergence is actually very powerful even for discount rates greater than 1.0, depending principally on the dominant eigenvalue of the transition matrix. The implications of this fact for the relative efficiencies of modified value interation, policy interation, policy iteration via successive approximations, or possible hybrids, are discussed. Author
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