The variance of two game tree algorithms
- Southern Methodist Univ., Dallas, TX (United States)
This paper studies the variance of two game tree algorithms {alpha}-{beta} search and SCOUT, in the stochastic i.i.d. model. The problem of determining the variance of the classic {alpha}-{beta} search algorithm in the i.i.d. model has been long open. This paper resolves this problem partially. It is shown, by the martingale method, that the standard deviation of the weaker {alpha}-{beta} search without deep cutoffs is of the same order as the expected number of leaves evaluated. A nearly-optimal upper bound on the variance of the general {alpha}-{beta} search is obtained, and this upper bound yields an optimal bound if the current upper bound on the expected number of leaves evaluated by {alpha}-{beta} search can be improved. A thorough treatment of the two-pass SCOUT algorithm is presented. The variance of the SCOUT algorithm is determined.
- OSTI ID:
- 471682
- Report Number(s):
- CONF-970142--
- Country of Publication:
- United States
- Language:
- English
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