Probably Approximately Optimal Derivation Strategies

An inference graph can have many \deriva-tion strategies", each a particular ordering of the steps involved in reducing a given query to a sequence of database retrievals. An \optimal strategy" for a given distribution of queries is a complete strategy whose \expected cost" is minimal, where the expected cost depends on the conditional probabilities that each requested retrieval succeeds , given that a member of this class of queries is posed. This paper describes the PAO algorithm that rst uses a set of training examples to approximate these probability values, and then uses these estimates to produce a \probably approximately optimal" strategy | i.e., given any ; > 0, PAO produces a strategy whose cost is within of the cost of the optimal strategy, with probability greater than 1 ?. This paper also shows how to obtain these strategies in time polynomial in 1==, 1== and the size of the inference graph, for many important classes of graphs, including all and-or trees.