Probabilistic Hill-climbing: Theory and Applications

Many learning systems search through a space of possible performance elements, seeking an element with high expected utility. As the task of nding the globally optimal element is usually intractable, many practical learning systems use hill-climbing to nd a local optimum. Unfortunately, even this is diicult, as it depends on the distribution of problems, which is typically unknown. This paper addresses the task of approximating this hill-climbing search when the utility function can only be estimated by sampling. We present an algorithm that returns an element that is, with provably high probability, essentially a local optimum. We then demonstrate the generality of this algorithm by sketching three meaningful applications, that respectively nd an element whose eeciency, accuracy or completeness is nearly optimal. These results suggest approaches to solving the utility problem from explanation-based learning, the multiple extension problem from nonmonotonic reasoning and the tractability/completeness tradeoo problem from knowledge representation.

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