Abstract. Learning by explaining failures and avoiding similar ones thereafter is an attractive way to speed up problem solving. However, previous methods for explanation-based learning from failure can take too long to detect failures, explain them, or test the learned rules. This expense is especially critical for adaptive search, in which control knowledge acquired while solving an individual problem instance must be learned quickly enough to speed up its solution.We present an adaptive search technique that speeds up state-space search by learning heuristic censors while searching. The censors speed up search by pruning away more and more of the space until a solution is found in the pruned space. Censors are learned by explaining dead ends and other search failures. To learn quickly, the technique overgeneralizes by assuming that certain constraints are preservable, i.e., remain true along at least one solution path. A recovery mechanism detects violations of this assumption and selectively relaxes learned censors. The technique, implemented in an adaptive problem solver named FAILSAFE-2, learns useful heuristics that cannot be learned by other reported methods.We present experimental evidence that FAILSAFE-2 is effective (learns useful rules, even in recursive domains where PRODIGY and STATIC do not), adaptive (learns fast enough to pay off even within a single problem), and general (speeds up diverse problem solvers, even initially strong ones).