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Artificial.intelligence_0160 - Graceful Decay of...

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Graceful Decay of Admissibility • Theorem: If h(n) rarely overestimates the actual minimum cost by more than e, then A* search will rarely find a solution whose cost is more than e greater than the cost of the optimal solution. • Let n 1 be the first goal node found and n 0 be the goal node on the optimal path. We need to show: g(n 1 ) <= g(n 0 ) + e. • Suppose that at the time n1 is selected, m from the fringe is a node on the optimal path from s to n0. • Then, we know: f(n1) <= f(n), since n1 was selected before m. Thus, g(n1) = f(n1) <= f(m) = g(m) + h(m), since n1 is a goal node. • Let h*(m) be the actual cost from m to n0, then by the condition in the theorem:
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