What is the difference between monotonicity and the admissibility of a heuristic?

Question

I\'m reading over my AI textbook and I\'m curious about what the difference is between monotonicity and admissibility of heuristics (I know they aren\'t mutually exclusive).

Answer 1

Russel and Norvig, 2ed page 99 says:

The second solution is to ensure that the optimal path to any repeated state is always the first one followed -- as is the case with uniform-cost search. This property holds if we impose an extra requirement on h(n), namely the requirement of consistency (also called monotonicity).

When you're talking about functions, monotone means that a function increases or decreases, but not both. In other words, the ordering in the range stays the same throughout the domain. For this reason in your problem, the solution maintains the shortest path no matter what step you start at.

The admissibility property of a heuristic means that the cost to reach the goal is never overestimated (i.e. it's optimistic) (page 98).