单调性和启发式的可接受性之间有什么区别？
我正在阅读我的人工智能教科书，我很好奇启发式的单调性和可接受性之间有什么区别（我知道它们并不相互排斥）。
据我所知，可接受的启发式方法仅仅意味着您可以确保获得解决方案的最短路径（如果存在）。
我正在努力解决的是单调属性的概念。有人可以用我可以理解的方式向我描述这一点吗？
同样，我如何确定给定的启发式是否单调/可接受？书中给出的例子之一是 8 片滑动拼图。我正在考虑的一个启发是不合适的瓷砖的数量，直观上我可以说我知道它是可接受的，但我没有正式的方式来显示它是否可接受/单调。
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).
As far as I can tell, an admissible heuristic simply means you are ensured to get the shortest path to a solution if one exists.
What I'm struggling with is the concept of the monotonic property. Can someone describe this to me in a way I might understand?
Similarly, how can I determine if a given heuristic is monotonic/admissible? One of the examples given in the book is the 8-Piece Sliding Puzzle. One heuristic I'm considering is the # of out of place tiles, and intuitively I can say that I know that it is admissible but I have no formal way of showing if it is admissible/monotonic.
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Russel 和 Norvig，第 2 版第 99 页 说道：
当您谈论函数时，单调意味着函数增加或减少，但不能同时增加或减少。换句话说，范围内的顺序在整个域中保持不变。因此，在您的问题中，无论您从哪一步开始，解决方案都会保持最短路径。
启发式的可接纳性属性意味着达到目标的成本永远不会被高估（即乐观）（第98页）。
Russel and Norvig, 2ed page 99 says:
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).
可接受性：
如果只要存在解，就能保证找到解的最小路径，则搜索算法是可接受的。广度优先搜索是可接受的，因为它在考虑第 n+1 层的任何状态之前先查看第 n 层的每个状态。
单调性：
该属性询问算法是否是局部可接受的——也就是说，它总是低估搜索空间中任意两个状态之间的成本。回想一下，A* 不需要 g(n) = g*(n)。启发式函数，h 是单调的，如果：
1.对于所有状态ni和nj，其中nj是ni的后代，h(ni) - h(nj) <= cost(ni,nj)。
2.目标状态的启发式评估为0：h(Goal) = 0。
Admissibility :
A search algorithm is admissible if it is guaranteed to find a minimal path to a solution whenever such a solution exists. Breadth first search is admissible, because it looks at every state at level n before considering any state at level n+1.
Monotonicity :
This property asks if an algorithm is locally admissible---that is, it always underestimates the cost between any two states in the search space. Recall that A* does not require that g(n) = g*(n). A heuristic function, h is monotone if:
1.For all states ni and nj, where nj is a descendant of ni, h(ni) - h(nj) <= cost(ni,nj).
2.The heuristic evaluation of the goal state is 0: h(Goal) = 0.
单调学习是指代理不能学习任何与其已知知识相矛盾的知识。例如，它不能用其否定来替换语句。因此，知识库只能以单调的方式随着新事实的增长而增长。单调学习的优点是：
1. 极大地简化真相维护
2. 学习策略有更多选择
非单调学习是指智能体可能学到与其已知知识相矛盾的知识。因此，如果它认为有足够的理由，它可能会用新知识取代旧知识。非单调学习的优点是：
1. 增加对实际领域的适用性，
2. 学习的顺序有更大的自由度
一个相关的属性是知识的一致性。如果一个架构必须保持一致的知识库，那么它使用的任何学习策略都必须是单调的。
Monotonic learning is when an agent may not learn any knowledge that contradicts what it already knows. For example, it may not replace a statement with its negation. Thus, the knowledge base may only grow with new facts in a monotonic fashion. The advantages of monotonic learning are:
1.greatly simplified truth-maintenance
2.greater choice in learning strategies
Non-monotonic learning is when an agent may learn knowledge that contradicts what it already knows. So it may replace old knowledge with new if it believes there is sufficient reason to do so. The advantages of non-monotonic learning are:
1.increased applicability to real domains,
2.greater freedom in the order things are learned in
A related property is the consistency of the knowledge. If an architecture must maintain a consistent knowledge base then any learning strategy it uses must be monotonic.