📗 Additional information can be given in the form of a heuristic cost from any state to the goal state: this is an estimate or guess of the minimum cost from \(s\) to a goal state: Wikipedia.
➩ The cost from the initial state to a state \(s\) is denoted by \(g\left(s\right)\).
➩ The cost from the state \(s\) to the goal state is denoted by \(h^\star\left(s\right)\), which is unknown during the search.
➩ The estimated value of \(h^\star\left(s\right)\) is called the heuristic cost, denoted by \(h\left(s\right)\).
📗 Heuristic costs can be used to speed up the search.
TopHat Discussion
📗 Search for a page containing an image. Describe how you find the image.
📗 UCS (Uniform Cost Search, or Dijkstra's Algorithm) expands the state with the lowest current cost \(g\left(s\right)\): Wikipedia.
📗 It is BFS with a priority queue based on \(g\left(s\right)\), and it is equivalent to BFS if the cost of every action is 1.
📗 UCS is complete.
📗 UCS is optimal.
TopHat Quiz
📗 [4 points] Given initial state \(S\) and goal state \(G\), write down the expansion path (list of expanded nodes) for . In case the diagram is not clear, the edge costs are (heuristic on the diagonal).
📗 (Best First) Greedy Search expands the state with the lowest heuristic cost \(h\left(s\right)\): Wikipedia.
📗 BFGS is not an abbreviation of Greedy Search, since it usually stands for Broyden Fletcher Goldfarb Shanno algorithm (a version of a gradient descent algorithm).
📗 Greedy uses a priority queue based on \(h\left(s\right)\).
📗 Greedy is incomplete.
📗 Greedy is not optimal.
TopHat Quiz
📗 [4 points] Given initial state \(S\) and goal state \(G\), write down the expansion path (list of expanded nodes) for . In case the diagram is not clear, the edge costs are (heuristic on the diagonal).
📗 A Search expands the state with the lowest total cost \(g\left(s\right) + h\left(s\right)\): Wikipedia (for A*).
📗 A Search uses a priority queue based on \(g\left(s\right) + h\left(s\right)\).
📗 A is complete.
📗 A is not optimal.
TopHat Quiz
📗 [4 points] Given initial state \(S\) and goal state \(G\), write down the expansion path (list of expanded nodes) for . In case the diagram is not clear, the edge costs are (heuristic on the diagonal).
📗 Answer: .
TopHat Quiz
📗 [4 points] Given initial state \(S\) and goal state \(G\), write down the expansion path (list of expanded nodes) for . In case the diagram is not clear, the edge costs are (heuristic on the diagonal).
📗 Answer: .
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📗 Notes and code adapted from the course taught by Professors Jerry Zhu, Yingyu Liang, and Charles Dyer.
📗 Content from note blocks marked "optional" and content from Wikipedia and other demo links are helpful for understanding the materials, but will not be explicitly tested on the exams.
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