Download CMPUT 650: Learning To Make Decisions

CSE 4705
Artificial Intelligence
Jinbo Bi
Department of Computer Science & Engineering
http://www.engr.uconn.edu/~jinbo
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Search fundamentals
• Chapter 3.3
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Useful concepts
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Useful concepts
• After we formulate a problem, how do we find
the solutions for it?
•
•
•
Enumerate in some order all possible paths from
the initial state
Here: search through explicit tree generation
• ROOT = initial state
• Nodes and leafs generated through transition
model
In general, search generates a graph (same state
through multiple paths), but we will just look at trees
in lecture
• Treats different paths to the same node as
distinct
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Simple tree search example
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Simple tree search example
Determines
search process
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8-Puzzle: states and nodes
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8-Puzzle: search tree
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Uninformed search strategies
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Uninformed search strategies
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Uninformed search strategies
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Breadth-first search
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Breadth-first search
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Breadth-first search (simplified)
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Properties of breadth-first search
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Exponential space/time complexity
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Depth-first search
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Depth-first search
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Properties of depth-first search
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Breadth-first vs depth-first search
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Breadth-first vs depth-first search
How can we get the best of both?
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Depth-limited search: a building block
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Iterative deepening search
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Iterative deepening search
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Iterative deepening search, example
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Iterative deepening search, example
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Iterative deepening search, example
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Iterative deepening search, example
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Properties of iterative deepening search
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Iterative deepening search:
time complexity
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Summary of the algorithms
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Bidirectional search: very brief review
• Two simultaneous searches from start and goal
• Motivation:
• Check whether the node belongs to the other frontier
before expansion
• Space complexity is the most significant weakness
• Complete and optimal if both searches are breadth-first
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Bidirectional search: very brief review
• The predecessor of each node can be efficiently
computable
• Works well when actions are easily reversible
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“Uniform cost” search
• Motivation: an example Romanian Holiday Problem
• All our search methods so far assume
• Step-cost = 1
• This is not always true
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“Uniform cost” search
g(N): the path cost function
•
If all moves equal in cost
•
Assigning a (potentially) unique cost to each
step
• Cost = # of nodes in path – 1
• g(n) = depth(n)
• Equivalent to what we have been assuming so far
• N0, N1, N2, N3 are nodes visited on path p
• C(i,j): Cost of going from Ni to Nj
• g(N1) = C(0,1) + C(1,2) + C(2,3)
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“Uniform cost” search
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“Uniform cost” search
Start
Goal
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“Uniform cost” search
Example: Romania Holiday Problem
Start S
g(R) =80
g(P) =177
g(B) =278
P
R 1
3
2 F
g(F) =99
is updated
4 B g(B) =310
to 278
Goal
B 4
Goal
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Summary of uninformed search
C* is the cost of the optimal solution, and e is step cost
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Informed search strategies
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Informed search
•
Part I (classical search)
• Informed = use problem-specific knowledge
• Best-first search and its variants
• A* - Optimal search using knowledge
• Proof of optimality of A*
• A* for maneuvering AI agents in games
• Heuristic functions
•
Part II (beyond classical search, Chap 4)
• Local search and optimization
• Local search in continuous space
• Hill climbing, local bean search, …
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Informed search
•
Is Uniform cost search the best we can do?
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A better idea
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The straight-line
distance from each city
to Bucharest:
Start
Goal
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A heuristic function
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Breadth first for games, robots
http://theory.stanford.edu/~amitp/GameProgramming/
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An optimal informed search (A*)
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Breadth first for a world with obstacles
Pink: start node;
Dark blue: goal
Breadth-first search expands many nodes
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Informed search (A*) in that world
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Questions?
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