Adversarial Search
CS 171/271
(Chapter 6)
Some text and images in these slides were drawn from
Russel & Norvig’s published material
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Games
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Multi-agent environment
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Agent needs to consider actions of other
agents
Games: Adversarial Search Problems
Considerations
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Many possible moves of other player
Time (need to optimize, or approximate)
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Game as a Search Problem
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Initial State
Successor Function
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Terminal test
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Note the turn-taking aspect (“ply”)
“Goal”: game over (leaf nodes)
Utility Function
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Score or outcome (examples?)
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Game Tree
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Infallible Opponent
Assumption
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Strategy: select the best move that assumes
the your opponent will make the best play
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Need to consider all possible opponent moves
Minimax value of a node in the game tree
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Leaf node: minimax value = utility value
Agent (called MAX) picks a move that results in a
state with maximum utility; minimax value of the
node is that maximum
Opponent picks the move that minimizes utility for
the agent; minimax value of the node is that
minimum
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Minimax Values
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Minimax Algorithm
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α-β (alpha-beta) Pruning
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May skip examination of some nodes
If a node has no impact on the min/max
choice at upper levels, prune that node
Need to maintain
 α -> highest valued choice so far along
path for MAX
 β -> lowest valued choice so far along path
for MIN
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α-β pruning: omit examination of these nodes;
Minimum of 2 cannot yield a maximum higher than 3
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About α-β pruning
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Effectiveness is highly dependent on
order in which successors are examined
Can reduce effective tree depth to half
its value
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Other Considerations
in Games
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Because of time constraints, may have
to settle with estimate of utility
(evaluation function)
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Non-terminal nodes turned into leaves
Elements of chance
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e.g., dice and cards
Min, max, and chance nodes
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State of the Art
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Checkers: Chinook ended 40-year-reign of human
world champion Marion Tinsley in 1994. Used a
precomputed endgame database defining perfect
play for all positions involving 8 or fewer pieces on
the board, a total of 444 billion positions.
Chess: Deep Blue defeated human world champion
Garry Kasparov in a six-game match in 1997. Deep
Blue searches 200 million positions per second, uses
very sophisticated evaluation, and undisclosed
methods for extending some lines of search up to 40
ply.
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State of the Art
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Othello: human champions refuse to compete
against computers, who are too good.
Go: human champions refuse to compete
against computers, who are too bad. In go, b
> 300, so most programs use pattern
knowledge bases to suggest plausible moves.
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