Adversarial Search

1
Adversarial Search

• CS 171/271
• (Chapter 6)
• Some text and images in these slides were drawn
  fromRussel Norvigs published material

2
Games

• Multi-agent environment
• Agent needs to consider actions of other agents
• Games Adversarial Search Problems
• Considerations
• Many possible moves of other player
• Time (need to optimize, or approximate)

3
Game as a Search Problem

• Initial State
• Successor Function
• Note the turn-taking aspect (ply)
• Terminal test
• Goal game over (leaf nodes)
• Utility Function
• Score or outcome (examples?)

4
Game Tree
5
Infallible Opponent Assumption

• Strategy select the best move that assumes the
  your opponent will make the best play
• Need to consider all possible opponent moves
• Minimax value of a node in the game tree
• 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

6
Minimax Values
7
Minimax Algorithm
8
a-ß (alpha-beta) Pruning

• 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
• a -gt highest valued choice so far along path for
  MAX
• ß -gt lowest valued choice so far along path for
  MIN

9
a-ß pruning omit examination of these
nodes Minimum of 2 cannot yield a maximum higher
than 3
10
About a-ß pruning

• Effectiveness is highly dependent on order in
  which successors are examined
• Can reduce effective tree depth to half its value

11
Other Considerationsin Games

• Because of time constraints, may have to settle
  with estimate of utility (evaluation function)
• Non-terminal nodes turned into leaves
• Elements of chance
• e.g., dice and cards
• Min, max, and chance nodes

12
State of the Art

• 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.

13
State of the Art

• 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 gt 300, so
  most programs use pattern knowledge bases to
  suggest plausible moves.