Last time: Simulated annealing algorithm

26 Pages·2009·0.34 MB·English

Last time: Simulated
annealing algorithm
Idea: Escape local extrema by allowing
(cid:132)
“bbaadd mmoovveess,,” bbuutt ggrraadduuaallllyy ddeeccrreeaassee
their size and frequency.
Note: goal here is to
-
maximize E.
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Last time: Simulated
annealing algorithm
Idea: Escape local extrema by allowing
(cid:132)
“bbaadd mmoovveess,,” bbuutt ggrraadduuaallllyy ddeeccrreeaassee
their size and frequency.
Algorithm when goal
-
is to minimize E.
<
-
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This time: Outline
Game playing
(cid:132)
The minimax
(cid:132)
allgoriitthhm
Resource limitations
(cid:132)
aallpphhaa-bbeettaa pprruunniinngg
(cid:132)(cid:132)
Elements of chance
(cid:132)
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What kind of games?
Abstraction: To describe a game we
(cid:132)
must capture every relevant aspect of
the game. Such as:
Chess
(cid:132)
Tic-tac-toe
(cid:132)
…
(cid:132)
Accessible environments: Such
(cid:132)
ggaammeess aarree cchhaarraacctteerriizzeedd bbyy ppeerrffeecctt
information
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What kind of games?
Search: game-playing then consists of
(cid:132)
a search through possible game
positions
Unpredictable opponent: introduces
(cid:132)
uunncceerrttaaiinnttyy tthhuuss ggaammee-ppllaayyiinngg mmuusstt
deal with contingency problems
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Searching for the next move
Complexity: many games have a huge
(cid:132)
sseeaarrcchh ssppaaccee
Chess: b = 35, m=100 ⇒ nodes =35 100
(cid:132)
if each node takes about 1 ns to expplore
then each move will take about 10 50
millennia to calculate.
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Searching for the next move
Resource (e.g., time, memory) limit:
(cid:132)
ooppttiimmaall ssoolluuttiioonn nnoott ffeeaassiibbllee//ppoossssiibbllee,,
thus must approximate
PPrruunniinngg:: mmaakkeess tthhee sseeaarrcchh mmoorree eeffffiicciieenntt
11.
by discarding portions of the search tree
that cannot improve quality result.
Evaluation functions: heuristics to
2.
evaluate utility of a state without exhaustive
search.
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Two-player games
A game formulated as a search problem:
(cid:132)
Initial state: ?
(cid:132)
OOppeerraattoorrss:: ??
(cid:132)
Terminal state: ?
(cid:132)
UUttiilliitty ffuncttiion: ??
(cid:132)
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Game vs. search problem
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Example: Tic-Tac-Toe
Question:
1. b (branching factor) = ?
22. mm ((mmaaxx ddeepptthh)) == ??
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