Temperature Discovery

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Temperature Discovery

• Martin Müller, Markus Enzenberger and Jonathan
  Schaeffer
• Introduction local and global search
• Local search algorithms
• Temperature
• Environments and coupon stacks
• Temperature discovery search
• First results

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Local and Global Search

• Local search
• Partition game into sum of subgames
• Local analysis
• Problem how to evaluate local results?
• Central questionwhich sums of games are wins?

• Global search
• Single, monolithic game state
• Full board evaluation
• Single game tree,minimax backup
• Central questionwhat is the minimax score?

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Why Local Search?

• Global Alpha-beta Search time exponential in
  size of full problem
• Local search time exponential in size of
  subproblems

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(No Transcript)
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Results of Local Searches

• 1. Exact combinatorial game value(Winning Ways,
  my Ph.D. thesis on Go endgames)
• 2. Inexact, but very good temperatures,
  thermographs(Go Berlekamp, Spight, Fraser,
  Müller,Amazons Theo Tegos)
• 3. Even less exact heuristic search to estimate
  the temperature (This work, with Markus and
  Jonathan)

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1. Decomposition Search

• Usual global game tree search
• DSDivide-and-conquer approach
• Idea
• Divide game into sub-games
• Do a local search
• Combine local resultsCombinatorial game theory

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2. Temperatures, Thermographs
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3. Temperature Discovery

• Problem Thermographs computed bottom-up
• Needs complete local game tree
• Sometimes too expensive
• Heuristic evaluation works well in global search
• Idea use it in local search to estimate
  temperature

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Temperature Discovery

• A different way to compute temperatures
  (Berlekamp)
• Play local game Coupon stack
• Choose between play on the board and coupon
  (move of known value)
• Temperature of coupon of value t is t. So can
  estimate temp of board!

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Example

• Coupon stack 3,2,1,0,-1
• Amazons board
• Search depth 4
• 1. B Coupon(3)2. W C8-C7xC83. B Coupon(2)
• 4. W Coupon(1)

9 . . X . 8 . . W . 7 X . . B 6 . X . . A B
C D
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Example (contd)

• Uses heuristic evaluation of board
• Depth-limited search
• Result
• when does it change from taking coupons to board?
• Estimate for the temperature

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Experiments (1)

• Run temp. discovery search on small areas
• Compare estimated t against exact t from Theo
  Tegos Databases
• Plot real t vs estimated t
• Works OK, but still some problems/bugs?

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Experiments (2)

• Sample starting positions with 2, 4 and 6
  subgames
• Subgame size 4x4, 5x5
• Temperature discovery in each local game
• Simple hotstrat player
• Play 2x200 games against Arrow (full board search)

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Two, four, six 4x4 subgames

• Coupon player vs Arrow
• About 10 sec./move

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Two, four, six 4x4 subgames
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Two and Four 5x5 subgames
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5x5 subgames

• 13.25 average over 200 pairs of games (stdDev
  11.5)

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Control experiment

• Arrow(10sec) vs Arrow on four 4x4
• Different time limits for opponent

5s
1s
30s
10s
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Sample 4x5x5 Game
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To Do...

• More experiments, e.g. 6x5x5, 6x6,...
• Try on real games
• Better sum game algorithm
• Tune, fix temperature discovery search
• Optimal solver? (Needs global search too)
• The real goal - apply to Go!

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Summary

• Local search algorithm
• Try to discover temperature by minimax search
• Applications Amazons, future Go
• First results it works...
• Still lots of open questions