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administrivia

administrivia. Exam format – take home, open book Suicide rule for King’s court. Illegal moves cannot move last piece from court. OK. Focusing Game Search. improvements on Minimax. Minimax in large state space. maximization. minimization. heuristic evaluation from viewpoint of Max.

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administrivia

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  1. administrivia • Exam format – take home, open book • Suicide rule for King’s court Illegal moves cannot move last piece from court OK D Goforth - COSC 4117, fall 2003

  2. Focusing Game Search improvements on Minimax

  3. Minimax in large state space maximization minimization heuristic evaluation from viewpoint of Max see p.166, Fig. 6.3 D Goforth - COSC 4117, fall 2003

  4. Minimax depth-limited DFS (1) maximization >-∞,<=3 minimization 3 heuristic evaluation from viewpoint of Max: bigger  better for Max D Goforth - COSC 4117, fall 2003

  5. Minimax depth-limited DFS (2) >=-1,<∞ maximization -1 minimization 3 2 -1 4 0 heuristic evaluation from viewpoint of Max: bigger  better for Max D Goforth - COSC 4117, fall 2003

  6. Minimax depth-limited DFS (3) >=-1,<∞ maximization -2 -1 -2 3 2 -1 4 0 0 3 2 1 heuristic evaluation from viewpoint of Max: bigger  better for Max D Goforth - COSC 4117, fall 2003

  7. Minimax depth-limited DFS (4) 1 -2 -1 1 minimization -2 1 3 2 -1 4 0 0 3 2 1 1 4 5 1 heuristic evaluation from viewpoint of Max: bigger  better for Max D Goforth - COSC 4117, fall 2003

  8. Alpha-beta pruning (3’a) >=-1,<∞ maximization >-∞,<=0 -1 minimization 3 2 -1 4 0 0 heuristic evaluation from viewpoint of Max: bigger  better for Max D Goforth - COSC 4117, fall 2003

  9. Alpha-beta pruning (3’b) >=-1,<∞ maximization -1 >-∞,<=-2 minimization -2 3 2 -1 4 0 0 heuristic evaluation from viewpoint of Max: bigger  better for Max D Goforth - COSC 4117, fall 2003

  10. Alpha-beta pruning (4’) 1 >-∞,<=-2 -1 1 -2 1 3 2 -1 4 0 0 1 4 5 1 heuristic evaluation from viewpoint of Max: bigger  better for Max D Goforth - COSC 4117, fall 2003

  11. Alpha beta pruning • alpha, beta are limits on evaluation of non-terminal node • eliminates some search at no risk • optimized alpha-beta can reduce branching factor n  n1/2  double depth of search with same cost D Goforth - COSC 4117, fall 2003

  12. 1 1 1 1 4 5 Factor: order of traversal 1 <=-1 <=-2 0 -1 0 2 3 4 -2 1 2 3 heuristic evaluation from viewpoint of Max: bigger  better for Max D Goforth - COSC 4117, fall 2003

  13. 1 1 1 1 4 5 How to improve order 1 expand in order of heuristic evaluation 0 -1 3 <=-1 <=-2 0 -1 0 2 3 4 -2 1 2 3 heuristic evaluation from viewpoint of Max: bigger  better for Max D Goforth - COSC 4117, fall 2003

  14. Problems with Minimax • searching to edge of disaster - lack of ‘quiescence’ – values don’t change a lot from ply to ply • horizon effect – search finds a path that delays but doesn’t avoid bad move • partial solution: singular extension – mini-search beyond chosen path D Goforth - COSC 4117, fall 2003

  15. Pruning with risk • alpha beta pruning is proven to find best solution • other methods risk missing best solution • forward pruning: eliminate branches based on preliminary evaluation • absolute: below certain value • competitive: limit branching factor • extended rules: ignore entirely some expansions D Goforth - COSC 4117, fall 2003

  16. Evaluation functions • properties • optimistic, well ordered (if possible) • efficient, fast • features correlated to win/loss • functions of state (incremental maintenance) • combine in weighted evaluation function • best model for ‘tuning’ D Goforth - COSC 4117, fall 2003

  17. Evaluation function: example e.g. King’s Court: • f1: difference in number of pieces in Court • f2: number of pieces vulnerable to jumping by opponent evaluation = w1f1 + w2f2 where w’s weigh relative importance of functions D Goforth - COSC 4117, fall 2003

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