COMP9414: Artificial Intelligence Adversarial Search - AI Study

COMP9414, Wednesday 24 March, 2004 Adversarial Search 2COMP9414: Artificial IntelligenceAdversarial SearchAdversarial Search In many problems — especially game playing — you’re are pittedagainst an opponent This means that certain operators are beyond your controlWayne WobckeRoom J17-433wobcke@cse.unsw.edu.auBased on slides by Maurice Pagnucco That is, you cannot control your opponent’s moves You cannot search the entire space from the outset looking for asolution since your opponent may make a move which makes anypath you find obsolete What you need is a strategy that leads to a winning position regardlessof how your opponent playsCOMP9414 c○UNSW, 2004COMP9414 c○UNSW, 2004 Generated: 31 March 2004COMP9414, Wednesday 24 March, 2004 Adversarial Search 1COMP9414, Wednesday 24 March, 2004 Adversarial Search 3Adversarial Search Shall investigate two uses of search where we can apply otherstrategies to search the state space In particular we shall investigate adversarial search in which wesearch through a space where not all operators (choices) are under ourcontrol We shall also briefly discuss constraint satisfaction problemsOverview Minimax Alpha-Beta Pruning Constraint Satisfaction as Search Conclusion Reference:◮ Ivan Bratko, Prolog Programming for Artificial Intelligence,Addison-Wesley, 2001. (Chapter 22)◮ Stuart J. Russell and Peter Norvig, Artificial Intelligence: AModern Approach, Second Edition, Pearson Education, 2003.(Chapter 6)COMP9414 c○UNSW, 2004 Generated: 31 March 2004COMP9414 c○UNSW, 2004 Generated: 31 March 2004

COMP9414, Wednesday 24 March, 2004 Adversarial Search 8Minimax AlgorithmCOMP9414, Wednesday 24 March, 2004 Adversarial Search 10Alpha-Beta Pruningfunction MinimaxValue(state, game) returns utility valueif TerminalTest[game](state)then return Utility[game](state)else if Max is to move in statethen return highest MinimaxValue of successors(state)else return lowest MinimaxValue of successors(state) Idea: Consider node n in search tree such that certain player has achoice of moving to that node If the player has a better choice m either at the parent node of n, orat any choice point further up, then n will never be reached in actualplay Once we have ascertained enough information about n by looking atsome of its successors to reach this decision, we can prune itCOMP9414 c○UNSW, 2004 Generated: 31 March 2004COMP9414 c○UNSW, 2004 Generated: 31 March 2004COMP9414, Wednesday 24 March, 2004 Adversarial Search 9Alpha-Beta PruningCOMP9414, Wednesday 24 March, 2004 Adversarial Search 11Alpha-Beta Pruning In most games it will be impossible to try and calculate minimax asdescribed — the game tree will be just too big There is however a way of pruning the amount of work to be doneand still make the correct minimax decision Pruning — elimination of branches from the search withoutexamination Alpha-beta pruning returns a pruned minimax treemnCOMP9414 c○UNSW, 2004 Generated: 31 March 2004COMP9414 c○UNSW, 2004 Generated: 31 March 2004

COMP9414, Wednesday 24 March, 2004 Adversarial Search 12Alpha-Beta PruningCOMP9414, Wednesday 24 March, 2004 Adversarial Search 14Alpha-Beta Pruning Algorithm Minimax is depth-first At any point we only have to consider the nodes on a single path inthe search tree Suppose α is the value of the best choice for Max on the path and βthe value of the best choice for Min on the path Alpha-beta updates the values of α and β and prunes any subtree assoon as it can determine whether it is worse than the current α or βfunction MaxValue(state, game, α, β) returns minimax value of stateif CutoffTest(state) then return Eval(state)for each s in Successors(state) doα ← Max(α,MinValue(s, game, α,β))if α ≥ β then return βreturn αfunction MinValue(state, game, α, β) returns minimax value of stateif CutoffTest(state) then return Eval(state)for each s in Successors(state) doβ ← Min(β,MaxValue(s, game, α,β))if β ≤ α then return αreturn βCOMP9414 c○UNSW, 2004 Generated: 31 March 2004COMP9414 c○UNSW, 2004 Generated: 31 March 2004COMP9414, Wednesday 24 March, 2004 Adversarial Search 13Alpha-Beta Pruning ExampleCOMP9414, Wednesday 24 March, 2004 Adversarial Search 15Games of ChanceMax5Min 5

COMP9414, Wednesday 24 March, 2004 Adversarial Search 16Constraint Satisfaction ProblemsCOMP9414, Wednesday 24 March, 2004 Adversarial Search 18Conclusion Constraint Satisfaction Problems (CSPs) are problems in which statesare defined by the values taken by a set of variables and the goal testspecifies a set of constraints the values must satisfy Problems that can be expressed as CSPs: N-queens, VLSI layout,scheduling, cryptarithmetic Can use search to look for an assignment of values to variables suchthat the constraints are satisfied CSP has become a powerful and commonly used technique in AIwith its own algorithms for determining variable assignments (e.g.arc consistency, hill climbing, simulated annealing, etc.) Search is a common technique in problem solving especially whenour knowledge of the problem or domain is limited It is important to spend some time thinking about the problem inorder to decide how the problem states will be represented and whichsearch strategy to apply We have only investigated a small number of search techniques We have examined some uninformed (blind) and informed (heuristic)strategies plus some techniques for adversarial search and constraintsatisfaction problemsCOMP9414 c○UNSW, 2004 Generated: 31 March 2004COMP9414 c○UNSW, 2004 Generated: 31 March 2004COMP9414, Wednesday 24 March, 2004 Adversarial Search 17Constraint Satisfaction ProblemsS E N DM O R E+MO N E YCOMP9414 c○UNSW, 2004 Generated: 31 March 2004