1/19/2010. Usually for static, deterministic environment

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1 To download the discussion slides, go to eterministic, tochastic and trategic nvironment eterministic ompletely predictable ource of Non-determinism tochasticity trategic actions of other agents strategic environment is not necessarily otherwise deterministic xample: poker is both stochastic and strategic rror occurred during initialization of VM ould not reserve enough space for object heap ould not create the Java virtual machine. olution: Limit the size of maximum memory for VM (Max memory of 512M) tep 1: setenv NT_OPT "-Xmx512m" on command line tep 2: add memorymaximumize="512m" to javac block in build-java section of your build.xml file tep 3: run java with Xmx512m parameter 1. ormulate the problem 2. ind a sequence of actions (offline) that achieves the goal Offline vs. Online search 3. xecute the sequence of action Usually for static, deterministic environment tates tate: Internal representation of an agent about the world; what the agent cares about Not necessarily be correct Initial state ctions iven a state, what the available actions are Transition model Result(s,a) that returns state resulting from doing action a in state s oal states Path cost Vacuum world tates: gent location + dirt location? 8 states Initial tate: ny ctions: Left, Right and uck Transition model: xpected effects. xcept for no effects on Left in leftmost square, Right in rightmost square and uck in a clean square oal state: ll squares are clean Path cost: 1 (?) 1

2 7-queen tates: Initial tate: ctions: Transition model: oal tate Path cost: 7-queen tates: ll possible arrangements of n queens, one per column in the leftmost n columns, with no queen attacking another Initial tate: No queens on the board ctions: dd a queen to any square in the leftmost empty column such that it is not attacked by any other queen Transition model: or any addition, return the board with a queen added to the specified square oal tate: 8 queens on the board, none attacked Path cost:1 tate: agent s representation of the world configuration tate space: all reachable states from initial state earch space: a data structure that abstracts the state space Nodes: a data structure that represent states and related information (state, parent node, path cost ) dges represent actions and path costs(reflects transition model ) olution is the path from initial to goal state Optimal solution is the solution of the shortest path cost Uninformed search Only uses information in problem formulation Informed search Has heuristics that guides an agent on where to look for solutions earch trategy Order of node expansion xpansion: iven a node, creates all children of the node according to transition model function Tree-search(problem) returns a solution, or failure fringe = new Queue(); fringe.put(problem.initialtate) loop do if fringe.ismpty() then return failure node = fringe.get() if problem.isoaltate(node) then return node; fringe.putll(problem.expand(node)) Only the order of the queue makes the difference void repeated states (raph search) function Tree-search(problem) returns a solution, or failure closed = new et(); closed.add(problem.initialtate); fringe = new Queue(); fringe.put(problem.initialtate) loop do if fringe.ismpty() then return failure node = fringe.get() if problem.isoaltate(node) then return node; for each child in problem.expand(node) if!closed.contain(child) fringe.put(child) void repeated states 2

3 readth-irst: IO queue, returning the oldest item Uniform-ost: Priority queue, returning the least-cost item epth-irst: LIO, returning the newest item epth-limited : Run, cut off search at depth L Iterative eepening : Run epth-limited with L from 1 to infinity = start, = goal Queue = {} elect oal() = true? Queue = {, } elect oal() = true? If not, xpand() If not, xpand() Queue = {,, } elect oal() = true? Queue = {,,, } elect etc. If not, expand() 3

4 4 Level 3 Queue = {,,,,,,, } Level 4 xpand queue until is at front elect oal() = true Queue = {,} Queue = {,,} Queue = {,,,} Queue = {,,,}

5 Queue = {,,} 5

6 ompleteness: uaranteed to find a solution if it exists Optimality: The minimum path cost solution is found Time omplexity: How long it takes to find a solution pace omplexity: How much memory is needed Notes: 1. and iterative deepening only optimal when action cost is uniform; 2. U only optimal when action cost is nonnegative; Informed (heuristic) search Use heuristic function as a guidance on which node to expand Heuristic function for * f(n) = g(n) + h(n) where g(n) is the path cost (cost so far to reach n) and h(n) is the heuristic (estimated cost from n go goal) f(n) is an estimated total cost To expand the nodes with smallest f(n) dmissible: Heuristic functions should never overestimate the path cost 6