CSEP 573 Artificial Intelligence Winter 2016

Transcription

1 CSEP 573 Artificil Intelligence Winter 2016 Luke Zettlemoyer Problem Spces nd Serch slides from Dn Klein, Sturt Russell, Andrew Moore, Dn Weld, Pieter Abbeel, Ali Frhdi

2 Outline Agents tht Pln Ahed Serch Problems Uninformed Serch Methods (prt review for some) Depth-First Serch Bredth-First Serch Uniform-Cost Serch Heuristic Serch Methods (new for ll) Best First / Greedy Serch

3 Review: Agents An gent: Perceives nd cts Selects c2ons tht mximize its u2lity func2on Hs gol Environment: Input nd output to the gent Agent Sensors? Actutors Percepts Actions Environment Serch -- the environment is: fully observble, single gent, deterministic, sttic, discrete

4 Reflex gents: Choose ction bsed on current percept (nd mybe memory) Do not consider the future consequences of their ctions Act on how the world IS Cn reflex gent chieve gols? Reflex Agents

5 Gol Bsed Agents Gol-bsed gents: Pln hed Ask wht if Decisions bsed on (hypothesized) consequences of ctions Must hve model of how the world evolves in response to ctions Act on how the world WOULD BE

6 Serch thru Input: Set of sttes Successor Function [nd costs - defult to 1.0] Strt stte Gol stte [test] Output: Problem Spce / Stte Spce Pth: strt stte stisfying gol test [My require shortest pth] [Sometimes just need stte pssing test]

7 Exmple: Simplified Pc-Mn Input: A stte spce A successor function N, 1.0 A strt stte E, 1.0 A gol test Output:

8 Ex: Route Plnning: Romni à Buchrest Input: Set of sttes Opertors [nd costs] Strt stte Gol stte (test) Output:

9 Exmple: N Queens Input: Set of sttes Q Q Q Opertors [nd costs] Q Strt stte Gol stte (test) Output

10 Algebric Simplifiction Input: Set of sttes Opertors [nd costs] Strt stte Gol stte (test) Output:

11 Wht is in Stte Spce? A world stte includes every detil of the environment orld#stte#includes#every#lst#detil#of#the#enviro A serch stte includes only detils needed for plnning Problem: Pthing Sttes: {x,y} loctions Actions: NSEW moves Successor: updte loction Gol: is (x,y) End? Problem: Et-ll-dots Sttes: {(x,y), dot boolens} Actions: NSEW moves Successor: updte loction nd dot boolen Gol: dots ll flse?

12 Stte Spce Sizes? World sttes: Pcmn positions: 10 x 12 = 120 Pcmn fcing: up, down, left, right Food Count: 30 Ghost positions: 12

13 Stte Spce Sizes? How mny? World Stte: 120*(2 30 )*(12 2 )*4 Sttes for Pthing: 120 Sttes for et-ll-dots: 120*(2 30 )

14 Quiz:#Sfe#Pssge#! Problem:#et#ll#dots#while#keeping#the#ghosts#permJscred#! Wht#does#the#stte#spce#hve#to#specify?#! (gent#posi)on,#dot#boolens,#power#pellet#boolens,#remining#scred#)me)#

15 Stte Spce Grphs Stte spce grph: Ech node is stte The successor function is represented by rcs Edges my be lbeled with costs We cn rrely build this grph in memory (so we don t)

16 Serch Trees N, 1.0 E, 1.0 A serch tree: Strt stte t the root node Children correspond to successors Nodes contin sttes, correspond to PLANS to those sttes Edges re lbeled with ctions nd costs For most problems, we cn never ctully build the whole tree

17 Exmple: Tree Serch Stte Grph: b c G S d h e f Wht is the serch tree? p q r Ridiculously tiny serch grph for tiny serch problem

18 Stte Grphs vs. Serch Trees S b d c h e f G Ech NODE in in the serch tree is n entire PATH in the problem grph. p q r S d e p We construct both on demnd nd we construct s little s possible. b c p h e q r f h r p q f q c G q q c G

19 Sttes vs. Nodes Nodes in stte spce grphs re problem sttes Represent n bstrcted stte of the world Hve successors, cn be gol / non-gol, hve multiple predecessors Nodes in serch trees re plns Represent pln (sequence of ctions) which results in the node s stte Hve problem stte nd one prent, pth length, depth & cost The sme problem stte my be chieved by multiple serch tree nodes Problem Sttes Serch Nodes Action Prent Depth 5 Node Depth 6

20 Quiz:#Stte#Grphs#vs.#Serch#Trees# Consider#this#4Jstte#grph:## How#big#is#its#serch#tree#(from#S)?# S G b Importnt:#Lots#of#repeted#structure#in#the#serch#tree!#

21 Building Serch Trees Serch: Expnd out possible plns Mintin fringe of unexpnded plns Try to expnd s few tree nodes s possible

22 Generl Tree Serch Importnt ides: Fringe Expnsion Explortion strtegy Detiled pseudocode is in the book! Min question: which fringe nodes to explore?

23 Serch Methods Uninformed Serch Methods (prt review for some) Depth-First Serch Bredth-First Serch Uniform-Cost Serch Heuristic Serch Methods (new for ll) Best First / Greedy Serch

24 Review: Depth First Serch Strtegy: expnd deepest node first b c G Implementtion: Fringe is LIFO queue ( stck) S d h e f p q r

25 Review: Depth First Serch S b d p c e p h f r q q c G q e p h f r q q c G S G d b p q c e h f r q p h f d b c e r Expnsion ordering: (d,b,,c,,e,h,p,q,q,r,f,c,,g)

26 Review: Bredth First Serch Strtegy: expnd shllowest node first Implementtion: Fringe is FIFO queue S b p d q c h e r f G

27 Review: Bredth First Serch S b d p c e p h f r q q c G q e p h f r q q c G S G d b p q c e h f r Serch Tiers Expnsion order: (S,d,e,p,b,c,e,h,r,q,,,h,r,p,q,f,p,q,f,q,c,G)

28 Serch Algorithm Properties Complete? Gurnteed to find solution if one exists? Optiml? Gurnteed to find the lest cost pth? Time complexity? Spce complexity? Vribles: n b Number of sttes in the problem The mximum brnching fctor B (the mximum number of successors for stte) C* Cost of lest cost solution d m Depth of the shllowest solution Mx depth of the serch tree

29 DFS Algorithm Complete Optiml Time Spce DFS Depth First Serch N No N No O(B Infinite LMAX ) O(LMAX) Infinite START Infinite pths mke DFS incomplete How cn we fix this? Check new nodes ginst pth from S Infinite serch spces still problem If the left subtree hs unbounded depth b GOAL

30 DFS m tiers b 1 node b nodes b 2 nodes b m nodes Algorithm Complete Optiml Time Spce DFS w/ Pth Checking Y if finite N O(b m ) O(bm) * Or grph serch next lecture.

31 BFS Algorithm Complete Optiml Time Spce DFS BFS w/ Pth Checking Y N O(b m ) O(bm) Y Y* O(b d ) O(b d ) d tiers b 1 node b nodes b 2 nodes b d nodes b m nodes

32 Comprisons When will BFS outperform DFS? When will DFS outperform BFS?

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35 Itertive Deepening Itertive deepening uses DFS s subroutine: 1. Do DFS which only serches for pths of length 1 or less. 2. If 1 filed, do DFS which only serches pths of length 2 or less. 3. If 2 filed, do DFS which only serches pths of length 3 or less..nd so on. b Algorithm Complete Optiml Time Spce DFS BFS ID w/ Pth Checking Y N O(b m ) O(bm) Y Y* O(b d ) O(b d ) Y Y* O(b d ) O(bd)

36 Costs on Actions 2 2 GOAL b 3 1 d c e f 2 START 1 p 4 15 q 4 h r 1 Notice tht BFS finds the shortest pth in terms of number of trnsitions. It does not find the lest-cost pth.

37 Best-First Serch Generliztion of bredth-first serch Priority queue of nodes to be explored Cost function f(n) pplied to ech node Add initil stte to priority queue While queue not empty Node = hed(queue) If gol?(node) then return node Add children of node to queue

38 Priority Queue Refresher A priority queue is dt structure in which you cn insert nd retrieve (key, vlue) pirs with the following opertions: pq.push(key, vlue) pq.pop() inserts (key, vlue) into the queue. returns the key with the lowest vlue, nd removes it from the queue. You cn decrese key s priority by pushing it gin Unlike regulr queue, insertions ren t constnt time, usully O(log n) We ll need priority queues for cost-sensitive serch methods

39 Uniform Cost Serch Expnd chepest node first: Fringe is priority queue b d 2 c e GOAL 2 f START 1 p 4 15 q 4 h r 1

40 Uniform Cost Serch Expnsion order: (S,p,d,b,e,,r,f,e,G) 2 b 1 3 S 1 p d q 2 c h e 8 1 r G 2 f 1 S 0 d 3 e 9 p 1 Cost contours b 4 6 c 11 p h e 13 q 5 r f 7 8 h p 17 r 11 q f q c G q 16 q 11 c G 10

41 Uniform Cost Serch Algorithm Complete Optiml Time Spce DFS BFS UCS w/ Pth Checking Y N O(b m ) O(bm) Y Y* O(b d ) O(b d ) Y* Y O(b C*/ε ) O(b C*/ε ) b C*/ε tiers

42 Uniform Cost Issues Remember: explores incresing cost contours The good: UCS is complete nd optiml! c 1 c 2 c 3 The bd: Explores options in every direction No informtion bout gol loction Strt Gol

43 Uniform Cost: Pc-Mn Cost of 1 for ech ction Explores ll of the sttes, but one

44 Serch Heuristics Any estimte of how close stte is to gol Designed for prticulr serch problem Exmples: Mnhttn distnce, Eucliden distnce

45 Heuristics

46 Best First / Greedy Serch Best first with f(n) = heuristic estimte of distnce to gol

47 Best First / Greedy Serch Expnd the node tht seems closest Wht cn go wrong?

48 Best First / Greedy Serch A common cse: Best-first tkes you stright to the (wrong) gol Worst-cse: like bdlyguided DFS in the worst cse Cn explore everything Cn get stuck in loops if no cycle checking Like DFS in completeness (finite sttes w/ cycle checking) b b