CS 188: Artificial Intelligence Fall 2008

Transcription

1 CS 188: Artificil Intelligence Fll 2008 Lecture 2: Queue-Bsed Serc 9/2/2008 Dn Klein UC Berkeley Mny slides from eiter Sturt Russell or Andrew Moore

2 Announcements Written ssignments: One mini-omework ec week (1-2 rolems) We ll dro your two lowest scores First one osted soon! L Wednesdy 11m to 4m in Sod 275 Lern Pyton Come wtever times you like Project 1.1 osted soon, too, due 9/12

3 Agents tt Pln Aed Serc Prolems Tody Uniformed Serc Metods Det-First Serc Bredt-First Serc Uniform-Cost Serc Heuristic Serc Metods Greedy Serc A* Serc

4 Reflex gents: Coose ction sed on current ercet nd memory My ve memory or model of te world s current stte Do not consider te future conseuences of teir ctions Cn reflex gent e rtionl? Reflex Agents [demo: reflex otiml / loo ]

5 Gol Bsed Agents Gol-sed gents: Pln ed Decisions sed on (yotesized) conseuences of ctions Must ve model of ow te world evolves in resonse to ctions [demo: ln fst / slow ]

6 Serc Prolems A serc rolem consists of: A stte sce A successor function N, 1.0 A strt stte nd gol test E, 1.0 A solution is seuence of ctions ( ln) wic trnsforms te strt stte to gol stte

7 Serc Trees N, 1.0 E, 1.0 A serc tree: Tis is wt if tree of lns nd outcomes Strt stte t te root node Cildren corresond to successors Nodes leled wit sttes, corresond to PLANS to tose sttes For most rolems, cn never ctully uild te wole tree So, ve to find wys of using only te imortnt rts of te tree!

8 Stte Sce Grs Tere s some ig gr in wic Ec stte is node Ec successor is n outgoing rc Imortnt: For most rolems we could never ctully uild tis gr S d c e r f G How mny sttes in Pcmn? Lugly tiny serc gr for tiny serc rolem

9 Exmle: Romni

10 Anoter Serc Tree Serc: Exnd out ossile lns Mintin fringe of unexnded lns Try to exnd s few tree nodes s ossile

11 Generl Tree Serc Imortnt ides: Fringe Exnsion Exlortion strtegy Detiled seudocode is in te ook! Min uestion: wic fringe nodes to exlore?

12 Exmle: Tree Serc c G S d e f r

13 Stte Grs vs Serc Trees S d c e f G Ec NODE in in te serc tree is n entire PATH in te rolem gr. r S d e We lmost lwys construct ot on demnd nd we construct s little s ossile. c e r f r f c G c G

14 Review: Det First Serc S d c e f r c G e f r c G S G d c e f r f d c e r Strtegy: exnd deeest node first Imlementtion: Fringe is LIFO stck

15 Review: Bredt First Serc Strtegy: exnd sllowest node first Imlementtion: Fringe is FIFO ueue S d c e r f G S Serc Tiers d c e r e r f f c G c G

16 Serc Algoritm Proerties Comlete? Gurnteed to find solution if one exists? Otiml? Gurnteed to find te lest cost t? Time comlexity? Sce comlexity? Vriles: n Numer of sttes in te rolem Te verge rncing fctor B (te verge numer of successors) C* Cost of lest cost solution s Det of te sllowest solution m Mx det of te serc tree

17 DFS Algoritm Comlete Otiml Time Sce DFS Det First Serc N N N N O(B Infinite LMAX ) O(LMAX) Infinite START GOAL Infinite ts mke DFS incomlete How cn we fix tis?

18 DFS Wit cycle cecking, DFS is comlete. m tiers 1 node nodes 2 nodes m nodes Algoritm Comlete Otiml Time Sce DFS w/ Pt Cecking Y N O( m+1 ) O(m) Wen is DFS otiml?

19 BFS Algoritm Comlete Otiml Time Sce DFS BFS w/ Pt Cecking Y N O( m+1 ) O(m) Y N* O( s+1 ) O( s ) s tiers 1 node nodes 2 nodes s nodes m nodes Wen is BFS otiml?

20 Comrisons Wen will BFS outerform DFS? Wen will DFS outerform BFS?

21 Itertive Deeening Itertive deeening uses DFS s suroutine: 1. Do DFS wic only serces for ts of lengt 1 or less. (DFS gives u on ny t of lengt 2) 2. If 1 filed, do DFS wic only serces ts of lengt 2 or less. 3. If 2 filed, do DFS wic only serces ts of lengt 3 or less..nd so on. Algoritm Comlete Otiml Time Sce DFS BFS ID w/ Pt Cecking Y N O( m+1 ) O(m) Y N* O( s+1 ) O( s ) Y N* O( s+1 ) O(s)

22 Costs on Actions d 2 c e GOAL 2 f START r 1 Notice tt BFS finds te sortest t in terms of numer of trnsitions. It does not find te lest-cost t. We will uickly cover n lgoritm wic does find te lest-cost t.

23 Uniform Cost Serc Exnd ceest node first: Fringe is riority ueue d 9 S 1 15 S 0 2 c e 8 1 f r G 2 1 d 3 e 9 1 Cost contours 4 6 c 11 e 13 5 r f r 11 f c G c G 10

24 Priority Queue Refreser A riority ueue is dt structure in wic you cn insert nd retrieve (key, vlue) irs wit te following oertions:.us(key, vlue).o() inserts (key, vlue) into te ueue. returns te key wit te lowest vlue, nd removes it from te ueue. You cn romote or demote keys y resetting teir riorities Unlike regulr ueue, insertions into riority ueue re not constnt time, usully O(log n) We ll need riority ueues for most cost-sensitive serc metods.

25 Uniform Cost Serc Algoritm Comlete Otiml Time Sce DFS BFS UCS w/ Pt Cecking Y N O( m+1 ) O(m) Y N O( s+1 ) O( s ) Y* Y O(C* C*/ε ) O( C*/ε ) C*/ε tiers We ll tlk more out uniform cost serc s filure cses lter

26 Uniform Cost Prolems Rememer: exlores incresing cost contours Te good: UCS is comlete nd otiml! c 1 c 2 c 3 Te d: Exlores otions in every direction No informtion out gol loction Strt Gol [demo: ucs contours ]

27 Heuristics

28 Best First / Greedy Serc Exnd te node tt seems closest Wt cn go wrong?

29 Best First / Greedy Serc START 2 = =12 =8 1 d =8 =11 2 c 2 8 =5 =4 2 e = =9 GOAL =0 5 f =4 5 r =6

30 Best First / Greedy Serc A common cse: Best-first tkes you strigt to te (wrong) gol Worst-cse: like dlyguided DFS in te worst cse Cn exlore everyting Cn get stuck in loos if no cycle cecking Like DFS in comleteness (finite sttes w/ cycle cecking)

31 Serc Gone Wrong?

32 Extr Work? Filure to detect reeted sttes cn cuse exonentilly more work. Wy?

33 Gr Serc In BFS, for exmle, we souldn t oter exnding te circled nodes (wy?) S d e c e r r f f c G c G

34 Gr Serc Very simle fix: never exnd stte tye twice Cn tis wreck comleteness? Wy or wy not? How out otimlity? Wy or wy not?

35 Some Hints Gr serc is lmost lwys etter tn tree serc (wen not?) Te collection of lredy-exnded stte is sometimes clled closed lists ut tey re relly closed sets. Don t imlement tem wit lists (use sets)! Nodes re concetully ts, ut etter to reresent wit stte, cost, nd reference to rent node (usully wit n oject undling tese tree tings)