CS 188: Artificial Intelligence

Transcription

1 C 188: Atiiil Intllign Toy Agnts tt Pln A Polms Instuto: Mo Alvz Univsity o Ro Isln (Ts slis w t/moii y Dn Klin, Pit Al, An Dgn o C188 t UC Bkly) Uninom Mtos Dt-Fist Bt-Fist Uniom-Cost Agnts tt Pln Rlx Agnts Rlx gnts: Coos tion s on unt t (n my mmoy) My v mmoy o mol o t wol s unt stt Do not onsi t utu onsuns o ti tions Consi ow t wol I Cn lx gnt tionl? [Dmo: lx otiml (L2D1)] [Dmo: lx otiml (L2D2)]

2 Vio o Dmo Rlx Otiml Vio o Dmo Rlx O Plnning Agnts Vio o Dmo Mstmin Plnning gnts: Ask wt i Disions s on (yotsiz) onsuns o tions Must v mol o ow t wol volvs in sons to tions Must omult gol (tst) Consi ow t wol WOULD BE Otiml vs. omlt lnning Plnning vs. lnning [Dmo: -lnning (L2D3)] [Dmo: mstmin (L2D4)]

3 Vio o Dmo Rlnning Polms Polms Polms A Mols A s olm onsists o: A stt s A susso untion (wit tions, osts) A stt stt n gol tst N, 1.0 E, 1.0 A solution is sun o tions ( ln) wi tnsoms t stt stt to gol stt

4 Exml: Tvling in Romni Wt s in tt? tt s: Citis usso untion: Ros: o to jnt ity wit ost = istn tt stt: A ol tst: Is stt == Bust? olution? T wol stt inlus vy lst til o t nvionmnt A s stt ks only t tils n o lnning (sttion) Polm: Pting tts: (x,y) lotion Ations: NEW usso: ut lotion only ol tst: is (x,y)=end Polm: Et-All-Dots tts: {(x,y), ot oolns} Ations: NEW usso: ut lotion n ossily ot ooln ol tst: ots ll ls tt izs? Quiz: Pssg Wol stt: Agnt ositions: 120 Foo ount: 30 ost ositions: 12 Agnt ing: NEW How mny Wol stts? 120x(2 30 )x(12 2 )x4 tts o ting? 120 tts o t-ll-ots? 120x(2 30 ) Polm: t ll ots wil king t gosts m-s Wt os t stt s v to siy? (gnt osition, ot oolns, ow llt oolns, mining s tim)

5 tt s n Ts tt s tt s g: A mtmtil snttion o s olm Nos (stt) wol onigutions As snt sussos (tion sults) T gol tst is st o gol nos (my only on) In stt s g, stt ous only on! W n ly uil tis ull g in mmoy (it s too ig), ut it s usul i tt s Ts tt s g: A mtmtil snttion o s olm Nos (stt) wol onigutions As snt sussos (tion sults) T gol tst is st o gol nos (my only on) N, 1.0 E, 1.0 Tis is now / stt Possil utus In s g, stt ous only on! W n ly uil tis ull g in mmoy (it s too ig), ut it s usul i Tiny s g o tiny s olm A s t: A wt i t o lns n ti outoms T stt stt is t oot no Ciln oson to sussos Nos sow stts, ut oson to PLAN tt iv tos stts Fo most olms, w n nv tully uil t wol t

6 tt s vs. Ts Quiz: tt s vs. Ts tt E NODE in in t s t is n nti PATH in t stt s g. W onstut ot on mn n w onstut s littl s ossil. T Consi tis 4-stt g: How ig is its s t (om )? Imotnt: Lots o t stutu in t s t! T Exml: Romni

7 ing wit T nl T : Exn out otntil lns (t nos) Mintin ing o til lns un onsition Ty to xn s w t nos s ossil Imotnt is: Fing Exnsion Exlotion sttgy Min ustion: wi ing nos to xlo? Exml: T Dt-Fist

8 Dt-Fist Algoitm Potis ttgy: xn st no ist Imlmnttion: Fing is LIFO stk Algoitm Potis Dt-Fist (DF) Potis Comlt: unt to in solution i on xists? Otiml: unt to in t lst ost t? Tim omlxity? omlxity? Ctoon o s t: is t ning to m is t mximum t solutions t vious ts m tis 1 no nos 2 nos Wt nos DF xn? om lt ix o t t. Coul oss t wol t! I m is init, tks tim O( m ) How mu s os t ing tk? Only s silings on t to oot, so O(m) Is it omlt? m oul ininit, so only i w vnt yls (mo lt) m tis 1 no nos 2 nos m nos Num o nos in nti t? m = O( m ) m nos Is it otiml? No, it ins t ltmost solution, glss o t o ost

9 Bt-Fist Bt-Fist ttgy: xn sllowst no ist Imlmnttion: Fing is FIFO uu Tis Bt-Fist (BF) Potis Quiz: DF vs BF Wt nos os BF xn? Posss ll nos ov sllowst solution Lt t o sllowst solution s tks tim O( s ) s tis 1 no nos 2 nos How mu s os t ing tk? Hs ougly t lst ti, so O( s ) s nos Is it omlt? s must init i solution xists, so ys! m nos Is it otiml? Only i osts ll 1 (mo on osts lt)

10 Quiz: DF vs BF Vio o Dmo Mz Wt DF/BF (t 1) Wn will BF outom DF? Wn will DF outom BF? [Dmo: s/s mz wt (L2D6)] Vio o Dmo Mz Wt DF/BF (t 2) Ittiv Dning I: gt DF s s vntg wit BF s tim / sllow-solution vntgs Run DF wit t limit 1. I no solution Run DF wit t limit 2. I no solution Run DF wit t limit 3... Isn t tt wstully unnt? nlly most wok ns in t lowst lvl s, so not so!

11 Cost-nsitiv Uniom Cost TART OAL 2 2 BF ins t sotst t in tms o num o tions. It os not in t lst-ost t. W will now ov simil lgoitm wi os in t lst-ost t. Uniom Cost Uniom Cost (UC) Potis ttgy: xn st no ist: Fing is ioity uu (ioity: umultiv ost) Wt nos os UC xn? Posss ll nos wit ost lss tn st solution! I tt solution osts C* n s ost t lst ε, tn t tiv t is ougly C*/ε Tks tim O( C*/ε ) (xonntil in tiv t) C*/ε tis Cost ontous How mu s os t ing tk? Hs ougly t lst ti, so O( C*/ε ) Is it omlt? Assuming st solution s init ost n minimum ost is ositiv, ys! Is it otiml? Ys! (Poo nxt ltu vi A*)

12 Uniom Cost Issus Vio o Dmo Emty UC Rmm: UC xlos insing ost ontous T goo: UC is omlt n otiml! T : Exlos otions in vy ition No inomtion out gol lotion W ll ix tt soon! tt ol [Dmo: mty gi UC (L2D5)] [Dmo: mz wit /sllow wt DF/BF/UC (L2D7)] Vio o Dmo Mz wit D/llow Wt --- DF, BF, o UC? (t 1) Vio o Dmo Mz wit D/llow Wt --- DF, BF, o UC? (t 2)

13 Vio o Dmo Mz wit D/llow Wt --- DF, BF, o UC? (t 3) T On Quu All ts s lgoitms t sm xt o ing sttgis Contully, ll ings ioity uus (i.. olltions o nos wit tt ioitis) Ptilly, o DF n BF, you n voi t log(n) ov om n tul ioity uu, y using stks n uus Cn vn o on imlmnttion tt tks vil uuing ojt n Mols on Wong? ots ov mols o t wol T gnt osn t tully ty ll t lns out in t l wol! Plnning is ll in simultion You s is only s goo s you mols