Announcements. CS 188: Artificial Intelligence. Costs on Actions. Recap: Search. Lecture 3: A* Search

Transcription

1 Announcmnts Pojcts: Looking fo ojct tns? --- Com to font ft lctu. Ty i ogmming, not divid-nd-conu Account foms vill u font duing k nd ft lctu Assignmnts Looking fo studnts to wok on ssignmnts with? --- Com to font ft lctu. Lctu vidos: link will ostd on cous wg onc I know wh thy ctions stt tomoow Hv fun solving xciss! olutions will ostd ft lst sction. If not ostd within fw hous ft lst sction, it mns th I fogot, so ing us on izz so thy mindd. C 88: Atificil Intllignc Lctu : A* ch Pit Al UC Bkly Mny slids fom Dn Klin ch on Wong? This Lctu Unifom cost (t) sch dy (t) sch A* (t) sch Huistic dsign Admissiility, Consistncy T sch à h sch Rc: ch ch olm: tts (configutions of th wold) uccsso function: function fom stts to lists of (stt, ction, cost) tils; dwn s gh tt stt nd gol tst ch t: Nods: snt lns fo ching stts Plns hv costs (sum of ction costs) ch Algoithm: ystmticlly uilds sch t Chooss n oding of th fing (unxlod nods) TART Costs on Actions d 8 OAL Notic tht BF finds th shotst th in tms of num of tnsitions. It dos not find th lst-cost th. W will uickly cov n lgoithm which dos find th lst-cost th. c 9 8 h 4 4 f

2 Unifom Cost (T) ch Pioity Quu Rfsh Exnd chst nod fist: Fing is ioity uu Cost contous d 4 c 6 9 h 7 f 8 c 0 c 8 d 9 h 7 0 c f h 8 f 6 A ioity uu is dt stuctu in which you cn inst nd tiv (ky, vlu) is with th following otions:.ush(ky, vlu).o() insts (ky, vlu) into th uu. tuns th ky with th lowst vlu, nd movs it fom th uu. You cn dcs ky s ioity y ushing it gin Unlik gul uu, instions n t constnt tim, usully O(log n) W ll nd ioity uus fo cost-snsitiv sch mthods Unifom Cost (T) ch Unifom Cost Issus Algoithm Comlt Otiml Tim (in nods) c DF BF UC w/ Pth Chcking Y N O( m ) O(m) Y N O( s+ ) O( s+ ) Y* Y O( C*/ε ) O( C*/ε ) Rmm: xlos incsing cost contous Th good: UC is comlt nd otiml! c c c C*/ε tis * UC cn fil if ctions cn gt itily ch Th d: Exlos otions in vy diction No infomtion out gol loction tt ol Unifom Cost ch Exml ch Huistics Any stimt of how clos stt is to gol Dsignd fo ticul sch olm Exmls: Mnhttn distnc, Euclidn distnc 0.

3 Huistics Bst Fist / dy ch Exnd th nod tht sms closst Wht cn go wong? Bst Fist / dy ch dy A common cs: Bst-fist tks you stight to th (wong) gol Wost-cs: lik dlyguidd DF in th wost cs Cn xlo vything Cn gt stuck in loos if no cycl chcking Lik DF in comltnss (finit stts w/ cycl chcking) Unifom Cost Comining UC nd dy Unifom-cost ods y th cost, o ckwd cost g(n) Bst-fist ods y gol oximity, o fowd cost h(n) d h=6 h= h= c h=7 h=6 A* ch ods y th sum: f(n) = g(n) + h(n) h= h=0 Whn should A* tmint? hould w sto whn w nuu gol? A h = h = B h = No: only sto whn w duu gol h = 0 Exml: Tg ng

4 Is A* Otiml? Admissil Huistics A h = 6 A huistic h is dmissil (otimistic) if: h = 7 h = 0 wh is th tu cost to nst gol Wht wnt wong? Actul d gol cost < stimtd good gol cost W nd stimts to lss thn ctul costs! Exmls: 66 Coming u with dmissil huistics is most of wht s involvd in using A* in ctic. Otimlity of A*: Blocking Potis of A* Poof: Wht could go wong? W d hv to hv to o suotiml gol off th fing fo * This cn t hn: Imgin suotiml gol is on th uu om nod n which is suth of * must lso on th fing (why?) n will od fo Unifom-Cost A* UC vs A* Contous Exml: Exlod tts with A* Unifom-cost xndd in ll dictions tt ol A* xnds minly towd th gol, ut dos hdg its ts to nsu otimlity tt ol Huistic: mnhttn distnc ignoing wlls 4

5 Comison Cting Admissil Huistics dy Most of th wok in solving hd sch olms otimlly is in coming u with dmissil huistics Oftn, dmissil huistics solutions to lxd olms, with nw ctions ( som chting ) vill Unifom Cost 66 A st Indmissil huistics oftn usful too (why?) Exml: 8 Puzzl 8 Puzzl I Huistic: Num of tils mislcd Why is it dmissil? Wht th stts? How mny stts? Wht th ctions? Wht stts cn I ch fom th stt stt? Wht should th costs? h(stt) = 8 This is lxdolm huistic Avg nods xndd whn otiml th hs lngth 4 sts 8 sts sts UC 6,00.6 x 0 6 TILE 9 7 Wht if w hd n si 8-uzzl wh ny til could slid ny diction t ny tim, ignoing oth tils? Totl Mnhttn distnc Why dmissil? h(stt) = = 8 8 Puzzl II Avg nods xndd whn otiml th hs lngth 4 sts 8 sts sts TILE 9 7 MANHATTAN 7 8 Puzzl III How out using th ctul cost s huistic? Would it dmissil? Would w sv on nods xndd? Wht s wong with it? With A*: td-off twn ulity of stimt nd wok nod!

6 Tivil Huistics, Dominnc Dominnc: h h c if Huistics fom smi-lttic: Mx of dmissil huistics is dmissil Tivil huistics Bottom of lttic is th zo huistic (wht dos this giv us?) To of lttic is th xct huistic Oth A* Alictions Pthing / outing olms Rsouc lnning olms Root motion lnning Lngug nlysis Mchin tnsltion ch cognition T ch: Ext Wok! Filu to dtct td stts cn cus xonntilly mo wok. Why? h ch In BF, fo xml, w shouldn t oth xnding th cicld nods (why?) d c h h f f c c h ch Id: nv xnd stt twic How to imlmnt: T sch + list of xndd stts (closd list) Exnd th sch t nod-y-nod, ut Bfo xnding nod, chck to mk su its stt is nw Python tick: sto th closd list s st, not list h ch Vy siml fix: nv xnd stt twic Cn gh sch wck comltnss? Why/why not? How out otimlity? Cn this wck comltnss? Otimlity? 6

7 Otimlity of A* h ch Poof: Nw ossil olm: nods on th to * tht would hv n in uu n t, cus som wos n fo th sm stt s som n ws duud nd xndd fist (disst!) Tk th highst such n in t Lt th ncsto which ws on th uu whn n ws xndd Assum f() < f(n) f(n) < f(n ) cus n is suotiml would hv n xndd fo n o n would hv n xndd fo n, too Contdiction! Consistncy Wit, how do w know nts hv tt f-vls thn thi succssos? Couldn t w o som nod n, nd find its child n to hv low f vlu? YE: h = 0 h = 8 B g = 0 Wht cn w ui to vnt ths invsions? Consistncy: A h = 0 Rl cost must lwys xcd duction in huistic Otimlity T sch: A* otiml if huistic is dmissil (nd nonngtiv) UC is scil cs (h = 0) h sch: A* otiml if huistic is consistnt UC otiml (h = 0 is consistnt) Consistncy imlis dmissiility ummy: A* A* uss oth ckwd costs nd (stimts of) fowd costs A* is otiml with dmissil huistics Huistic dsign is ky: oftn us lxd olms In gnl, ntul dmissil huistics tnd to consistnt 7