Reminder. CS 188: Artificial Intelligence. A reflex agent for pacman. Reflex Agent. A reflex agent for pacman (3) A reflex agent for pacman (2)

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1 C 88: Atiiil Intllign Ltus n : Rmin Only vy smll tion o AI is out mking omuts ly gms intlligntly Rll: omut vision, ntul lngug, ootis, min lning, omuttionl iology, t. Pit Al UC Bkly Mny slis om Dn Klin Tt ing si: gms tn to ovi ltivly siml xml sttings wi gt to illustt onts n ln out lgoitms wi unli mny s o AI Rlx Agnt A lx gnt o mn 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 At on ow t wol I Cn lx gnt tionl? 4 tions: mov Not, Est, out o Wst Rlx gnt Wil(oo lt) ot t ossil itions to mov oing to t mount o oo in ition o in t ition wit t lgst mount o oo A lx gnt o mn () A lx gnt o mn () Rlx gnt Wil(oo lt) ot t ossil itions to mov oing to t mount o oo in ition o in t ition wit t lgst mount o oo Rlx gnt Wil(oo lt) ot t ossil itions to mov oing to t mount o oo in ition o in t ition wit t lgst mount o oo But, i ot otions vill, xlu t ition w just m om

2 A lx gnt o mn (4) A lx gnt o mn (5) Rlx gnt Wil(oo lt) I n k going in t unt ition, o so Otwis: ot itions oing to t mount o oo o in t ition wit t lgst mount o oo But, i ot otions vill, xlu t ition w just m om Rlx gnt Wil(oo lt) I n k going in t unt ition, o so Otwis: ot itions oing to t mount o oo o in t ition wit t lgst mount o oo But, i ot otions vill, xlu t ition w just m om Rlx Agnt 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 At on ow t wol I Cn lx gnt tionl? ol-s Agnts Pln Ask wt i Disions s on (yotsiz) onsuns o tions Must v mol o ow t wol volvs in sons to tions At on ow t wol WOULD BE Polms A s olm onsists o: A stt s A susso untion A stt stt n gol tst N,.0 E,.0 A solution is sun o tions ( ln) wi tnsoms t stt stt to gol stt Exml: Romni Wt s in tt? tt s: Citis usso untion: o to j ity wit ost = ist tt stt: A ol tst: Is stt == Bust? olution? T wol stt siis vy lst til o t nvionmnt A s stt ks only t tils n (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

3 tt s tt izs? tt s g: A mtmtil snttion o s olm Fo vy s olm, t s osoning stt s g T susso untion is snt y s W n ly uil tis g in mmoy (so w on t) Riiulously tiny stt s g o tiny s olm Polm: Et ll o t oo Pmn ositions: 0 x = 0 Foo ount: 0 ost ositions: Pmn ing: u, own, lt, igt Ts Anot T N,.0 E,.0 A s t: Tis is wt i t o lns n outoms tt stt t t oot no Ciln oson to sussos Nos ontin stts, oson to PLAN to tos stts Fo most olms, w n nv tully uil t wol t : Exn out ossil lns Mintin ing o unxn lns Ty to xn s w t nos s ossil nl T Exml: T Imotnt is: Fing Exnsion Exlotion sttgy Dtil suoo is in t ook! Min ustion: wi ing nos to xlo?

4 tt s vs. Ts Rviw: Dt Fist (T) W onstut ot on mn n w onstut s littl s ossil. E NODE in in t s t is n nti PATH in t olm g. ttgy: xn st no ist Imlmnttion: Fing is LIFO stk Rviw: Bt Fist (T) Algoitm Potis ttgy: xn sllowst no ist Imlmnttion: Fing is FIFO uu Tis Comlt? unt to in solution i on xists? Otiml? unt to in t lst ost t? Tim omlxity? omlxity? Vils: n Num o stts in t olm T vg ning to B (t vg num o sussos) C* Cost o lst ost solution s m Dt o t sllowst solution Mx t o t s t DF DF Algoitm Comlt Otiml Tim DF Dt Fist N N N N O(B Ininit LMAX ) O(LMAX) Ininit Wit yl king, DF is omlt.* m tis no nos nos TART OAL m nos Ininit ts mk DF inomlt How n w ix tis? Algoitm Comlt Otiml Tim DF w/ Pt Cking Y N O( m ) O(m) Wn is DF otiml? * O g s nxt ltu. 4

5 BF Algoitm Comlt Otiml Tim DF BF w/ Pt Cking Y N O( m ) O(m) Y N* O( s+ ) O( s+ ) Comisons Wn will BF outom DF? s tis no nos nos Wn will DF outom BF? s nos m nos Wn is BF otiml? Ittiv Dning Ittiv ning uss DF s suoutin:. Do DF wi only ss o ts o lngt o lss.. I il, o DF wi only ss ts o lngt o lss.. I il, o DF wi only ss ts o lngt o lss..n so on. Algoitm Comlt Otiml Tim DF BF ID w/ Pt Cking Y N O( m ) O(m) Y N* O( s+ ) O( s+ ) Y N* O( s+ ) O(s) TART Costs on Ations 5 8 OAL Noti tt BF ins t sotst t in tms o num o tnsitions. It os not in t lst-ost t. W will uikly ov n lgoitm wi os in t lst-ost t Uniom Cost (T) Pioity Quu Rs Exn st no ist: Fing is ioity uu Cost ontous A ioity uu is t stutu in wi you n inst n tiv (ky, vlu) is wit t ollowing otions:.us(ky, vlu).o() insts (ky, vlu) into t uu. tuns t ky wit t lowst vlu, n movs it om t uu. You n s ky s ioity y using it gin Unlik gul uu, instions n t onstnt tim, usully O(log n) W ll n ioity uus o ost-snsitiv s mtos 5

6 Uniom Cost (T) Uniom Cost Issus Algoitm Comlt Otiml Tim (in nos) DF BF UC w/ Pt Cking Y N O( m ) O(m) Y N O( s+ ) O( s+ ) Y* Y O( C*/ε ) O( C*/ε ) Rmm: xlos insing ost ontous T goo: UC is omlt n otiml! C*/ε tis * UC n il i tions n gt itily T : Exlos otions in vy ition No inomtion out gol lotion tt ol Uniom Cost Exml Huistis Any stimt o ow los stt is to gol Dsign o tiul s olm Exmls: Mnttn istn, Eulin istn 0 5. Exml: Huisti Funtion Bst Fist / y Exn t no tt sms losst (x) Wt n go wong? 6

7 Bst Fist / y y A ommon s: Bst-ist tks you stigt to t (wong) gol Wost-s: lik lygui DF in t wost s Cn xlo vyting Cn gt stuk in loos i no yl king Lik DF in omltnss (init stts w/ yl king) Uniom Cost Comining UC n y Uniom-ost os y t ost, o kw ost g(n) Bst-ist os y gol oximity, o ow ost (n) =6 =5 = =7 =6 A* os y t sum: (n) = g(n) + (n) 5 = =0 Wn soul A* tmint? oul w sto wn w nuu gol? A = = B = No: only sto wn w uu gol = 0 Exml: Tg ng Is A* Otiml? Amissil Huistis A = 6 A uisti is missil (otimisti) i: = 7 = 0 w is t tu ost to nst gol 5 Wt wnt wong? Atul gol ost < stimt goo gol ost W n stimts to lss tn tul osts! Exmls: 66 Coming u wit missil uistis is most o wt s involv in using A* in ti. 5 7

8 Otimlity o A*: Bloking Potis o A* Poo: Wt oul go wong? W v to v to o suotiml gol o t ing o * Tis n t n: Imgin suotiml gol is on t uu om no n wi is sut o * must lso on t ing (wy?) n will o o Uniom-Cost A* UC vs A* Contous Exml: Exlo tts wit A* Uniom-ost xn in ll itions tt ol A* xns minly tow t gol, ut os g its ts to nsu otimlity tt ol Huisti: mnttn istn ignoing wlls Comison y Uniom Cost A st Cting Amissil Huistis Most o t wok in solving s olms otimlly is in oming u wit missil uistis Otn, missil uistis solutions to lx olms, wit nw tions ( som ting ) vill 66 Inmissil uistis otn usul too (wy?) 5 8

9 Exml: 8 Puzzl 8 Puzzl I Huisti: Num o tils misl Wy is it missil? Wt t stts? How mny stts? Wt t tions? Wt stts n I om t stt stt? Wt soul t osts? (stt) = 8 Tis is lxolm uisti Avg nos xn wn otiml t s lngt 4 sts 8 sts sts UC 6,00.6 x 0 6 TILE 9 7 Wt i w n si 8-uzzl w ny til oul sli ny ition t ny tim, ignoing ot tils? Totl Mnttn istn Wy missil? (stt) = = 8 8 Puzzl II Avg nos xn wn otiml t s lngt 4 sts 8 sts sts TILE 9 7 MANHATTAN Puzzl III How out using t tul ost s uisti? Woul it missil? Woul w sv on nos xn? Wt s wong wit it? Wit A*: t-o twn ulity o stimt n wok no! Tivil Huistis, Dominn Dominn: i Huistis om smi-ltti: Mx o missil uistis is missil Tivil uistis Bottom o ltti is t zo uisti (wt os tis giv us?) To o ltti is t xt uisti Ot A* Alitions Pting / outing olms Rsou lnning olms Root motion lnning Lngug nlysis Min tnsltion ognition 9

10 T : Ext Wok! Filu to tt t stts n us xonntilly mo wok. Wy? In BF, o xml, w souln t ot xning t il nos (wy?) I: nv xn stt twi How to imlmnt: T s + list o xn stts (los list) Exn t s t no-y-no, ut Bo xning no, k to mk su its stt is nw Pyton tik: sto t los list s st, not list Vy siml ix: nv xn stt twi Cn g s wk omltnss? Wy/wy not? How out otimlity? Cn tis wk omltnss? Otimlity? Otimlity o A* Poo: Nw ossil olm: nos on t to * tt woul v n in uu n t, us som wos n o t sm stt s som n ws uu n xn ist (isst!) Tk t igst su n in t Lt t nsto wi ws on t uu wn n ws xn Assum () < (n) (n) < (n ) us n is suotiml woul v n xn o n o n woul v n xn o n, too Contition! Consistny Wit, ow o w know nts v tt -vlus tn ti sussos? Couln t w o som no n, n in its il n to v low vlu? YE: = 0 = 8 B g = 0 Wt n w ui to vnt ts invsions? Consistny: A = 0 Rl ost must lwys x ution in uisti 0

11 A* on Wong Consistny = tt s g A =4 C = B = =0 t (0+) A (+4) B (+) C (+) C (+) C is ly in t los-list, n not l in t ioity uu (6+0) A =4 = C T stoy on Consistny: Dinition: ost(a to C) + (C) (A) Consun in s t: Two nos long t: N A, N C g(n C ) = g(n A ) + ost(a to C) g(n C ) + (C) g(n A ) + (A) T vlu long t nv ss Non-sing mns you otiml to vy stt (not just gols) Otimlity ummy T s: A* otiml i uisti is missil (n non-ngtiv) Uniom Cost is sil s ( = 0) s: A* otiml i uisti is onsistnt UC otiml ( = 0 is onsistnt) Consistny imlis missiility Cllng:Ty to ov tis. Hint: ty to ov t uivlnt sttmnt not missil imlis not onsistnt In gnl, ntul missil uistis tn to onsistnt Rmm, osts lwys ositiv in s! ummy: A* A* uss ot kw osts n (stimts o) ow osts A* is otiml wit missil uistis Huisti sign is ky: otn us lx olms A* Mmoy Issus à IDA* IDA* (Ittiv Dning A*). st mx = (o som ot smll vlu). Exut DF tt os not xn stts wit > mx. I DF tuns t to t gol, tun it 4. Otwis mx = mx + (o lg inmnt) n go to st Comlt n otiml Mmoy: O(s), w mx. ning to, s s t o otiml t Comlxity: O(k s ), w k is t num o tims DF is ll 69 R I Agnts tt ln à omliztion: olm: tts (onigutions o t wol) usso untion: untion om stts to lists o (stt, tion, ost) tils; wn s g tt stt n gol tst t: Nos: snt lns o ing stts Plns v osts (sum o tion osts) Algoitm: ystmtilly uils s t Cooss n oing o t ing (unxlo nos)

12 R II T vs. Pioity uu to sto ing: int ioity untions à int s mto Uninom Mtos Dt-Fist Bt-Fist Uniom-Cost Huisti Mtos y A* --- uisti sign! Amissiility: (n) <= ost o st t to gol stt. Ensus wn gol no is xn, no ot til lns on ing oul xtn into t to gol stt Consistny: (n->n ) >= (n) (n ). Ensus wn ny no n is xn uing g s t til ln tt n in n is t st wy to n. Tim n s omlxity, omltnss, otimlity Ittiv Dning: nls to tin otimlity wit littl omuttionl ov n tt s omlxity