CE 573: Atiiil Intllign Autumn 0 Intoution & Dn Wl Wit slis om Dn Klin, tut Russll, Anw Moo, Luk Zttlmoy Agnt vs. Envionmnt An gnt is n ntity tt ivs n ts. A tionl gnt slts tions tt mximiz its utility untion. Ctistis o t ts, nvionmnt, n tion s itt tnius o slting tionl tions. Agnt nsos? Atutos Pts Ations Env vionmnt Pln Ask wt i ol Bs Agnts 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 tu Polm / tt Inut: t o stts Otos [n osts] tt stt ol stt [tst] Outut: Pt: stt stt stisying gol tst [My ui sotst t] [omtims just n stt ssing tst] Exml: N uns Min Lning : it ul iiny Inut: t o stts Otos [n osts] tt stt ol stt (tst) Dist Dt Pit MP mg ylins islmnt osow wigt ltion moly mk goo 4 low low low ig 75to78 si 6 mium mium mium mium 70to74 mi 4 mium mium mium low 75to78 uo 8 ig ig ig low 70to74 mi 6 mium mium mium mium 70to74 mi 4 low mium low mium 70to74 si 4 low mium low low 70to74 si 8 ig ig ig low 75to78 mi : : : : : : : : : : : : : : : : : : : : : : : : 8 ig ig ig low 70to74 mi goo 8ig mium ig ig 79to83 mi 8 ig ig ig low 75to78 mi goo 4 low low low low 79to83 mi 6 mium mium mium ig 75to78 mi goo 4 mium low low low 79to83 mi goo 4 low low mium ig 79to83 mi 8 ig ig ig low 70to74 mi goo 4 low mium low mium 75to78 uo 5 mium mium mium mium 75to78 uo Outut Y N to in Hyotsis : X : X Y
Hyotss: ision ts : X Y tu o Dision Ts E intnl no tsts n ttiut x i E n ssigns n ttiut vlu x i =v E l ssigns lss y To lssiy inut x? tvs t t om oot to l, outut t ll y Cylins 3 4 5 6 8 goo Mk Hosow mi si uo low m ig goo goo goo 8 Mtos Blin Dt ist s Bt ist s Ittiv ning s Uniom ost s Lol Inom Constint tistion Avsy tt s tt s g: E no is stt T susso untion is snt y s Egs my ll wit osts W n ly uil tis g in mmoy (so w on t) Riiulously tiny s g o tiny s olm tt izs? Ts Polm: Et ll o t oo Pmn ositions: 0 x = 0 Pmn ing: u, own, lt, igt Foo Count: 30 ost ositions: N,.0 E,.0 A s t: tt stt t t oot no Ciln oson to sussos Nos ontin stts, oson to PLAN to tos stts Egs ll wit tions n osts Fo most olms, w n nv tully uil t wol t
Exml: T tt s vs. Ts tt : Wt is t s t? W onstut ot on mn n w onstut s littl s ossil. E NODE in in t s t nots n nti PATH in t olm g. tts vs. Nos Nos in stt s gs olm stts Rsnt n stt stt o t wol Hv sussos, n gol / non-gol, v multil ssos Nos in s ts lns Rsnt ln (sun o tions) wi sults in t no s stt Hv olm stt n on nt, t lngt, t & ost T sm olm stt my iv y multil s t nos T Nos Polm tts Pnt Dt 5 Ation No Dt 6 Builing Ts : Exn out ossil lns Mintin ing o unxn lns Ty to xn s w t nos s ossil nl T Rviw: Dt Fist Imotnt is: Fing Exnsion Exlotion sttgy Dtil suoo is in t ook! ttgy: xn st no ist Imlmnttion: Fing is LIFO uu ( stk) Min ustion: wi ing nos to xlo? 3
Rviw: Dt Fist Rviw: Bt Fist Exnsion oing: (,,,,,,,,,,,,,,) ttgy: xn sllowst no ist Imlmnttion: Fing is FIFO uu Rviw: Bt Fist Algoitm Potis Exnsion o: (,,,,,,,,,,,,,,,,,,,,,,) Comlt? unt to in solution i on xists? Otiml? unt to in t lst ost t? Tim omlxity? omlxity? Vils: Tis n Num o stts in t olm T mximum ning to B (t mximum num o sussos o stt) C* Cost o lst ost solution Dt o t sllowst solution m Mx t o t s t DF DF Algoitm Comlt Otiml Tim DF Dt Fist N N No No O(B Ininit LMAX ) O(LMAX) Ininit no nos nos TART m tis Ininit ts mk DF inomlt How n w ix tis? Ck nw nos ginst t om Ininit s ss still olm OAL m nos Algoitm Comlt Otiml Tim DF w/ Pt Cking Y i init N O( m ) O(m) * O g s nxt ltu. 4
BF Algoitm Comlt Otiml Tim DF w/ Pt Cking Y N O( m ) O(m) BF Y Y O( ) O( ) Ext Wok? Filu to tt t stts n us xonntilly mo wok (wy?) tis no nos nos nos m nos In BF, o xml, w souln t ot xning t il nos (wy?) Vy siml ix: nv xn stt ty twi Cn tis wk omltnss? Wy o wy not? How out otimlity? Wy o wy not? om Hints s is lmost lwys tt tn t s (wn not?) Imlmnt you los list s it o st! Nos ontully ts, ut tt to snt wit stt, ost, lst tion, n n to t nt no Mmoy Limittion? uos: 4 Hz CPU 6 B min mmoy 00 instutions / xnsion 5 yts / no 400,000 xnsions / s Mmoy ill in 300 s 5 min 5
Comisons Wn will BF outom DF? Wn will DF outom BF? 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. 3. I il, o DF wi only ss ts o lngt 3 o lss..n so on. Algoitm Comlt Otiml Tim DF w/ Pt Cking Y N O( m ) O(m) BF Y Y O( ) O( ) ID Y Y O( ) O() Cost o Ittiv Dning tio ID to DF 3 3 5.5 0. 5.08 00.0 33 8 Puzzl xx Ruik s 5 Puzzl 3x3x3 Ruik s 4 Puzzl Assuming 0M nos/s & suiint mmoy BF Nos Tim 0 5.0 s 0 6. s 0 3 6 ys 0 9 68k ys 0 5 B ys Wy t in? Ruik s ig ning to 5 uzzl s gt t Mx 8x It. D. Nos Tim 0 5.0 s 0 6. s 0 7 0k ys 0 0 574k ys 0 37 0 3 ys # o ulits li t om Ri Ko snttion Wn to Us Ittiv Dning Costs on Ations N uns? 3 8 9 8 3 OAL TART 5 4 4 Noti tt BF ins t sotst t in tms o num o tnsitions. It os not in t lst-ost t. Dnil. Wl 35 6
Uniom Cost Uniom Cost Exn st no ist: Fing is ioity uu TART 3 8 3 9 8 4 4 5 OAL Exnsion o: (,,,,,,,,,) Cost ontous 8 3 9 8 5 0 3 9 4 5 7 6 6 3 7 8 0.us(ky, vlu).o() o() Pioity uu Rs A ioity uu is t stutu in wi you n inst n tiv (ky, vlu) is wit t ollowing otions: 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 Uniom Cost Algoitm Comlt Otiml Tim DF w/ Pt Cking Y N O( m ) O(m) BF Y Y O( ) O( ) UC Y* Y O( C*/ ) O( C*/ ) C*/ tis Uniom Cost Issus Uniom Cost: P-Mn Rmm: xlos insing ost ontous T goo: UC is omlt n otiml! 3 Cost o o tion Exlos ll o t stts, ut on T : Exlos otions in vy ition No inomtion out gol lotion tt ol 7
Exonntils Evyw Huistis I tink w going to n stong onky 43 44 Huistis Huistis Any stimt o ow los stt is to gol Dsign o tiul s olm 0 5. Exmls: Mnttn istn, Eulin istn Bst Fist / y Exn losst no ist: Fing is ioity uu Bst Fist / y Exn t no tt sms losst Wt n go wong? 8
y Bst Fist / y Exn t no tt sms losst A ommon s: Bst-ist tks you stigt to t (wong) gol stt B A gol Wost-s: lik ly- gui DF in t wost s Cn xlo vyting Cn gt stuk in loos i no yl king Wt n go wong? Lik DF in omltnss (init stts w/ yl king) Bst Fist y Algoitm Comlt Otiml Tim y Bst-Fist Y* N O( m ) O( m ) m Wt o w n to o to mk it omlt? Cn w mk it otiml? A* Ht, Nilsson & Rl 968 Bst ist s wit (n) = g(n) + (n) g(n) = sum o osts om stt to n (n) = stimt o lowst ost t n gol (gol) = 0 I (n) is missil n monotoni tn A* is otiml } Dtil stt Euon Exml Wn o w k o gols? Wn ing to uu? Wn moving om uu? n 54 9
A* Exml A* Exml 55 56 A* Exml A* Exml 57 58 A* Exml A* Exml 59 60 0
Otimlity o A* Otimlity Continu 6 6 Pos Cons A* ummy Ittiv-Dning A* Lik ittiv-ning t-ist, ut... Dt oun moii to n -limit tt wit -limit = (stt) Pun ny no i (no) > -limit Nxt -limit = min-ost o ny no un FL=5 FL= 63 64 IDA* Anlysis Comlt & Otiml (l A*) usg t o solution E ittion is DF - no ioity uu! # nos xn ltiv to A* Dns on # uniu vlus o uisti untion In 8 uzzl: w vlus los to # A* xns In tvling slsmn: vlu otn uniu +++n = O(n ) w n=nos A* xns i n is too ig o min mmoy, n is too long to wit! nts ulit nos in yli gs Fogtulnss A* us xonntil mmoy How mu os IDA* us? Duing un? In twn uns? 65 Dnil. Wl 66
MA* Us ll vill mmoy tt lik A* Wn mmoy is ull Es no wit igst -vlu Fist, ku nt wit tis -vlu o nt knows ost-oun on st il Altntiv Ao to Finit Mmoy Otimlity is ni to v, ut Dnil. Wl 67 Dnil. Wl 68 Dt-Fist Bn & Boun ingl DF s uss lin s K tk o st solution so I (n) = g(n)+(n) ost(st-soln) Tn un n Ruis Finit s t, o oo u oun on solution ost nts ulit nos in yli gs At om Ri Ko snttion 69 Bm I Bst ist ut only k N st itms on ioity uu Evlution Comlt? No Tim Comlxity? O(^) Comlxity? O( + N) Dnil. Wl 70 Hill Climing I Alwys oos st il; no ktking Bm s wit uu = Polms? Lol mxim int snt Rnomizing Hill Climing Rnomly isoying uisti Rnom stts ( vy til istiutions ) Pltus Digonl igs Lol Dnil. Wl 7 Dnil. Wl 7
imult Annling Ojtiv: voi lol minim Tniu: Fo t most t us ill liming Wn no imovmnt ossil Coos nom nigo Lt t s in ulity Mov to nigo wit oility - -/T Ru tmtu t (T) ov tim Otiml? I T s slowly noug, will otiml stt Wily us lso WlkAT tm Dnil. Wl 73 3