Logistics. Today s Topics. Overview. Planning. Simplifying Assumptions. CSE 473 Automated Planning. HW1 due in one week (Fri 5/4)

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1 SE 473 utomted Plnning Dn Weld (With slides y UW I fulty & Dn Nu I hve ln - ln tht nnot ossily fil. - Inseto lousseu Logistis HW1 due in one week (Fi 5/4) Pts due in etween: Mondy dft nswe to olem 1 Wed give feedk on nothe eson s s nswe Oveview Tody s Tois Intodution & gents Seh, Heuistis & SPs dvesil Seh Logil Knowledge Reesenttion Plnning & MDPs Reinfoement Lening Unetinty & yesin Netwoks Mhine Lening NLP & Seil Tois Logi fo seifying lnning domins Plnning gh fo omuting heuistis omiling lnning to ST Plnning Given logil desition of the initil sitution, logil desition of the gol onditions, nd logil desition of set of ossile tions, Find seuene of tions ( ln of tions) tht ings us fom the initil sitution to sitution in whih the gol onditions hold. Stti vs. Dynmi Pefet vs. Noisy Peets Simlifying ssumtions Fully Osevle vs. Ptilly Osevle Envionment Wht tion next? Instntneous Deteministi vs. vs. Dutive Stohsti tions D. Weld, D. Fox 5 Dniel S. Weld 6 1

2 lssil Oetos unstk(x,y) Peond: on(x,y), le(x), hndemty Effets: on(x,y), le(x), hndemty, holding(x), le(y) stk(x,y) Peond: holding(x), le(y) Effets: holding(x), le(y), on(x,y), le(x), hndemty iku(x) Peond: ontle(x), le(x), hndemty Effets: ontle(x), le(x), hndemty, holding(x) utdown(x) Peond: holding(x) Effets: holding(x), ontle(x), le(x), hndemty Diving Stti fts Plnning vs. Polem Solving? si diffeene: Exliit, logi sed eesenttion Sttes/Situtions: desitions of the wold y logil fomule gent n exliitly eson out the wold. Gol onditions s logil fomule vs. gol test (lk ox) gent n eflet on its gols. Initil Stte Fowd Wold Se Seh Gol Stte Oetos/tions: Tnsfomtions on logil fomule gent n eson out the effets of tions y inseting the definition of its oetos. s 5 lotion 1 lotion 2 10 Dniel S. Weld 11 Heuistis fo Stte Se Seh ount nume of flse gol oositions in uent stte dmissile? NO Sugol indeendene ssumtion: ost of solving onjuntion is sum of ost of solving eh sugol indeendently Otimisti: ignoes negtive intetions Pessimisti: ignoes edundny dmissile? No n you mke this dmissile? Heuisti Genetion II unstk(x,y) Peond: on(x,y), le(x), hndemty Effets: on(x,y), le(x), hndemty, holding(x), le(y) stk(x,y) Peond: holding(x), le(y) Effets: holding(x), le(y), on(x,y), le(x), hndemty iku(x) Peond: ontle(x), le(x), hndemty Effets: ontle(x), le(x), hndemty, holding(x) utdown(x) Peond: holding(x) Effets: holding(x), ontle(x), le(x), hndemty Delete eonditions Solve elxed e ed lnning olem dmissle? D. Weld, D. Fox 12 2

3 Heuisti Genetion III unstk(x,y) Peond: on(x,y), le(x), hndemty Effets: on(x,y), le(x), hndemty, holding(x), le(y) stk(x,y) Peond: holding(x), le(y) Effets: holding(x), le(y), on(x,y), le(x), hndemty iku(x) Peond: ontle(x), le(x), hndemty Effets: ontle(x), le(x), hndemty, holding(x) utdown(x) Peond: holding(x) Effets: holding(x), ontle(x), le(x), hndemty Delete negtive effets Solve elxed e ed lnning olem dmissle? Plnning Gh: si ide onstut lnning gh: enodes onstints on ossile lns Use this lnning gh to omute n infomtive heuisti (Fowd *) Plnning gh n e uilt fo eh olem in olynomil time D. Weld, D. Fox 15 The Plnning Gh PG Exmle level P0 level P1 level P2 level P3 level 1 level 2 level 3 Init(Hve(ke)) Gol(Hve(ke) Eten(ke)) tion(et(ke), PREOND: Hve(ke) EFFET: Hve(ke) Eten(ke)) tion(ke(ke), PREOND: Hve(ke) EFFET: Hve(ke)) Note: few noos missing fo lity D. Weld, D. Fox 16 PG Exmle Gh Exnsion Poosition level 0 initil onditions tion level i no-o fo eh oosition t level i-1 tion fo eh oeto instne whose eonditions exist t level i-1 Poosition level i effets of eh no-o nd tion t level i 0 i-1 i i+1 ete level 0 fom initil olem stte. No-o-tion(P), PREOND: P EFFET: P Hve no-o tion fo eh gound ft D. Weld, D. Fox 21 3

4 PG Exmle PG Exmle dd ll lile tions. dd ll effets to the next stte. dd esistene tions (k no-os) to m ll litels in stte S i to stte S i+1. Mutul Exlusion Mutul Exlusion Two tions e mutex if one loes the othe s effets o eonditions they hve mutex eonditions Two tions e mutex if one loes the othe s effets o eonditions they hve mutex eonditions Two oositions e mutex if one is the negtion of the othe Two oosition e mutex if one is the negtion of the othe ll wys of hieving them e mutex Mutul Exlusion Mutul Exlusion Two tions e mutex if they hve mutex eonditions one loes the othe s eonditions o effets Two oosition e mutex if one is the negtion of the othe ll wys of hieving them e mutex Light fuse(mth, om) Peond: lit(mth), holding(om) Effets: will exlode(om) Extinguish(mth) gus Peond: lit(mth) Effets: lit(mth) 26 4

5 If Result of N>1 tions is miguous Mk Envionment Them Mutex Instntneous vs. Dutive PG Exmle Wht tion next? tions Identify mutul exlusions etween tions nd litels sed on otentil onflits. Dniel S. Weld 28 ke exmle ke exmle Level S 1 ontins ll litels tht might esult fom iking ny suset of tions in 0 onflits etween litels tht n t ou togethe (s onseuene of seletion tion) e eesented y mutex links. S1 defines multile sttes nd the mutex links e the onstints tht define this set of sttes. Osevtion 1 Osevtion 2 Litels monotonilly inese (lwys ied fowd y no-os) D. Weld, D. Fox 34 tions monotonilly inese D. Weld, D. Fox 35 5

6 Osevtion 3 Osevtion 4 s s s mutex eltionshis etween litels monotonilly deese Mutex eltionshis etween tions monotonilly deese D. Weld, D. Fox 36 D. Weld, D. Fox 37 Osevtion 5 Poeties of Plnning Gh Plnning Gh levels off. fte some time k, ll levels e identil euse it s finite se & montoniity If gol is sent fom lst level? Then gol nnot e hieved! If thee exists ln to hieve gol? Then gol is esent in the lst level & No mutexes etween onjunts If gol is esent in lst level (w/ no mutexes)? Thee still my not exist ny vile ln D. Weld, D. Fox 38 D. Weld, D. Fox 39 Heuistis sed on Plnning Gh onstut lnning gh stting fom s h(s) = level t whih gol es non mutex dmissile? YES Plnning Gh is Otimisti Suose you wnt to ee suise dinne fo you sleeing sweethet s 0 = {gge, lenhnds, uiet} g = {dinne, esent, gge} tion Peonditions Effets ook() lenhnds dinne w() uiet esent y() none gge, lenhnds dolly() none gge, uiet lso hve esistene tions: one fo eh litel D. Weld, D. Fox 40 6

7 Exmle (ontinued) Rell the gol is { gge, dinne, esent} Note tht in stte level 1, ll of them e thee None e mutex witheh othe Thus, thee s hne tht ln exists ut no tul ln does Piwise, the gols e onsistent ut no onsistent wy to hieve ll thee Plnning gh ~ k onsisteny ut with no fixed limit on k stte level 0 tion level 1 stte level 1 Fst Fowd (FF) Fstest lssil lnne ~2009 Stte se lol seh Guided y elxed lnning gh Full est fist seh to ese lteus few othe ells nd whistles Initil Stte Gol Stte dinne dinne esent esent Musm Tody s Tois Fluent Logi fo seifying lnning domins Plnning gh fo omuting heuistis omiling lnning to ST Gound litel whose tuth vlue my hnge ove time Eg, t(oie, lotion5) Not oot(oie) i Move lo5 lo7 lo5 lo7 T0 T1 Enoding Fluents in Logi t(oie, lotion7, time1) Enoding Initil onditions & Gols Suose we only ed out 1 ste lns Stte desied end onditions: = t(oie, lo5, time0) t(oie, lo7, time1) Is stisfile? Is P Q stisfile? lo5 lo7 lo5 lo7 lo5 lo7 lo5 lo7 T0 T1 T0 T1 7

8 Enoding tion Effets in Logi, l1, l2, t move(, l1, l2) Peond: oot(), t(,l1), Effets: t(,l2) move(,l1,l2,t) => t(, l2, t+1), l1, l2, t move(,l1,l2,t) l2 => t(, l, t) move(,l1,l2,t) t(, l, t) Move lo5 lo7 lo5 lo7 T1 T2 omiling to Poositionl Logi, l1, l2, t move(, l1, l2) Peond: oot(), t(,l1), Effets: t(,l2) move(,l1,l2,t) => t(, l2, t+1) Infinite wolds: imossile ut suose only 2 oots (oie, sue), 2 lotions, 1 tion time move(oie,lo5,lo7,1) => t(oie, lo7, 2) move(oie,lo7,lo5,1) => t(oie, lo5, 2) move(sue,lo5,lo7,1) => t(sue, lo7, 2) move(sue,lo7,lo5,1) => t(sue, lo5, 2) Ovell oh ounded lnning olem is i (P,n): P is lnning olem; n is ositive intege ny solution fo P of length n is solution fo (P,n) Plnning lgoithm: Do itetive deeening like we did with Ghln: fo n = 0, 1, 2,, enode (P,n) s stisfiility olem if is stisfile, then Fom the set of tuth vlues tht stisfies, solution ln n e onstuted, so etun it nd exit Enoding Plnning Polems Enode (P,n) s fomul suh tht π = 0, 1,, n 1 is solution fo (P,n) if nd only if n e stisfied in wy tht mkes the fluents 0,, n 1 tue Let = {ll tions in the lnning domin} S = {ll sttes in the lnning domin} L = {ll litels in the lnguge} is the onjunt of mny othe fomuls Fomul desiing the initil stte: Fomuls in /\{l 0 l s 0 } /\{ l 0 l L s 0 } Fomul desiing the gol: /\{l n l g + } /\{ l n l g } Fo evey tion in, fomuls desiing wht hnges would mke if it wee the i th hste of the ln: i /\{ i Peond()} /\ {e i+1 e Effets()} omlete exlusion xiom: Fo ll tions nd, fomuls sying they n t ou t the sme time i i this guntees thee n e only one tion t time Is this enough? Fme xioms Fme xioms: Fomuls desiing wht doesn t hnge etween stes i nd i+1 Sevel wys to wite these One wy: exlntoy fme xioms One xiom fo evey litel l Sys tht if l hnges etween s i nd s i+1, then the tion t ste i must e esonsile: ( l i l i+1 V in { i l effets + ()}) (l i l i+1 V in { i l effets ()}) 8

9 Exmle Plnning domin: one oot 1 two djent lotions l1, l2 one oeto (move the oot) Enode (P,n), whee n = 1 Initil stte: {t(1,l1)} Enoding: t(1,l1,0) t(1,l2,0) Gol: {t(1,l2)} Enoding: t(1,l2,1) t(1,l1,1) Oeto: see next slide Exmle (ontinued) Oeto: move(,l,l ) eond: t(,l) effets: t(,l ), t(,l) Enoding: move(1,l1,l2,0) t(1,l1,0) t(1,l2,1) t(1,l1,1) move(1,l2,l1,0) t(1,l2,0) t(1,l1,1) t(1,l2,1) move(1,l1,l1,0) t(1,l1,0) t(1,l1,1) t(1,l1,1) move(1,l2,l2,0) t(1,l2,0) t(1,l2,1) 1) t(1,l2,1) 1) move(l1,1,l2,0) move(l2,l1,1,0) nonsensil move(l1,l2,1,0) move(l2,l1,1,0) How to void geneting the lst fou tions? ssign dt tyes to the onstnt symols like we did fo stte vile eesenttion ontditions (esy to detet) Lotions: l1, l2 Roots: 1 Exmle (ontinued) Oeto: move( : oot, l : lotion, l : lotion) eond: t(,l) effets: t(,l ), t(,l) Enoding: move(1,l1,l2,0) t(1,l1,0) t(1,l2,1) t(1,l1,1) move(1,l2,l1,0) t(1,l2,0) t(1,l1,1) t(1,l2,1) Exmle (ontinued) omlete exlusion xiom: move(1,l1,l2,0) move(1,l2,l1,0) Exlntoy fme xioms: t(1,l1,0) t(1,l1,1) move(1,l2,l1,0) t(1,l2,0) t(1,l2,1) move(1,l1,l2,0) t(1,l1,0), t(1,l1,1) (,, ) move(1,l1,l2,0),, t(1,l2,0) t(1,l2,1) move(1,l2,l1,0) Extting Pln Suose we find n ssignment of tuth vlues tht stisfies. This mens P hs solution of length n Plnning How to find n ssignment of tuth vlues tht stisfies? Use stisfiility lgoithm Exmle: the Dvis Putnm lgoithm Fo i=1,,n, thee will e extly one tion suh tht i = tue This is the i th tion of the ln. Exmle (fom the evious slides): n e stisfied with move(1,l1,l2,0) = tue Thus move(1,l1,l2,0) is solution fo (P,0) It s the only solution no othe wy to stisfy Fist need to ut into onjuntive noml fom eg e.g., = D ( D ) ( D ) ( D ) Wite s set of luses (disjunts of litels) = {{D}, { D,, }, { D,, }, { D,, }, {}} Two seil ses: If = then is lwys tue If = {,, } then is lwys flse (hene unstisfile) 9