Popular Application. Planning & Logic. Overview. Logistics. Planning. CSE 473 Automated Planning. Dan Weld (With slides by UW AI faculty & Dana Nau

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1 SE 473 utomated Planning Poula lication Dan Weld (With slides by UW I faculty & Dana Nau I have a lan - a lan that cannot ossibly fail. - Insecto lousseau Mausam Oveview Planning & Logic Intoduction & gents Seach, Heuistics & SPs dvesaial Seach Logical Knowledge Reesentation Planning & MDPs Reinfocement Leaning Uncetainty & ayesian Netwoks Machine Leaning NLP & Secial Toics ctions secified using fist ode logic Planning imlemented using ST solve E.g., DPLL o WalkST lso an examle of solving FOL using oositional ST Logistics PS2 due today HW1 due in one week Pats due in between: Fid Fiday witten oblem Monday feedback on anothe eson s answe Wed evise you answe Planning Given a logical descition of the initial situation, a logical descition of the goal conditions, and a logical descition of a set of ossible actions, Find a seuence of actions (a lan of actions) that bings us fom the initial situation to a situation in which the goal conditions hold. D. Weld, D. Fox 6 1

2 Examle: lockswold Planning Inut: State Vaiables/Poositions Tyes: block --- a, b, c (on-table a) (on-table b) (on-table c) (clea a) (clea b) (clea c) (am-emty) (holding a) (holding b) (holding c) (on a b) (on a c) (on b a) (on b c) (on c a) (on c b) (on-table?b); clea (?b) (am-emty); holding (?b) (on?b1?b2) No. of state vaiables =16 No. of states = 2 16 No. of eachable states =? Daniel S. Weld 7 D. Weld, D. Fox 8 Planning Inut: ctions Planning Inut: ctions (contd) icku a b, icku a c, lace a b, lace a c, icku-table a,,icku-table b, lace-table a, lace-table b, icku?b1?b2 lace?b1?b2 icku-table?b lace-table?b Total: = 18 gound actions Total: 4 action schemata :action icku?b1?b2 :econdition (on?b1?b2) (clea?b1) (am-emty) :effect (holding?b1) (not (on?b1?b2)) (clea?b2) (not (am-emty)) :action icku-table?b :econdition (on-table?b) (clea?b) (am-emty) :effect (holding?b) (not (on-table?b)) (not (am-emty)) D. Weld, D. Fox 9 D. Weld, D. Fox 10 Planning Inut: Initial State Planning Inut: Goal (on-table a) (on-table b) (am-emty) (clea c) (clea b) (on c a) (on-table c) ND (on b c) ND (on a b) Is this a state? D ll othe oositions false not mentioned assumed false losed wold assumtion In lanning a goal is a set of states Like the goal test in oblem solving seach ut secified declaatively (in logic) athe than with code D. Weld, D. Fox 11 D. Weld, D. Fox 12 2

3 Planning vs. Poblem Solving? One Planne Solves Many Domains no code euied asic diffeence: Exlicit, logic based eesentation States/Situations: descitions of the wold by logical fomulae agent can exlicitly eason about the wold. s 5 Goal conditions as logical fomulae vs. goal test (black box) agent can eflect on its goals. location 1 location 2 Oeatos/ctions: Tansfomations on logical fomulae agent can eason about the effects of actions by insecting the definition of its oeatos. D. Weld, D. Fox 13 Dana Nau: This wok is licensed unde a eative ommons License. Secifying a Planning Poblem Descition of initial state of wold Set of oositions Descition of goal: E.g., Logical conjunction ny wold satisfying conjunction is a goal Descition of available actions lassical Planning Simlifying assumtions tomic time gent is omniscient (no sensing necessay). gent is sole cause of change ctions have deteministic effects STRIPS eesentation Wold = set of tue oositions (conjunction) ctions: Pecondition: (conjunction of ositive liteals, no functions) Effects (conjunction of liteals, no functions) Goal = conjunction of ositive liteals on(,) on(, ) D. Weld, D. Fox 15 D. Weld, D. Fox 16 Fowad Wold Sace Seach Fowad State Sace Seach Initial State Goal State Initial state: set of ositive gound liteals W: liteals not aeaing ae false ctions: alicable if econditions satisfied add ositive effect liteals emove negative effect liteals Goal test: does state logically satisfy goal? Ste cost: tyically 1 Daniel S. Weld 18 D. Weld, D. Fox 19 3

4 Heuistics fo State Sace Seach ount numbe of false goal oositions in cuent state dmissible? NO Subgoal indeendence assumtion: ost of solving conjunction is sum of cost of solving each subgoal indeendently Otimistic: ignoes negative inteactions Pessimistic: ignoes edundancy dmissible? No an you make this admissible? D. Weld, D. Fox 21 Heuistics fo State Sace Seach (contd) Delete all econditions fom actions, solve easy elaxed oblem, use length dmissible? YES :action icku-table?b :econdition (and (on-table?b) (clea?b) (am-emty)) :effect (and (holding?b) (not (on-table?b)) (not (am-emty))) 22 SE 573 Planning Gah: asic idea onstuct a lanning gah: encodes constaints on ossible lans Use this lanning gah to comute an infomative heuistic (Fowad *) Planning gah can be built fo each oblem in olynomial time The Planning Gah level P0 level P1 level P2 level P3 level 1 level 2 level 3 D. Weld, D. Fox 26 Note: a few noos missing fo claity D. Weld, D. Fox 27 Regession seach Planning Gahs States Oeatos Initial State Goal Planning gahs consists of a se of levels that coesond to time stes in the lan. Level 0 is the initial state. Each level consists of a set of liteals and a set of actions that eesent what might be ossible at that ste in the lan Might be is the key to efficiency Recods only a esticted subset of ossible negative inteactions among actions. 4

5 Planning Gahs ltenate levels Liteals = all those that could be tue at that time ste, deending uon the actions executed at eceding time stes. ctions = all those actions that could have thei econditions satisfied at that time ste, deending on which of the liteals actually hold. PG Examle Init(Have(ake)) Goal(Have(ake) Eaten(ake)) ction(eat(ake), PREOND: Have(ake) EFFET: Have(ake) Eaten(ake)) ction(ake(ake), PREOND: Have(ake) EFFET: Have(ake)) PG Examle Gah Exansion Poosition level 0 initial conditions ction level i no-o fo each oosition at level i-1 action fo each oeato instance whose econditions exist at level i-1 Poosition level i effects of each no-o and action at level i 0 i-1 i i+1 eate level 0 fom initial oblem state. No-o-action(P), PREOND: P EFFET: P Have a no-o action fo each gound fact D. Weld, D. Fox 33 PG Examle PG Examle dd all alicable actions. dd all effects to the next state. dd esistence actions (aka no-os) to ma all liteals in state S i to state S i+1. 5

6 Mutual Exclusion PG Examle Two actions ae mutex if one clobbes the othe s effects o econditions they have mutex econditions Two oosition ae mutex if one is the negation of the othe all ways of achieving them ae mutex Identify mutual exclusions between actions and liteals based on otential conflicts. D. Weld, D. Fox 36 ake examle ake examle Level S 1 contains all liteals that might esult fom icking any subset of actions in 0 onflicts between liteals that can not occu togethe (as a conseuence of the selection action) ae eesented by mutex links. S1 defines multile states and the mutex links ae the constaints that define this set of states. Obsevation 1 Obsevation 2 Poositions monotonically incease (always caied fowad by no-os) D. Weld, D. Fox 45 ctions monotonically incease D. Weld, D. Fox 46 6

7 Obsevation 3 Obsevation 4 s s s Poosition mutex elationshis monotonically decease ction mutex elationshis monotonically decease D. Weld, D. Fox 47 D. Weld, D. Fox 48 Obsevation 5 Poeties of Planning Gah Planning Gah levels off. fte some time k all levels ae identical ecause it s a finite sace, the set of liteals neve deceases and mutexes don t eaea. If goal is absent fom last level? Then goal cannot be achieved! If thee exists a lan to achieve goal? Then goal is esent in the last level & No mutexes between conjuncts If goal is esent in last level (w/ no mutexes)? Thee still may not exist any viable lan D. Weld, D. Fox 49 D. Weld, D. Fox 50 Heuistics based on Planning Gah onstuct lanning gah stating fom s h(s) = level at which goal aeas non mutex dmissible? YES Relaxed Planning Gah Heuistic Remove negative econditions build lan. gah Use heuistic as above dmissible? YES Moe infomative? NO Seed: FSTER FF Tomost classical lanne until 2009 State sace local seach Guided by elaxed lanning gah Full best fist seach to escae lateaus few othe bells and whistles D. Weld, D. Fox 51 Mausam 7

8 Planning Summay Poblem solving algoithms that oeate on exlicit oositional eesentations of states and actions. Make use of domain indeendent heuistics. STRIPS: estictive oositional language Heuistic seach fowad (ogession) backwad (egession) seach [didn t cove] Local seach FF [didn t cove] Geneative Planning Inut Descition of (initial state of) wold (in some KR) Descition of goal (in some KR) Descition of available actions (in some KR) Outut ontolle E.g. Seuence of actions E.g. Plan with loos and conditionals E.g. Policy = f: states > actions D. Weld, D. Fox 55 Daniel S. Weld 56 Inut Reesentation Descition of initial state of wold E.g., Set of oositions: ((block a) (block b) (block c) (on-table a) (on-table b) (clea a) (clea b) (clea c) (am-emty)) Descition of goal: i.e. set of wolds o?? E.g., Logical conjunction ny wold satisfying conjunction is a goal (and (on a b) (on b c))) Descition of available actions Daniel S. Weld 57 Pefect Static Fully Obsevable lassical Planning Envionment Full Daniel S. Weld 58 Instantaneous I = initial state G = goal state (ec) O i [ I ] O i O j O k O m [ G ] (effects) Deteministic omilation to ST Init state ctions? Goal The Idea Suose a lan of length n exists Encode this hyothesis in ST Init state tue at t 0 Goal tue at T n ctions imly effects, etc Look fo satisfying assignment Decode into lan Daniel S. Weld 59 RIS: The Revolutionay Excitement Daniel S. Weld 60 8

9 xioms xiom Descition / Examle Init The initial state holds at t=0 Goal The goal holds at t=2n P, E Paint(,Red,t) lock(, t-1) Paint(,Red,t) olo(, Red, t+1) Fame lassical / Exlanatoy t-least-one ct1(, t) ct2(, t) Exclude ct1(, t) ct2(, t) Sace of Encodings ction Reesentations Regula Simly Slit Oveloaded Slit itwise Fame xioms lassical Exlanitoy Daniel S Weld 61 Daniel S. Weld 62 lassical Fame xioms P,, t if P@t doesn t affect P then P@t+1 Exlanatoy P,, t if P@t-1 P@t+1 then foall i that do affect P Daniel S. Weld 63 Reesentation ction Reesentation One Poositional Vaiable e Examle Regula fully-instantiated action Paint--Red, Paint--lue, Move--Table Simly-slit Oveloaded-slit itwise Daniel S Weld fully-instantiated action s agument fully-instantiated agument inay encodings of actions Paint-g1- Paint-g2-Red ct-paint g1- g2-red it1 ~it2 it3 Paint--Red = 5 moe vas moe clses 64 Otimization 1: Factoed Slitting - use atially-instantiated actions Hasolo--lue-(t-1) ^ Paint-g1--t ^ Paint-g2-Red-t Hasolo--lue-(t+1) factoed unfactoed Vaiables lauses Liteals Exlanatoy Fames Simle Oveloaded Otimization 2: Tyes tye is a fluent which no actions affects. tye intefeence une imossible oeato instantiations tye elimination Tye ots No tye ots Liteals Regula Simle Oveloaded itwise lassical Exlanatoy Daniel S Weld 65 Daniel S Weld 66 9