1 BLACKBOX: A New Paradigm for Planning Bart Selman Cornell University

2 Search as Inference: Direct Abstract problem specification General inference (NP complete) Solution Model in propositional logic

3 State-space Planning Find a sequence of operators that transform an initial state to a goal state State = complete truth assignment to a set of variables (fluents) Goal = partial truth assignment (set of states) Operator = a partial function State  State specified by three sets of variables: precondition, add list, delete list

4 Some Applications of Planning Autonomous systems NASA Deep Space One Remote Agent Softbots - software robots Internet agents, program assistants Bots, characters in games Program verification Jackson (1998) - finding bugs in protocols - is there a sequence of actions that reaches an error state?

5 SATPLAN (Kautz & Selman 1996) STRIPS Model in propositional logic Walksat SAT engine Solution

6 Lessons from SATPLAN A general propositional theorem prover outperformed traditional AI planning systems (UCPOP, Nonlin, Prodigy,...) Power of propositional logic –much better scaling than attempts in 1970’s using first-order theorem proving Fast SAT engines –stochastic search - walksat –large SAT/CSP community sharing ideas and code –older planning systems can be viewed as adhoc, incomplete, poorly understood theorem provers! Importance of modeling –different axiomatizations can have vastly different computational properties

7 Graphplan (Blum & Furst 1996) Planning as graph search Like SATPLAN... Two phases: instantiation of propositional structure, followed by search Plan graph is very close to CNF Unlike SATPLAN… Takes STRIPS operators directly as input Interleaves instantiation and pruning of plan graph –results in much smaller structure Employs specialized search engine Graphplan - better instantiation SATPLAN - better search Goal: Combine best features of both systems

8 Where Graphplan Gets its Power During instantiation, Graphplan computes mutex relationships between incompatible actions used for pruning, and later speeding search mutex algorithm is actually a form of limited resolution on binary negative clauses! polytime preprocessing O(n 2 ) Issue: research on graphplan failed to discover any useful extensions to mutex algorithm Can general polytime limited inference algorithms discover other kinds of useful local information?

9 Multistep Problem Reformulation Domain specific model Polytime domain specific inference Combinatorial core - general language Full general inference (NP complete) Solution Polytime general inference Abstract problem specification

10 Blackbox STRIPS Plan Graph Mutex computation CNF Translation Stochastic / Systematic SAT engines Solution Limited resolution - failed literal rule

11 Intuition Many real-world problems not tractable, but are nearly so domain specific polytime inference takes advance of special kinds of structure small number of practical methods for combinatorial core –can be highly optimized –limited inference: variations of constraint propagation –full inference: local search, smart backtracking, *randomized backtracking

12 Translation to CNF Fact  Act1  Act2 Act1  Pre1  Pre2 ¬Act1  ¬Act2 Act1 Act2 Fact Pre1 Pre2 Alternating layers of facts and actions fully factored (nodes are propositions, not states!) Not all atoms in a layer can hold simultaneously solution = subgraph containing all goals, all supports, no mutexes

13 General Limited Inference Generated wff can be further simplified by consistency propagation techniques Compact (Crawford & Auton 1996) unit propagation: is Wff inconsistant by resolution against unit clauses? O(n) failed literal rule: is Wff + { P } inconsistant by unit propagation? O(n 2 ) binary failed literal rule: is Wff + { P V Q } inconsistant by unit propagation? O(n 3 ) Complements domain specific limited inference Discovers hidden local structure!

14 General Limited Inference

15 Randomized Sytematic Solvers Stochastic local search solvers (walksat) when they work, scale well cannot show unsat fail on some domains Systematic solvers (Davis Putnam) complete seem to scale badly Can we combine best features of each approach?

16 Heavy Tails Bad scaling of systematic solvers can be caused by heavy tailed distributions Deterministic algorithms get stuck on particular instances but that same instance might be easy for a different deterministic algorithm! Expected (mean) solution time increases without limit over large distributions

17 Heavy Tailed Cost Distribution

18 Randomized Restarts Solution: randomize the systematic solver Add noise to the heuristic branching (variable choice) function Cutoff and restart search after a fixed number of backtracks Eliminates heavy tails In practice: rapid restarts with low cutoff can dramatically improve performance

19 Rapid Restart Speedup

20 Blackbox as Experimental Testbed All components of blackbox are parameterized Can experiment with different schedules for instantiating, simplifying, and solving problems blackbox -solver -maxsec 20 graphplan -then compact -l -then satz -cutoff 20 -restart 100 -then walksat -cutoff restart 10

21 blackbox version 9B command line: blackbox -o logistics.pddl -f logistics_prob_d_len.pddl -solver compact -l -then satz -cutoff 25 -restart Converting graph to wff 6151 variables clauses Invoking simplifier compact Variables undetermined: 4633 Non-unary clauses output: Invoking solver satz version satz-rand-2.1 Wff loaded [1] begin restart [1] reached cutoff back to root [2] begin restart [2] reached cutoff back to root [3] begin restart [3] reached cutoff back to root [4] begin restart [4] reached cutoff back to root [5] begin restart **** the instance is satisfiable ***** **** verification of solution is OK **** total elapsed seconds = Begin plan 1 drive-truck_ny-truck_ny-central_ny-po_ny

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23 Blackbox Results states 6,000 variables 125,000 clauses

24 AI Planning Systems Competition CMU, 1998 TeamNumber ofAverageFastestShortest problemssolutiononsolutions solvedtime (msec)for Blackbox (AT&T Labs) HSP (Venezuela) IPP8 (11)110361(3)6(8) (Germany) STAN (UK)

25 Notes All finalists based on SATPLAN, Graphplan, or A* ! Traditional non-linear planning no longer competitive Knowledge-intensive approaches require too much human effort Other new techniques Type-theoretic analysis of operators: can infer state invariants (package only in one vehicle, etc.) –powerful, generally applicable pre-processor Compilation of more expressive languages (conditional effects) to STRIPS Recent extensions to MDP’s of A* (Geffner), Graphplan (Blum), SATPLAN (Littman)

26 Summary Blackbox combines best features of Graphplan, SATPLAN, and new randomized systematic search engines Automatic generation of wffs from standard STRIPS input No performance penalty over hand-encodings! Testbed for bridging different planning paradigms

27 Current Research Issues Incorporating explicit domain knowledge (Kautz & Selman, 1998) state invariants optimality conditions declarative constraints - independent of search engine More expressive planning languages: optimizing resources can view bounded integer linear programming as generalization of SAT ILPPLAN - adapts SATPLAN framework to ILP, solve with WSAT(OIP) (local search for ILP) Initial results - can find better quality solutions (counting action costs) than previously known for benchmark logistics & scheduling problems (Kautz & Walser 1999)