BLACKBOX:%20A%20New%20Paradigm%20for%20Planning

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BLACKBOX A New Paradigm for Planning

• Bart Selman
• Cornell University

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Search as Inference Direct
Abstract problem specification
Model in propositional logic
General inference (NP complete)
Solution
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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 preconditio
  n, add list, delete list

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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?

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SATPLAN(Kautz Selman 1996)
Model in propositional logic
STRIPS
Walksat SAT engine
Solution
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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 1970s 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

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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

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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(n2)
• 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?

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Multistep Problem Reformulation
Polytime domain specific inference
Domain specific model
Abstract problem specification
Combinatorial core - general language
Full general inference (NP complete)
Polytime general inference
Solution
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Blackbox
Plan Graph
Mutex computation
STRIPS
CNF Translation
Stochastic / Systematic SAT engines
Limited resolution - failed literal rule
Solution
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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

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Translation to CNF
Act1
Pre1
Fact
Pre2
Act2
Fact ? Act1 ? Act2 Act1 ? Pre1 ? Pre2 Act1 ?
Act2

• 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

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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(n2)
• binary failed literal rule is Wff P V Q
  inconsistant by unit propagation?
• O(n3)
• Complements domain specific limited inference
• Discovers hidden local structure!

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General Limited Inference
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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?

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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

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Heavy Tailed Cost Distribution
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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

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Rapid Restart Speedup
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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 1000000 -restart 10

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blackbox version 9B command line blackbox -o
logistics.pddl -f logistics_prob_d_len.pddl
-solver compact -l -then satz -cutoff 25 -restart
10 ----------------------------------------------
------ Converting graph to wff 6151
variables 243652 clauses Invoking simplifier
compact Variables undetermined 4633 Non-unary
clauses output 139866 ---------------------------
------------------------- Invoking solver satz
version satz-rand-2.1 Wff loaded 1 begin
restart 1 reached cutoff 25 --- back to
root 2 begin restart 2 reached cutoff 25 ---
back to root 3 begin restart 3 reached
cutoff 25 --- back to root 4 begin restart 4
reached cutoff 25 --- back to root 5 begin
restart the instance is satisfiable
verification of solution is OK
total elapsed seconds 25.930000 ----------
------------------------------------------ Begin
plan 1 drive-truck_ny-truck_ny-central_ny-po_ny
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Blackbox Results
1016 states 6,000 variables 125,000 clauses
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AI Planning Systems CompetitionCMU, 1998

• Team Number of Average Fastest Shortest
• problems solution on solutions
• solved time (msec) for
• Blackbox 10 3171 3 6
• (ATT Labs)
• HSP 9 25875 1 5
• (Venezuela)
• IPP 8 (11) 11036 1(3) 6(8)
• (Germany)
• STAN 7 20947 5 4
• (UK)

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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 MDPs of A (Geffner),
  Graphplan (Blum), SATPLAN (Littman)

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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

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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)