AI Automated Planning In A Nutshell

1. Technion – Israel Institute of Technology Industrial Engineering & Management AI Automated Planning In A Nutshell Vitaly Mirkis March 4, 2013 Netanya Academic College Acknowledgments: Some slides are based slides of Prof. Carmel Domshlak and of Dr. Michael Katz

2. Planning “Adventure is just bad planning”  Roald Amundsen “Planning is the art and practice of thinking before acting: of reviewing the courses of action one has available and predicting their expected (and unexpected) results to be able to choose the most beneficial course of action, with respect to ones goals.” Patrik Haslum

3. Planning in today’s industry • Planning in today’s Industry: NASA’s mars rover, Hubble Space Telescope etc.

4. UAV Cooperative Mission x1 x2 x3 x4 x5 x6 x7 x8 x9 • An UAV is able to move to some of its neighbor cells. • An UAV is able to photograph a object in current cell. y1 y2 y3 y4 y5 y6 • The goal is to photograph all colored objects and return to its initial position.

5. UAV Cooperative Mission x1 x2 x3 x4 x5 x6 x7 x8 x9 y1 y2 y3 y4 y5 y6

6. Planning software principle • A Planning software (planner) execution flow description: • A given task is translated (compiled) to a planning problem. • Planning problem  supplied to a solver (planner). • The solution λ is also a solution for the task (or can be easily translated to such). task  λ Translator Planner

7. Planning software principle x1 x2 x3 x4 x5 x6 x7 x8 • A Planning software (planner) execution flow description: • A given task is translated (compiled) to a planning problem. • Planning problem  supplied to a solver (planner). • A solution λ is also a solution for the task (or can be easily translated to such). • Hence, it is sufficient to consider any convenient task, for planning principles introduction. y1 y2 y3 y4 y5 y6 task  λ Translator Planner Solution λ’ ’

8. Planning in blocks world Initial state Goal state Game rules: • No two blocks can be on top of the same block • Block can’t be on top of two blocks • Exact location on table or on block doesn’t matter B ? R R G Y B G Y Y G B B Y G

9. Planning in blocks world Initial state on-table(Y), clear(Y), on-table(G), on(R, G), on(B, R), clear(B) Goal state on-table(G), clear(G), on-table(Y), clear(Y), clear(R), on(R, B), on-table(B) B R R G Y B G Y on(i,j), on-table(i), clear(i)

10. Planning in blocks world Initial state Goal state Actions defined with: • Move-Block(i)-from-Block(j)-to-Table • Move-Block(i)-from-Table-to-Block(j) • Move-Block(i)-from-Block(j)-to-Block(k) B ? R R G Y B G Y

11. Planning in blocks world • Appling an action examples: = Move-Block(B)-from-Block(R)-to-Table: • = { clear(B) , on(B,R) } • = { on(B,R) } • = { on-table(B) , clear(R) } B R G Y

12. Planning in blocks world Initial state Goal state R B G R Y B G Y B R R G Y G = Move-Block(B)-from-Block(R)-to-Table = Move-Block(R)-from-Block(G)-to-Block(Y) = Move-Block(G)-from-Table-to-Block(B) = Move-Block(R)-from-Block(Y)-to-Block(G)

13. Planning in blocks world: states space • Plan as graph path: • Optimal plan as shortest graph path: • How to solve (= find a plan) the described problem? • Partial transition graph for 4 blocks: Y R R B B G Y B G G B G Y R R R B Y G Y R B G Y R B G Y R Y R B G B G Y Y B R G

14. How hard Planning is? • How to find an optimal solution? • Use Dijkstra’s to find optimal solution. • The problem has 73 states • For the general case? • The traversing time for all problem’s states is growing very fast with problem size (planning is hard,both satisficing and optimal) • State space of 100 blocks problem have more states than number of atoms in the universe (> 1087)  visiting all states is infeasible approach. • Yet, these problems are solved somehow. How? Y R R B B G Y B G G B G Y R R R B Y G Y R B G Y R B G Y R Y R B G B G Y Y B R G

15. - search algorithm • Good news : may visit only a subset of the problem states during its run. • Bad news : In the worst case, running time is still slow1. • Also known as Heuristic search. 1 Exponential in the problem size.

16. The intuition behind heuristic search • h : An oracle estimation of the coast of reaching the goal from a given state. • Partial transition graph for 4 blocks: Y R R B B G Y B G G B G Y R R R B Y G Y h = 1 R B G Y R B G Y R Y R ? B G B G Y h = 2 ? ? h = 2 h = 3 Y B R G

17. Heuristic search basic model • Heuristic search composed of two major, (usually) independent, parts: • State search algorithm • Heuristic evaluation function (h) • Search dynamics: The search algorithm uses a heuristic function to evaluate state to decide which state visit next. • Each part developed independently.

18. Heuristic function (h) • Intuitively, a heuristic function is “an estimation” or “a rule of thumb” of the real solution. • All heuristic functions for our today’s purpose are estimations of a solution (plan) cost. Definition: • A heuristic function maps a search state (node) into a non-negative real number. • A heuristic function called admissible if it never overestimate real state’s cost.

19. The intuition behind heuristic search • h : The coast of reaching the goal from the current state is no less than h (h  real cost). • Partial transition graph for 4 blocks: Y R R B B G Y B G G B G Y R R R B Y G Y h = 1 R B G Y R B G Y R Y R ? B G B G Y h = 2 ? ? h = 3 Y B R G

20. - search algorithm guided by an admissible heuristic • Good news : may visit only a subset of the problem states during its run. • Bad news : In the worst case, running time is still slow1. Theorem: (Hart, Nilsson & Raphael, 1968): guided with an admissible heuristic, guarantied to find an optimal path (plan). 1 Exponential in the problem size.

21. Constructing a heuristic function • The most common method to find a “good” heuristic is via a solution to an “easier” version of the problem. • Such easier problem can be obtained from the given problem, via two common techniques: • Relaxation: ignoring some constrains of the given problem. The outcome often called relaxed problem. • Abstraction: use a smaller version of the given problem, small enough to traverse all its states. • Practically, an “easy to compute” heuristics are preferable.

22. Relaxed Planning in blocks world • Each action will modified as follows: = Move-Block(B)-from-Block(R)-to-Table: • = { clear(B) , on(B,R) } • = { on(B,R) } • = { on-table(B) , clear(R) } B B R G Y

23. Delete free (relaxation) • One such relaxation technique named delete free. • Once fact achieved, it can’t be deleted: Initial state Goal R B B B G Y B R R R R R G Y • Satisficing / parallel plan can be found in polynomial time (finding an optimal plan is still hard)

24. Ignore all but the goals (abstraction) • One method can be to achieve an abstraction by choosing only the goal blocks: • Initial state: • Goal state: • But, how can it be utilized? B R R R G Y B B G Y B R

25. State of the art heuristics Delete relaxation: • (Hoffman & Nebel, 2001) • and (Bonet & Geffner, 2001) • (Hoffman & Nebel, 2001) • (M. & Domshlak, 2007) Abstractions: • PDBs (Edelkamp, 2001; Haslum et al., 2005, 2007) • Merge & Shrink (Helmert et al., 2007) • Implicit Abstractions (Katz & Domshlak, 2008, 2010) Landmarks: • Landmark count (Hoffman et al., 2004) • and (Karpas& Domshlak, 2009) • LM-cut (Helmert & Domshlak, 2009)

26. Beyond classical planning Planning variations: • Oversubscription planning • Given a plan cost limitation, achieve the most valuable goals. • Probabilistic planning • Some of the action’s effects are stochastic. • Planning with partial observability • The initial state is non-deterministic.

27. Summary • Planning is a model-based approach to a machine autonomous behavior, • Task independent problem solver, • Wide researchers interest, • Continue grow in usage in industrial applications.

28. The end Thank you

29. Appendix

30. Planning Model Definition: • Finite and discrete state space • Initial state • A set of goal states • A set of actions, and denotes a set of actions applicable in state • A deterministic transition function for • Non negative action costs A solution is a sequence of applicable actions that creates a path from to a state in . A solution is optimal if it minimizes actions costs.

31. STRIPS: A Formal Planning Language Definition: A STRIPS Planning task is a 5-tuple : • : finite set of atoms (boolean variables) • : finite set of operators (actions), each action is a 3-tuple : while Add/Delete/Preconditions are subsets of atoms. • : operator cost function ( ) • : Initial state (subset of atoms) • : goal description (subset of atoms)

32. From Language to Model A STRIPS Planning task defines a state model where: • the states in are collection of atoms from • the initial state is • the goal states are such that • the actions are the operators in such that • the next state is • action cost (Optimal) Solution of P is (optimal) solution of