Presentation on artificial intelligence planing

1. Perspectives on Artificial
Intelligence Planning
Based on the research paper
by,
Professor H´ector Geffner

2. General problem solvers
A general problem solver is a program that accepts
high-level descriptions of problems and
automatically computes their solution

3. Problem solvers con.
Problem Solver
General modeling
Algorithms
language

4. What is planning?
Planning is a key area in Artificial Intelligence. In its
general form, planning is concerned with the
automatic synthesis of action strategies (plans)
from a description of actions, sensors, and goals.

5. Elements of Planning
1. Representation languages for describing
problems conveniently.
2. Mathematical models for making the different
planning tasks precise
3. Algorithms for solving these models effectively

6. Models
Models needed to define scope of a planner
• What is a planning problem
• What is a solution(plan)
• What is an optimal solution

7. Classical Planning
Classical planning can be understood in terms of
deterministic state models characterized by the following
elements
• A finite and discrete state space S,
• An initial situation given by a state s0 ∈ S,
• A goal situation given by a non empty set SG ⊆ S,
• Actions a(s) ⊆ A applicable in each state s ∈ S,
• A deterministic state transition function f(a, s) for a ∈
a(s)
• Positive action costs c(a, s) for doing action a in s.

8. Classical Planning con.

9. Planning with Uncertainty
Unlike in classical planning here states of the
system and that state transitions are non
deterministic so we have to define how uncertainty
is modeled. Also we have to take sensing and
feedback in to the account.

10. Modeling Uncertainty
• Pure non determinism
Uncertainty about the state of the world is
represented by the set of states S’ ⊆ S that are
deemed possible
• Probability
Represented by a probability distribution over S.

11. Modeling uncertainty in state
transitions

12. Planning under uncertainty
without feedback
In both above cases the problem of planning under uncertainty
without feedback reduces to a deterministic search problem in belief
space, a space which can be characterized by the following
elements.
• A space B of belief states over S,
• An initial situation given by a belief state b0 ∈ B,
• A goal situation given by a set of target beliefs BG
• Actions a(b) ⊆ A applicable in each belief state b
• Deterministic transitions b to ba for a ∈ a(b) givenby (1) and (2)
above
• Positive action costs c(a, b).

13. Planning with Sensing
With the ability to sense the world, the choice of
the actions depends on the observation gathered
and thus the form of the plans changes.

14. Planning with Sensing con.
Full-state Observability
In the presence of sensing, the choice of the action ai at time
i depends on all observations o0, o1, . . . , oi−1 gathered up to
that point.
Partial Observability
observations reveal partial information about the true state
of the world and it is necessary to model how the two are
related. The solution then takes the form of functions
mapping belief states into actions, as states are no longer
known and belief states summarize all the information from
previous belief states and partial observations

15. Planning with Sensing con.

16. Temporal Planning
Temporal models extend classical planning in a
different direction. This is a simple but general
model where actions have durations and their
execution can overlap in time.
• we assume a duration d(a) > 0 for each action
a, and a predicate comp(A) that defines when a
set of actions A can be executed concurrently.

17. Model for temporal planning
• Need to replace the single actions a in that
model by sets of legal actions.
{A0,A1,A2,…..}
• each set Ai start their execution at the same time
ti. The end or completion time of an action a in Ai
is thus ti + d(a) where d(a) is the duration of a.
• t0 = 0 and ti+1 is given by the end time of the first
action in A0, . . . , Ai that completes after ti.

18. Model for temporal planning
con.
• The initial state s0 is given, while si+1 is a function of
the state si at time ti and the set of actions Ai in the
plan that complete exactly at time t + 1; i.e.,
si+1 = fT (Ai, si).
• The state transition function fT is obtained from the
representation of the individual actions
• A valid temporal plan is a sequence of legal sets of
actions mapping the initial state into a goal state.

19. Model for temporal planning
con.

20. Temporal planning vs.
sequential planning
• Though the model for sequential planning and
the model for temporal planning both appear to
be close from a mathematical point of view they
are quite different from a computational point of
view.
• Heuristic search is probably the best current
approach for optimal and non-optimal sequential
planning, it does not represent the best
approach for parallel planning

21. Languages
In large problems, the state space and state
transitions need to be represented implicitly in a
logical action language, normally through a set of
(state) variables and action rules. A good action
language is one that supports compact encodings
of the models of interest.

22. Strips
• In AI Planning, the standard language for many
years has been the Strips language introduced in
1971 by Fikes & Nilsson.
• While from a logical point of view, Strips is a very
limited language, Strips is well known and helps
to illustrate the relationship between planning
languages and planning models, and to motivate
some of the extensions that have been
proposed.

23. Strips con.
Strips
State language
Operator language

24. Elements of Strips
• The Strips language L is a simple logical language
made up of two types of symbols: relational and
constant symbols. E.g.
on(a, b)
relational constant
symbol symbols
• In Strips, there are no functional symbols and the
constant symbols are the only terms.

25. Elements of Strips con.
• Atoms
combination p(t1, . . . , tk) of a relational symbol p
and a tuple of terms ti of the same arity as p.
• Operators
defined over the set of atoms in L. Each operator
op has a precondition, add, and delete lists
Prec(op), Add(op), and Del(op) given by sets of
atoms.

26. Planning problems in Strips
P = <A,O, I,G>
• A stands for the set of all atoms in the domain
• O is the set of operators
• I and G are sets of atoms defining the initial and
goal situations.

27. Planning problems in Strips con.
The problem P defines a deterministic state model
S(P)like below
• The states s are sets of atoms from A
• The initial state s0 is I
• The goal states are the states s such that G ⊆ s
• A(s) is the set of operators o ∈ O s.t. Prec(o) ⊆ s
• The state transition function f is such that
f(a, s) =s + add(a) − del(a) for a ∈ a(s)
• Costs c(a, s) are all equal to 1

28. Advanced languages
• Domain-independent planners with expressive state
and action languages like GPT (Bonet &
Geffner2000) and MBP (Bertoli et al. 2001) has been
introduced. both of them provide additional
constructs for expressing non determinism and
sensing.
• Knowledge-based planners has been introduced
which provide very rich modeling languages, often
including facilities for representing time and
resources

29. Computation
This relates to the algorithms and techniques
use to solve planning problems.

30. Heuristic Search
• Simple , powerful and explains success of recent
approaches
• Maps planning problems into search problems
• Explicitly searches state space with heuristic h(s) that
estimates cost from s to Goal
• Heuristic h extracted automatically from problem
representation
• Uses A*, IDA*…… etc to plan

31. Heuristic Functions
• Heuristic search depends on the choice of heuristic
function
• Heuristics derived as optimal cost function of relaxed
problems
• Simple relaxation used in planning
• Ignore delete lists
• Reduce large goal sets to subsets
• Ignore certain atoms

32. Additive Heuristic

33. Additive Heuristic
• Assume atoms are independent
• Heuristic not admissible (not lower bounded )
• Informative and fast
• Useful for optimal planning
• The heuristic h+(s) of a state is h+(G) where G is
the goal, and is obtained by solving the above
first equation with single shortest path
algorithms.

34. Fast Forward Heuristic
• Does not assume that atoms are independent
• Solve the relaxation suboptimally
• Extracts useful information for guiding hill
climbing search

35. Max Heuristic

36. Generalisation: hm heuristics
• For fixed m=1,2…. Assume cost of achieving set C
given by cost of most costly subset of size m
– For m=1 , hm = hmax
– For m=2 , hm = hG (Graphplan)
– For any m , hm admisible and polinomial

37. Pattern databases
• Project the state space S of a problem into a
smaller state space S’
• S’ can be solved optimally or exhaustively
• Heuristic h(s) for the original state space is
obtained from the solution cost h’∗(s’) of the
projected state s’ in the relaxed space.

38. Branching Scheme
• A branch is an object that specifies a linear
sequence of versions of an element
• Enable parallel development
• Usually seldom mentioned in texts
• But has very strong influence on performance

39. Types of branching
• Forward Branching
– Start from the initial state and go forward till the goal
state is found
• Backward Branching
– start from the goal state and go backward till the
initial state
• Other
– When both above methods do not workout

40. Classification in AI planners
• State space planners
– Progression and regression planning
– Search in the space of states
– Build plans from head or tail only
– Estimated cost consists of two parts
• the accumulated cost of the plan g(p) that depends on p
• the estimated cost of the remaining plan h(s) that depends
only on the state s obtained by progression or regression
– High branching factor

41. Classification in AI planning
• Partial –order planners
– Search in the space of plans
– The partial plan heads or tails can be suitably
summarized
– Useful for computing the estimated cost f(p) of the
best complete plans

42. Heuristics and branching
convergence
it should be possible to combine informative lower
bounds and effective branching rules, thus allowing
us to prune partial solutions p whose estimated
completion cost f(p) exceeds a bound B.

43. Search in Non-Deterministic Spaces
• Heuristic and constraint-based approaches are
not directly applicable to problems involving
non-determinism and feedback
• The solution of these problems is not a sequence
of actions but a function mapping states into
actions.
• Dynamic programming is used

44. Dynamic programming

45. Mathematics…… 

46. More Mathematics …….  
Bellman equations

47. DP features
• Works well for spaces containing large number of
states
• For larger spaces, the time and space
requirements of pure DP methods is expensive
• In comparison heuristic search methods for
deterministic problems that can deal with huge
state spaces provided a good heuristic function

48. Converging DP and Heuristic
methods
New strategies that integrate DP and heuristic
search methods have been proposed.
• Real time dynamic programming
• In every non-goal state s, the best action a according to the
heuristic is selected
• Heuristic value h(s) of the state s is updated using Bellman
equation.
• Then a random successor state is selected
• This process is repeated until the goal is reached