1. Planning
CSE 573
A handful of GENERAL SEARCH TECHNIQUES lie at the heart of practically all work in AI
We will encounter the SAME PRINCIPLES again and again in this course, whether we are talking about
GAMES
LOGICAL REASONING
MACHINE LEARNING
These are principles for SEARCHING THROUGH A SPACE OF POSSIBLE SOLUTIONS to a problems.

2. Logistics PS1 Due Sat Reading Office Hours Midterm Tues 11/11
Chapters 7,8 & 11 (up thru 11.2)
Office Hours
Wed 4:30
Or after most classes
Or me
Midterm Tues 11/11
© Daniel S. Weld

3. Knowledge Representation & Inference
573 Topics
Reinforcement
Learning
Supervised
Learning
Planning
Knowledge Representation & Inference
Logic-Based
Probabilistic
Search
Problem Spaces
Agency
© Daniel S. Weld

4. Ways to make “plans” Generative Planning Case-Based Planning
Reason from first principles (knowledge of actions)
Requires formal model of actions
Case-Based Planning
Retrieve old plan which worked on similar problem
Revise retrieved plan for this problem
Reinforcement Learning
Act ”randomly” - noticing effects
Learn reward, action models, policy
© Daniel S. Weld

5. Generative Planning Input Output
Description of (initial state of) world (in some KR)
Description of goal (in some KR)
Description of available actions (in some KR)
Output
Controller
E.g. Sequence of actions
E.g. Plan with loops and conditionals
E.g. Policy = f: states -> actions
© Daniel S. Weld

6. Input Representation Description of initial state of world
E.g., Set of propositions:
((block a) (block b) (block c) (on-table a) (on-table b) (clear a) (clear b) (clear c) (arm-empty))
Description of goal: i.e. set of worlds or ??
E.g., Logical conjunction
Any world satisfying conjunction is a goal
(and (on a b) (on b c)))
Description of available actions
© Daniel S. Weld

7. Simplifying Assumptions
Environment
Static
vs.
Dynamic
Fully Observable
Partially
Observable
Deterministic
Stochastic
Instantaneous
Durative
Full vs. Partial satisfaction
Perfect
Noisy
What action next?
Percepts
Actions
© Daniel S. Weld

8. Classical Planning Environment Static Instantaneous Deterministic
Perfect
Fully Observable
Full Oi
(prec)
(effects)
I = initial state G = goal state
[ I ] Oi Oj Ok Om
[ G ]
© Daniel S. Weld

9. Planning Outline The planning problem Representation As Search
Forward
Regression
Heuristics
Compilation to SAT
Graphplan
Reachability analysis & heuristics
Planning under uncertainty
© Daniel S. Weld

10. How Represent Actions? Simplifying assumptions STRIPS representation
Atomic time
Agent is omniscient (no sensing necessary).
Agent is sole cause of change
Actions have deterministic effects
STRIPS representation
World = set of true propositions
Actions:
Precondition: (conjunction of literals)
Effects (conjunction of literals)
© Daniel S. Weld

11. How Encode STRIPS  Logic ?
© Daniel S. Weld

12. Time in STRIPS Representation
Action = function: worldState worldState
Precondition
says where function defined
Effects
say how to change set of propositions a
north11 W0 W1
Note: strips doesn’t
allow derived effects;
you must be complete!
effect: (and (agent-at 1 2)
(not (agent-at 1 1)))
north11
precond: (and (agent-at 1 1)
(agent-facing north))
© Daniel S. Weld

13. } Action Schemata Instead of defining: Define a schema:
pickup-A and pickup-B and …
Define a schema:
(:operator pick-up
:parameters ((block ?ob1))
:precondition (and (clear ?ob1)
(on-table ?ob1)
(arm-empty))
:effect (and (not (clear ?ob1))
(not (on-table ?ob1))
(not (arm-empty))
(holding ?ob1)))
Note: strips doesn’t
allow derived effects;
you must be complete! }
© Daniel S. Weld

14. Time Arguments in Logic
Initial Conditions
Goal
On(a, b, 0)
Have(bluePaint, 0)
Red(a, 0)
On(b,a, ?)
Blue(a, ?)
Closed World Assumption
© Daniel S. Weld

15. Planning Outline The planning problem Representation As Search
Forward
Regression
Heuristics
Compilation to SAT
Graphplan
Reachability analysis & heuristics
Planning under uncertainty
© Daniel S. Weld

16. Planning as Search Nodes Arcs Initial State Goal State World states
Action executions
The state satisfying the complete description of
the initial conds
Any state satisfying the goal propositions
© Daniel S. Weld

17. Forward-Chaining World-Space Search
Initial
State
Goal
State A C B A B C
© Daniel S. Weld

18. Backward-Chaining Search Thru Space of Partial World-States
Problem: Many possible goal states are equally acceptable.
From which one does one search? D C B A E
Initial State is completely defined
* * * C B A D E C D A B E
© Daniel S. Weld

19. Planning as Search - Backward
Nodes
Arcs
Initial State
Goal State
A conjunctive goal (“set of goals”)
Regression of goal through action defn
The goal of the planning problem
A set of goals  the planning problem’s initial description
© Daniel S. Weld

20. Represents a set of world states Represents a set of world states
Regression
Regressing a goal, G, thru an action, A
Yields the weakest precondition G’
Such that: if G’ is true before A is executed
G is guaranteed to be true afterwards A G’ G
precond
effect
Represents a set of world states
Represents a set of world states
© Daniel S. Weld

21. Regression Example A G G’ Disjunction  preconditions precond effect
(and (clear C)
(on-table C)
(arm-empty)
(on A B))
(and (holding C)
(on A B))
pick-up :parameters ((block ?ob1))
:precondition (and (clear ?ob1)
(on-table ?ob1)
(arm-empty))
:effect (and (not (clear ?ob1))
(not (on-table ?ob1))
(not (arm-empty))
(holding ?ob1)))
Disjunction
 preconditions
© Daniel S. Weld

22. Conditional Effects
© Daniel S. Weld

23. Regressing Conditional Effects
precond
effect
(and (at briefcase bank)
(in keys briefcase)
(not (in paycheck briefcase))
(at paycheck bank))
(and (at keys home)
(at paycheck bank))
bank
home
© Daniel S. Weld

24. Heuristics
© Daniel S. Weld