Agent-Centered Search

Mitja Luštrek

Department of Intelligent Systems,Jožef Stefan Institute

Introduction Setting: mobile agent (robot) in an known/unknown

environment (labyrinth with/without map). Objective: to reach the goal from the starting position in as

short time as possible. Two phases:

planning of the path, execution of the plan.

Traditional search: first planning of the whole path, then execution of the plan.

Agent-centered search: planning of the beginning of the path from the starting position, execution of the partial plan, planning from the new starting position...

Why Agent-Centered Search Planning long in comparison to execution:

environment very large, environment not wholly known, environment changing.

Agent must act in real time.

Results: shorter

planning, longer

execution(path notoptimal),

shortersum.

Traditional Search – A* Multiple paths from the starting position. Agent keeps expanding the most promising path until the

goal is reached. Evaluation function for path ending in position n:

f (n) = g (n) + h (n) g (n) ... the length of the shortest path found so far from

the starting position to n; h (n) ... heuristic evaluation of the length of the shortest

path from n to the goal. If h (n) is admissible (optimistic – always smaller or equal to

the length of the shortest path from n to the goal), A* finds the shortest path.

A* – Example The agent’s environment is divided into squares, some of

them impassable. The agent can move up, down, left and right. The distance between adjacent squares is 1. h (n) is the Manhattan distance from n to the goal.

A* – Example4 3 2 1 0

GOAL

5START

4 3 2 1

6 5 4 3 2

7 6 5 4 3

8 7 6 5 4

A* – Example4+1 3 2 1 0

GOAL

5START

4 3 2 1

6+1 5 4 3 2

7 6 5 4 3

8 7 6 5 4

A* – Example4+1 3+2 2 1 0

GOAL

5START

4 3 2 1

6+1 5 4 3 2

7 6 5 4 3

8 7 6 5 4

A* – Example4+1 3+2 2+3 1 0

GOAL

5START

4 3 2 1

6+1 5 4 3 2

7 6 5 4 3

8 7 6 5 4

A* – Example4+1 3+2 2+3 1 0

GOAL

5START

4 3+4 2 1

6+1 5 4 3 2

7 6 5 4 3

8 7 6 5 4

A* – Example4+1 3+2 2+3 1 0

GOAL

5START

4 3+4 2 1

6+1 5 4+5 3 2

7 6 5 4 3

8 7 6 5 4

A* – Example4+1 3+2 2+3 1 0

GOAL

5START

4 3+4 2 1

6+1 5 4+5 3 2

7+2 6 5 4 3

8 7 6 5 4

A* – Example4+1 3+2 2+3 1 0

GOAL

5START

4 3+4 2 1

6+1 5 4+5 3 2

7+2 6 5 4 3

8+3 7 6 5 4

A* – Example4+1 3+2 2+3 1 0

GOAL

5START

4 3+4 2 1

6+1 5 4+5 3+6 2

7+2 6 5+6 4 3

8+3 7 6 5 4

A* – Example4+1 3+2 2+3 1 0

GOAL

5START

4 3+4 2 1

6+1 5 4+5 3+6 2+7

7+2 6 5+6 4+7 3

8+3 7 6 5 4

A* – Example4+1 3+2 2+3 1 0

GOAL

5START

4 3+4 2 1+8

6+1 5 4+5 3+6 2+7

7+2 6 5+6 4+7 3+8

8+3 7 6 5 4

A* – Example4+1 3+2 2+3 1 0+9

GOAL

5START

4 3+4 2 1+8

6+1 5 4+5 3+6 2+7

7+2 6 5+6 4+7 3+8

8+3 7 6 5 4

A* – Example4+1 3+2 2+3 1 0+9

GOAL

5START

4 3+4 2 1+8

6+1 5 4+5 3+6 2+7

7+2 6 5+6 4+7 3+8

8+3 7 6 5 4

A* – Example4+1 3+2 2+3 1 0+9

GOAL

5START

4 3+4 2 1+8

6+1 5 4+5 3+6 2+7

7+2 6 5+6 4+7 3+8

8+3 7 6 5 4

Agent-Centered Search Agent searches local search space, which is a part of the

whole space centered on the agent. Makes some steps in the most promising direction. Repeats until it reaches the goal.

In game playing (chess), the search is performed around the current position: the whole game tree is too large (environment very

large), it is not known in which part of the space the game will

head (environment not wholly known). This is an example of two-agent search, I focus on single-

agent search.

LRTA* Learning real-time A*

Agent updates h (l) for every point l in the local search space:h (l) = min (d (l, n) + h (n)) d (l, n) ... the length of the shortest path from l to a point

n just outside the local search space, h (n) ... heuristic evaluation of the length of the shortest

path from n to the goal. Moves to the adjacent position l with the lowest h (l). Repeats until the goal is reached.

Updated h (l) can be used in later searches.

LRTA* – Example Same setting as for A*. The local search space is 3 x 3 squares centered on the

agent.

LRTA* – Example4START

3 2 1 0GOAL

5 4 3 2 1

6 5 4 3 2

7 6 5 4 3

8 7 6 5 4

LRTA* – Example4START

3 2 1 0GOAL

5 4 3 2 1

6 5 4 3 2

7 6 5 4 3

8 7 6 5 4

LRTA* – Example8START

7 6 1 0GOAL

7 6 5 2 1

6 5 4 3 2

7 6 5 4 3

8 7 6 5 4

LRTA* – Example10START

11 12 1 0GOAL

9 10 11 2 1

8 9 10 3 2

7 6 5 4 3

8 7 6 5 4

LRTA* – Example10START

11 12 1 0GOAL

9 10 11 2 1

8 9 10 3 2

7 6 5 4 3

8 7 6 5 4

LRTA* – Example10START

11 12 1 0GOAL

11 12 11 2 1

10 11 10 3 2

9 6 5 4 3

8 7 6 5 4

LRTA* – Example10START

11 12 1 0GOAL

11 12 11 2 1

10 11 10 3 2

9 6 5 4 3

8 7 6 5 4

LRTA* – Example10START

11 12 1 0GOAL

11 12 11 2 1

10 11 10 3 2

9 6 5 4 3

8 7 6 5 4

LRTA* – Example10START

11 12 1 0GOAL

11 12 11 2 1

10 11 10 3 2

9 6 5 4 3

8 7 6 5 4

LRTA* – Example10START

11 12 1 0GOAL

11 12 11 2 1

10 11 10 3 2

9 6 5 4 3

8 7 6 5 4

LRTA* – Example10START

11 12 1 0GOAL

11 12 11 2 1

10 11 10 3 2

9 6 5 4 3

8 7 6 5 4

LRTA* – Example10START

11 12 1 0GOAL

11 12 11 2 1

10 11 10 3 2

9 6 5 4 3

8 7 6 5 4

LRTA* – Example10START

11 12 1 0GOAL

11 12 11 2 1

10 11 10 3 2

9 6 5 4 3

8 7 6 5 4

LRTA* – Example10START

11 12 1 0GOAL

11 12 11 2 1

10 11 10 3 2

9 6 5 4 3

8 7 6 5 4

LRTA* – Example10START

11 12 1 0GOAL

11 12 11 2 1

10 11 10 3 2

9 6 5 4 3

8 7 6 5 4

LRTA* – Example10START

11 12 1 0GOAL

11 12 11 2 1

10 11 10 3 2

9 6 5 4 3

8 7 6 5 4

LRTA* – Example, search restarted

10START

11 12 1 0GOAL

11 12 11 2 1

10 11 10 3 2

9 6 5 4 3

8 7 6 5 4

LRTA* – Example, search restarted

10START

13 12 1 0GOAL

11 12 11 2 1

10 11 10 3 2

9 6 5 4 3

8 7 6 5 4

LRTA* – Example, search restarted

10START

13 12 1 0GOAL

11 12 11 2 1

10 11 10 3 2

9 6 5 4 3

8 7 6 5 4

LRTA* – Example, search restarted

10START

13 12 1 0GOAL

11 12 11 2 1

10 11 10 3 2

9 6 5 4 3

8 7 6 5 4

LRTA* – Example, search restarted

10START

13 12 1 0GOAL

11 12 11 2 1

10 11 10 3 2

9 6 5 4 3

8 7 6 5 4

LRTA* – Extensions Unknown environment, agent’s sensory range very limited:

minimal local search space (only the agent’s position). Unknown environment, the task is exploration:

maximal local search space (all known positions), agent moves towards the closest unvisited position;

node counting – agent moves towards the least frequently visited adjacent position.

Unknown starting position: minimize the worst-case execution time; min-max LRTA*:

a minimax tree is built around the agent’s position; the agent’s actions minimize the length of the path to

the goal; possible configurations of the environment maximize

the length of the path to the goal.

Search Pathology Minimax [Nau, 1979; Beal, 1980; Bratko & Gams, 1982; etc.]:

in practice, the more moves ahead one searches, the better he plays;

in theory, under apparently reasonable conditions, the more moves ahead one searches, the worse he plays;

this is caused by minimax amplifying the heuristic evaluation used in the leaves of the game tree.

Agent-centered search [Bulitko et al., 2003]: one would expect that the larger the local search space,

the more likely an agent is to choose the optimal path; in some cases, the larger the local search space, the less

likely an agent is to choose the optimal path.