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 not optimal), shorter sum.

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* – Example 4 3 2 1 GOAL 5 START 6 7 8

A* – Example 4+1 3 2 1 GOAL 5 START 4 6+1 7 6 8

A* – Example 4+1 3+2 2 1 GOAL 5 START 4 3 6+1 7 6 8

A* – Example 4+1 3+2 2+3 1 GOAL 5 START 4 3 2 6+1 7 6 8

A* – Example 4+1 3+2 2+3 1 GOAL 5 START 4 3+4 2 6+1 3 7 6 8

A* – Example 4+1 3+2 2+3 1 GOAL 5 START 4 3+4 2 6+1 4+5 3 7 6 8

A* – Example 4+1 3+2 2+3 1 GOAL 5 START 4 3+4 2 6+1 4+5 3 7+2 6 8 7

A* – Example 4+1 3+2 2+3 1 GOAL 5 START 4 3+4 2 6+1 4+5 3 7+2 6 8+3 7

A* – Example 4+1 3+2 2+3 1 GOAL 5 START 4 3+4 2 6+1 4+5 3+6 7+2 6 5+6 GOAL 5 START 4 3+4 2 6+1 4+5 3+6 7+2 6 5+6 3 8+3 7

A* – Example 4+1 3+2 2+3 1 GOAL 5 START 4 3+4 2 6+1 4+5 3+6 2+7 7+2 6 GOAL 5 START 4 3+4 2 6+1 4+5 3+6 2+7 7+2 6 5+6 4+7 3 8+3 7

A* – Example 4+1 3+2 2+3 1 GOAL 5 START 4 3+4 2 1+8 6+1 4+5 3+6 2+7 GOAL 5 START 4 3+4 2 1+8 6+1 4+5 3+6 2+7 7+2 6 5+6 4+7 3+8 8+3 7

A* – Example 4+1 3+2 2+3 1 0+9 GOAL 5 START 4 3+4 2 1+8 6+1 4+5 3+6 2+7 7+2 6 5+6 4+7 3+8 8+3 7

A* – Example 4+1 3+2 2+3 1 0+9 GOAL 5 START 4 3+4 2 1+8 6+1 4+5 3+6 2+7 7+2 6 5+6 4+7 3+8 8+3 7

A* – Example 4+1 3+2 2+3 1 0+9 GOAL 5 START 4 3+4 2 1+8 6+1 4+5 3+6 2+7 7+2 6 5+6 4+7 3+8 8+3 7

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* – Example 4 START 3 2 1 GOAL 5 6 7 8

LRTA* – Example 4 START 3 2 1 GOAL 5 6 7 8

LRTA* – Example 8 START 7 6 1 GOAL 5 2 4 3

LRTA* – Example 10 START 11 12 1 GOAL 9 2 8 3 7 6 5 4

LRTA* – Example 10 START 11 12 1 GOAL 9 2 8 3 7 6 5 4

LRTA* – Example 10 START 11 12 1 GOAL 2 3 9 6 5 4 8 7

LRTA* – Example 10 START 11 12 1 GOAL 2 3 9 6 5 4 8 7

LRTA* – Example 10 START 11 12 1 GOAL 2 3 9 6 5 4 8 7

LRTA* – Example 10 START 11 12 1 GOAL 2 3 9 6 5 4 8 7

LRTA* – Example 10 START 11 12 1 GOAL 2 3 9 6 5 4 8 7

LRTA* – Example 10 START 11 12 1 GOAL 2 3 9 6 5 4 8 7

LRTA* – Example 10 START 11 12 1 GOAL 2 3 9 6 5 4 8 7

LRTA* – Example 10 START 11 12 1 GOAL 2 3 9 6 5 4 8 7

LRTA* – Example 10 START 11 12 1 GOAL 2 3 9 6 5 4 8 7

LRTA* – Example 10 START 11 12 1 GOAL 2 3 9 6 5 4 8 7

LRTA* – Example 10 START 11 12 1 GOAL 2 3 9 6 5 4 8 7

LRTA* – Example, search restarted 10 START 11 12 1 GOAL 2 3 9 6 5 4 8 7

LRTA* – Example, search restarted 10 START 13 12 1 GOAL 11 2 3 9 6 5 4 8 7

LRTA* – Example, search restarted 10 START 13 12 1 GOAL 11 2 3 9 6 5 4 8 7

LRTA* – Example, search restarted 10 START 13 12 1 GOAL 11 2 3 9 6 5 4 8 7

LRTA* – Example, search restarted 10 START 13 12 1 GOAL 11 2 3 9 6 5 4 8 7

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.