Trading optimality for speed…

1. Trading optimality for speed… • The admissibility condition guarantees that an optimal path is found • In path planning a near-optimal path can be satisfactory • Try to minimise search instead of minimising cost: • i.e. find a near-optimal path (quickly)

2. CSC344: AI for GamesLecture 6Online and local search Patrick Olivier p.l.olivier@ncl.ac.uk

3. = - + f ( n ) ( 1 w ) g ( n ) wh ( n ) w Weighting… • w = 0.0 (breadth-first) • w = 0.5 (A*) • w = 1.0 (best-first, with f = h) • trading safety/optimality for speed • weight towards h when confident in the estimate of h

4. Local search algorithms • In many optimisation problems, paths are irrelevant; goal state the solution • State space = set of "complete" configurations • Find configuration satisfying constraints, e.g., n-queens: n queens on an n ×n board with no two queens on the same row, column, or diagonal • Use local search algorithms which keep a single "current" state and try to improve it

5. Hill-climbing search • "climbing Everest in thick fog with amnesia” • we can set up an objective function to be “best” when large (perform hill climbing) • …or we can use the previous formulation of heuristic and minimise the objective function (perform gradient descent)

6. Local maxima/minina • Problem: depending on initial state, can get stuck in local maxima/minina 1/(1+H(n)) = 1/17 1/(1+H(n)) = 1/2 Local minima

7. Local beam search • Keep track of k states rather than just one • Start with k randomly generated states • At each iteration, all the successors of all k states are generated • If any one is a goal state, stop; else select the k best successors from the complete list and repeat.

8. Simulated annealing search • Idea: escape local maxima by allowing some "bad" moves but gradually decrease their frequency and range (VSLI layout, scheduling)

9. Simulated annealing example • Point feature labelling

10. Genetic algorithm search • A successor state is generated by combining two parent states • Start with k randomly generated states (population) • A state is represented as a string over a finite alphabet (often a string of 0s and 1s) • Evaluation function (fitness function). Higher values for better states. • Produce the next generation of states by selection, crossover, and mutation

11. Genetic algorithms in games • Computationally expensive so primarily offline form of learning • Cloak, Dagger & DNA (Oidian Systems) • 4 DNA strands defining opponent behaviour • between battles, opponents play each other • Creatures (Millennium Interactive) • Genetic algorithms to learning the weights in a neural network that defines behaviour

12. “Real-time” search concepts • In A* the whole path is computed off-line, before the agent walks through the path • This solution is only valid for static worlds • If the world changes in the meantime, the initial path is no longer valid: • new obstacles appear • position of goal changes (e.g. moving target)

13. “Real-time” definitions • Off-line (non real-time): the solution is computed in a given amount of time before being executed • Real-time: One move is computed at a time, and that move executed before computing the next • Anytime: the algorithm constantly improves its solution through time capable of providing “current best” at any time

14. Agent-based (online) search • For example: • mobile robot • NPC without perfect knowledge • agent that must act now with limited information • Planning and execution are interleaved • Could apply standard search techniques: • Best-first (but we know it is poor) • Depth-first (has to physically back-track) • A* (but nodes in the fringe are not accessible)

15. LRTA*: Learning Real-time A* • Augment hill-climbing with memory • Store “current best estimate” • Follow path based on neighbours’ estimates • Update estimates based on experience • Experience  Learning • Flatten out local maxima…

16. 1 1 1 1 1 1 1 1 1 1 2 4 1 9 9 3 4 9 1 8 8 8 2 4 2 4 1 3 4 5 5 9 8 1 4 1 5 9 8 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 LRTA*: example

17. Learning real-time A*