An Adversarial Planning Approach to Go

1. Paper Authors: S. Willmott, J. Richardson, A. Bundy, J. Levine Presentation Author: A. Botea An Adversarial Planning Approach to Go

2. Outline • Motivation • Data Driven Search vs. Goal Driven Driven • HTN Planning • Adversarial Planning • Example • GOBI - An Adversarial Go Planner • Experimental Results • Discussion & Conclusion

3. Motivation • Classical Heuristic Search: • Successful in games such as Chess, Checkers, Othello... • Not enough in Go SO... • Other approaches (e.g., planning) should be tried

4. Data & Goals • Data Driven Search • Normal heuristic search framework • Search tree with game positions as nodes • Goal Driven Search • Agenda of abstract goals to be achieved • Search is focused on achieving a certain goal • HTN planning (single agent planning) • Adversarial planning (multi-agent planning)

5. Example - Rush Hour • Data driven approach: • (ID)A* • Goal driven approach: • Get red car out • Move blue car • Move green car • Move yellow car • Move light-blue car • ... http://www.eagle-i.com/JAVA/rush.html

6. HTN Planning • Hierarchical planning approach • Three types of objects: • Abstract goals • Atomic operators • Plan schemas • Used to expand abstract goals • G = G1 & G2 & G3 • Use objects to build an AND/OR tree

7. HTN Planning Tree • AND nodes are abstract goals • OR nodes are schemas • Operators can modify current world (i.e., change value of low-level features)

8. Adversarial Planning • Extends HTN planning to a 2- player framework • Two agents: Alpha & Beta • Each has an agenda of open goals • Initialized with abstract goals such as win or kill or live; • Take control over resources alternatively • Agents' actions change the world

9. Flow of Resource Control

10. Plan Refinement

11. Contingence Tree

12. Example • Alpha (black): • Kill-group • Surround-group & • Squeeze-space & • Prevent-eye-formation • Beta (white): • Save-group • Make-eye-space • Make-eyes

13. GOBI - An Adversarial Go Planner • 1400 lines of code in Common Lisp • Focused on life & death • Knowledge base: 45 goals at 5 different abstraction levels • Test suite: 85 problems from Graded Go Problems for Beginners, vol I • GOBI solves 74% of them

14. Knowldge Base - Example

15. Goal Driven Approach - Advantages • Representation and communication of domain knowledge • Easy to encode knowledge such as: • death lies in the hane or • Don't push along the fifth line • Search properties • No heuristic evaluator needed • Quiesence is defined automatically • Heuristically bad moves (e.g., sacrifices) are not discriminated • Search is focused on well defined goals

16. Goal Driven Approach - Disadvantages • Encoding strategies as goal decompositions is costly • Hard to express certain knowledge • e.g., how to express patterns in terms of abstract goals? ==> combination of data-driven and goal-driven approaches is a good idea • Less efficient than Data Driven Approach in domains with shallow search trees

17. Conclusion • Presented an adversarial planning framework as an alternative to data-driven solving approach • Application domain: Go • GOBI - tsume-go planner based on this framework