1. Towards Equilibrium Transfer in Markov Games 胡裕靖 2013-9-9

2. Outline  Background  Preliminary Ideas  Some Results

3. Background

4. Multi-agent Reinforcement Learning Single-agent RL: Mountain Car Path finding RL in multi-agent tasks Robot Soccer IKEA furniture robot

5. Markov Games Agent take joint actions from one agent to more than one

6. Equilibrium-based MARL Some equilibrium solution concepts in game theory can be adopted

7. Our Previous Work  Equilibrium-based MARL: Multi-agent reinforcement learning with meta equilibrium [] Multi-agent reinforcement learning by negotiation with unshared value functions [] Focusing on combining MARL with equilibrium solution concepts  Problematic issues: Equilibrium computing is complicated and time consuming A new complexity class: TFNP! [] For tasks with many agents, equilibrium-based MARL algorithms may take too much time How to accelerate the learning process of equilibrium-based MARL?

8. Transfer Learning in RL Matthew E Taylor, Peter Stone. Transfer learning for reinforcement learning domains. Journal of Machine Learning Research, 2009. instance/policy/value function/model/… Alessandra Lazaric. Transfer in reinforcement learning: a framework and a survey. Reinforcement Learning, Springer, 2012. accelerate Reuse learnt knowledge

9. Transfer Learning in Markov Games? instance/policy/value function/model/… …… Why not transfer between these normal-form games within a Markov game? Inter-task transfer Inner-task transfer

10. Inner-task Transfer  Transfer equilibrium between similar normal-form games during learning in a Markov game: Reuse the computed equilibria in previous games Reducing learning time  Key problems: Which games are similar? For example: the games occur on different visits of a state How to transfer equilibrium?

11. Preliminary Ideas

12. Game Similarity  Games with the same action space?  Games with different action space?  Similarity payoff distance?  Equilibrium-based similarity or equilibrium-independent similarity? Drew Fudenberg and David M. Kreps. A theory of learning, experimentation and equilibrium in games. 1990.

13. Game Similarity Equilibrium-based similarity Equilibrium transfer Find equilibria of two games and compute the similarity Transfer seems senseless! Weird Cycle

14. Our Idea Transfer equilibrium between games which are thought to be similar. Evaluate how much the loss brought by equilibrium transfer is. Transfer is acceptable when there is a little loss. The two games are different only in one item.

15. Problem Definition Approximate Nash equilibrium

16. Problem Definition

17. A Naïve Transfer Method Direct Transfer

18. A Naïve Transfer Method

20. Some Results

21. Future Work  Some problems: Other transfer methods? Only Nash equilibrium? Equilibrium finding algorithms  Transfer between games with different action space  Transfer between games with different agent numbers  Game abstraction

22. Thanks!