1. Pareto Coevolution Presented by KC Tsui Based on [1]

2. 2 Sorting Networks and MOO First work on coevolution with host-parasite model and two independent evolving but interacting gene pool –sorting networks (SNs) and test cases (TCs) Two fitness functions –SN: score according to number of test cases it succeeded in handling –TC: score according to number of failed SNs that tests on it In MOO, a pareto front defines a set of solutions that have the same fitness according to a aggregated measure of all objectives

3. 3 Motivations Coevolutionary systems plays an arms race game and provides a task for each other to tackle Each system requires the ability to dynamically adjust the learning environment There is no guarantee that coevolution will lead to effective learning Borrow idea from multi-objective optimization to formulate the task to be learned

4. 4 Search as Teaching and Learning Search involve a fitness landscape, but can be dynamically changed according to different objectives Teachers: create a search gradient Learners: following a search gradient A good teacher is one that is able to identify some knowledge ‘gap’ in some learners A good learner is one that has learned the tasks set by some teachers Evolution: The process of variation to discover better teachers and students

5. 5 Learning Pareto dominance, commonly used in MOO, is used to obtain a rank among the population concerned Learner x (pareto) dominates learner y iff G x,w > G y,w and G x,v > G y,v, G is a payoff matrix and w,v are teachers x and y are mutually non-dominating iff G x,w > G y,w and G x,v < G y,v

6. 6 Learning (cont.) Learning: a recursive process of identifying the non- dominated learners, exclude them from the population and start over again (find the pareto layers) –Pareto layer F n is less broad in competence than some learners in F n-1 –Every learner in F n-1 can do something better than some other learner in F n Ranking is done by some kind of tournament

7. 7 Teaching Given the payoff matrix G (row=learners; columns=teachers) for assessing student performance, transform it to become a student dominance matrix M (row=teachers, column=pair of students) for assessing teacher performance Score of a teacher j is –i.e. the value of a learner pair across the learners distinguished by j discounted by total number of teachers that distinguish it –j distinguish x from y if G x,j > G y,j

8. 8 Results Second best performance in the majority problem for cellular automata Similar idea has been applied to game strategy discovery [2]

9. 9 Discussion Pros –Smooth divide-and-conquer strategy Cons –Payoff matrix G (and hence M) is not always readily available or computed easily –Requires a lot of function evaluations

10. 10 References 1.Sevan G. Ficici and Jordan B. Pollack, Pareto Optimality in Coevolutionary Learning, Computer Science Technical Report CS-01-216, University of Brandeis.Pareto Optimality in Coevolutionary Learning 2.J. Noble and R.A. Watson, Pareto coevolution: Using performance against coevolved opponents in a game as dimensions for Pareto selection, in Proceedings of the Genetic and Evolutionary Computation Conference, GECCO-2001, pp. 493-500. Morgan Kauffman, San Francisco.Pareto coevolution: Using performance against coevolved opponents in a game as dimensions for Pareto selection