1. The normalized cell error for cell at time n |V(H c(1,1) )|=25 |E(H c(1,1) )|=40 |V(H c(2,1) )|=21 |E(H c(2,1) )|=24 |V(H c(3,1) )|=9 |E(H c(3,1) )|=8 |V(H c(1,2) )|=13 |E(H c(1,2) )|=12 |V(H c(2,2) )|=16 |E(H c(2,2) )|=16 |V(H c(3,2) )|=10 |E(H c(3,2) )|=10 |V(H c(1,3) )|=35 |E(H c(1,3) )|=32 |V(H c(3,3) )|=13 |E(H c(3,3) )|=16 Collectively Cooperative Learning: Learning Group Sizes in Computer Go Tae-Hyung “T” Kim Ganesh Kumar Venayagamoorthy Donald C. Wunsch II tk424@mst.edu gkumar@ieee.org dwunsch@mst.edutk424@mst.edugkumar@ieee.orgdwunsch@mst.edu Acknowledgement Authors would like to thank Intelligent Systems Center, Mary K. Finley Missouri Endowment, and National Science Foundation, contract number ECCS-0725382, for their financial support to perform this research. The authors also would like to thank Rui Xu, John Seiffertt, Sriram Chellapan and Sejun Kim for their insightful discussions. Introduction Collaborative learning is an educational approach that students team up to explore a question or create a meaningful project. Cooperative learning is a subset of collaborative learning to learn a subject in cooperation with team members. The students at different levels not only are responsible for learning the subject, but also help teammates to learn via interactions. They are individually accountable for their work and the work group as a whole is also assessed. Collectively cooperative learning (CCL) is a novel machine learning approach to learn a subject in cooperation with teams of learning agents. Both the individual and the group are assessed. The term collectively differentiates CCL from cooperative learning. Properties of CCL Goal-oriented. There is a goal each individual and team should learn. Independent. Each agent learns independently to meet the goal. Interactive. A team of learning agents cooperates to learn the goal. Adaptive. CCL can process various types of inputs. Scalable. CCL can deal with various sizes of the arena. Group size counting problem in computer Go A square lattice graph G=(V,E). The graph size set S of the graph G The size sn of a subgraph Hn=(Vn,En) The total number of subgraphs N in a graph G may vary. An autonomous processing unit (APU) learns the sub-graph size from zero- knowledge. (1) (Group size counting problem=a sub-problem in computer Go) | essential info. for judging the life and death of the group The proposed approaches Recursive approach Use function recursion giving a bird eye view of the board. Non-recursive approach Local/myopic visibility. Neighborhood status tree’s tree traversal mechanism is implemented via baton passing concept. The non-recursive approach 1 1 Baton passing concept ← recursive solution H scattered |V(H scattered )|=1 |E(H scattered )|=0 H spirangle |V(H spirangle )|=199 |E(H spirangle )|=198 H c(row,col) Pseudo-code of the non-recursive solution The recursive approach Neighborhood status tree Conclusions Neighborhood status tree (NST) One baton per group Only a cell with a baton is activated. Simulation configurations Board size b=2~5 (all settings), 6 (sample), 19 (100 professional games). b=2 b=3 b=6b=19 … Games in SGF format is reformatted and converted to a board status matrix B. The normalized system error at time n Simulation results 1 System input, system output and learning curve. (2x2 & 3x3) 1 All the system outputs are correct. (4x4) 1 1 2 3 4 5 6 7 8 b=6 b=11 b=10 We proposed collectively cooperative learning (CCL) as a novel machine learning approach to learn a subject in cooperation with teams of learning agents. Initially unknown group size/graph size is successfully learned by the proposed recursive/non-recursive solution. The excess waiting time ε trades off the accuracy and learning speed. There exists a region of ε, i.e. εg, guarantees correct an answer. A guideline to set ε is suggested, which is a convenient second order equation. The properties of CCL are: goal-oriented, independent, interactive, adaptive, scalable. Life and death of a group significantly impacts the entire game. Some Go rules: connectivity (↕ & ↔), black & white stones placed alternately … … … … Performance metric The normalized system error at time n All system outputs are correct and symmetry holds. Only interesting system inputs are shown here. Temperature map shows the system behavior. Recent contributions New experiments with novel performance metric: normalized cell error and normalized system error Temperature map that visualizes the system level progress of learning is developed and applied to experiments.