Projected Equation and Aggregation - based Approximate Dynamic Programming Methods for Tetris

In this thesis, we survey approximate dynamic programming (ADP) methods and test the methods with the game of Tetris. We focus on ADP methods where the costto-go function J is approximated with 5r, where 4 is some matrix and r is a vector with relatively low dimension. There are two major categories of methods: projected equation methods and aggregation methods. In projected equation methods, the cost-to-go function approximation 4or is updated by simulation using one of several policy-updated algorithms such as LSTD(A) [BB96], and LSPE(A) [B196]. Projected equation methods generally may not converge. We define a pseudometric of policies and view the oscillations of policies in Tetris. Aggregation methods are based on a model approximation approach. The original problem is reduced to an aggregate problem with significantly fewer states. The weight vector r is the cost-to-go function of the aggregate problem and P is the matrix of aggregation probabilities. In aggregation methods, the vector r converges to the optimal cost-to-go function of the aggregate problem. In this thesis, we implement aggregation methods for Tetris, and compare the performance of projected equation methods and aggregation methods. Thesis Supervisor: Dimitri P. Bertsekas Title: Professor of Engineering Lab. for Information and Decision Systems