1. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing1 A Reinforcement Learning Method Based on Adaptive Simulated Annealing Authored by: Amir F. Atiya Department of Computer Engineering Cairo University, Giza, Egypt Alexander G. Parlos Dept. mechanical Engineering Texas A&M University, College Station, Texas Lester Ingber Lester Ingber Research Ingber.com September 13, 2003 Presented by Doug Moody, May 18, 2004

2. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing2 Glass-Blowing and its Impact on Reinforcement Learning Considering the whole piece while focusing on a particular section Slow cooling to relieve stress and gain consistency Use of “annealing”

3. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing3 Paper Approach Review the reinforcement learning problem, and introduce the use of function approximation to determine state values Briefly review the use of an adaptation of “annealing” algorithms to find functions that will determine a state’s value Use this approach on a straight forward decision-making problem.

4. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing4 Function Approximation Introduction Much of our emphasis in reinforcement learning has treated a value function as one entry for each state-action pair Finite Markov Decision processes have a fixed number of states and actions This approach can, in some problems, introduce limitations when there are many states, insufficient samples across all states or a continuous state space. These limitations can be addressed by “generalization” Generalization also can be referred to as “function approximation” Function approximation has been widely studied in many fields (think regression analysis!)

5. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing5 Function Approximation Characteristics A “batch” or “supervised learning” approach versus the on-line approach we have encountered Requires a “static” training set from which to learn Can not handle dynamically changing target functions, which may have been bootstrapped. Hence, function approximation is not suitable for all types of reinforcement learning

6. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing6 Function Approximation Goals Requires a “static” training set from which to learn Can not handle dynamically changing target functions, which may have been bootstrapped. Hence, function approximation is not suitable for all types of reinforcement learning The value function is dependent upon a parameter vector which could be the vector of connection in a network Typically function approximation wants to minimize: P(s) are weights of the errors MSE: Mean Squared Error : vector of function parameters

7. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing7 Function Approximation Methods Step by Step Approach : Gradient Descent - move slowly toward optimal “fit” Linear Approach: Special case of Gradient where parameters are a column vector Coding Methods –Coarse –Tile –Radial Basis Functions

8. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing8 COARSE CODING features should relate to the characteristics of the state For instance for a robot, the location, remaining power may be used For chess, the number of pieces, moves for pawn queen, etc.. Slide from Sutton and Barto textbook

9. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing9 LEARNING AND COARSE CODING Slide from Sutton and Barto textbook

10. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing10 TILE CODING Binary feature for each tile Number of features present at any one time is constant Binary features means weighted sum easy to compute Easy to compute indices of the features present Slide from Sutton and Barto textbook

11. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing11 RADIAL BASIS FUNCTIONS (GAUSSIAN) reflects degrees which feature is present Look to variance to show relationship of feature in the state space

12. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing12 Paper’s Description of the Reinforcement Learning Model Basic System Value Definition Policy Definition Optimal Policy Maximal Value Eq. 4 Eq. 5

13. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing13 Value Function to Optimize basis function weight parameter GOAL: find the optimal set of that will lead to the most accurate evaluation

14. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing14 Use Simulated Annealing to find best set of W k Annealing algorithms seek to search the entire state space and slowing “cool” to appropriate local minima Algorithms trade off between fast convergence and continuous sampling of the entire Used typically to find the optimization of a combinatorial problem Requirements: –Concise definition of the system –Random generator of moves –Objective function to be optimized –Temperature schedule

15. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing15 Example of Simulated Annealing Problem - find the lowest valley in a mountainous region View the problem as having two directions - North-South and East-West Use a bouncing ball to explore the terrain at high temperature The ball can make high bounces exploring many regions Each point in the terrain has a “cost function” to optimize As the temperature cools, the ball’s range and exploration decreases as it focuses on a smaller region of the terrain Two distributions are used: generating distribution (for each parameter), acceptance distribution Acceptance distribution determines whether to stay in the valley or bounce out. Both distributions are affected by temperature

16. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing16 Glass-Blowing Example Larger changes are made to the glass piece at higher temperatures As glass is cooled, the piece is still scanned (albeit more quickly) for stress points Can not be “heated” up again and keep previous results

17. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing17 Adaptive Simulated Annealing (ASA) Has some approach as “simulated annealing” Uses a specific distribution with a wider tail Does not rely on “quenching” to achieve quick convergence Has been available as a C programming system Relies heavily upon a large set of tuning options: –scaling of temperatures, probabilities –limitation on searching in regions with certain parameters –linear vs. non-linear vector Supports re-annealing - time is wound back ( and hence temperature) after some results are achieved to take example of found sensitivities Good for non-linear functions More information and software available at www.ingber.com

18. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing18 Reinforcement learning with ASA Search

19. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing19 Sample Implementation Problem: Choose the highest number from a sequence of numbers –Numbers are generated from an unknown source, with a normal distribution having a mean between 0 and 1 and a standard deviation between 0 and.5 –As time passes the reward is discounted –Hence the tradeoff: more waiting provides more information, but a penalty is incurred Paper used 100 sources, with each generating 1000 numbers for a given sequence as the training set.

20. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing20 Solution Approach Define a state space as a combination of the following: –time t –the current mean at time t of observed numbers –the current standard deviation’ –the highest number chosen thus far Place 10 Gaussian basis functions throughout the State Space Use the algorithm to optimize a vector of weight parameters to the basis functions

21. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing21 RESULTS ASA achieved an overall reward value Q-Learning found the standard deviation Improvement is substantial given that picking the first number in each set would yield.5

22. May 18,2004A Reinforcement Learning Method Based on Adaptive Simlated Annealing22 Paper Comments Pros –Looked to use existing reinforcement taxonomies to discuss the problem –Selected a straight forward problem Negative –Did not fully describe the basis function placement –Insufficient parameter for Q-Learning used –Did not show an non-linear example –Could have provided more information on ASA Options used for results duplication