CHAPTER 11 R EINFORCEMENT L EARNING VIA T EMPORAL D IFFERENCES Organization of chapter in ISSO –Introduction –Delayed reinforcement –Basic temporal difference algorithm –Batch and online implementations of TD –Examples –Connections to stochastic approximation Slides for Introduction to Stochastic Search and Optimization (ISSO) by J. C. Spall

11-2 Reinforcement Learning Reinforcement learning is important class of methods in computer science, AI, engineering, etc. –Based on common-sense idea that good results are reinforced while bad results provide negative reinforcement Delayed reinforcement only provides output after several intermediate “actions” Want to create model for predicting state of system –Model depends on  –“Training” or “learning” (estimating  ) not based on methods such as stochastic gradient (supervised learning) because of delay in response –Need learning method to cope with delayed response

11-3 Schematic of Delayed Reinforcement Process Suppose time moves left to right in diagram below Z represents some system output at a future time represent some intermediate predictions of Z

11-4 Temporal Difference (TD) Learning Focus is delayed reinforcement problem Prediction function has form  h  ( ,  x  ), where  are parameters and x  is input Need to estimate  from sequence of inputs and outputs {x 0, x 1,..., x n  ; Z} TD learning is method for using in training rather than only inputs and outputs –Implies that some forms of TD allow for updating of  value before observing Z –TD exploits prior information embedded in predictions to modify  Basic form of TD for updating  is where (  )  is increment to be determined

11-5 Exercise 11.4 in ISSO: Conceptual Example of Benefits of TD. Circles denote game states. Novel Bad Loss Win 90% 10% Game outcome

11-6 Batch Version of TD Learning

11-7 Random-Walk Model (Example 11.3 in ISSO) All walks begin in state S 3 Each step involves 50–50 chance of moving left or right until terminal state T left or T right is reached Use TD to estimate probabilities of reaching T right from any of states S 1, S 2, S 3, S 4, or S 5 S1S1 T left S2S2 S3S3 S4S4 S5S5 T right Start