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Reinforcement Learning: Learning Algorithms for Group Assignments

This book provides a comprehensive guide to reinforcement learning algorithms for group assignments, with a focus on immediate execution. Topics include basics, learning algorithms, large state space algorithms, and function approximation. The book is available online.

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Reinforcement Learning: Learning Algorithms for Group Assignments

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  1. לביצוע מיידי! • להתחלק לקבוצות • 2 או 3 בקבוצה • להעביר את הקבוצות • היום בסוף השיעור! • ספר Reinforcement Learning • הספר קיים online (גישה מהאתר של הסדנה)

  2. Reinforcement Learning:Learning algorithmsFunction Approximation Yishay Mansour Tel-Aviv University

  3. Outline • Week I: Basics • Mathematical Model (MDP) • Planning • Value iteration • Policy iteration • Week II: Learning Algorithms • Model based • Model Free • Week III: Large state space

  4. Learning Algorithms Given access only to actions perform: 1. policy evaluation. 2. control - find optimal policy. Two approaches: 1. Model based (Dynamic Programming). 2. Model free (Q-Learning, SARSA).

  5. Learning: Policy improvement • Assume that we can compute: • Given a policy π, • The V and Q functions of π • Can perform policy improvement: • Π= Greedy (Q) • Process converges if estimations are accurate.

  6. Learning - Model FreeOptimal Control: off-policy Learn online the Q function. Qt+1 (st ,at ) = Qt (st ,at )+ a At At = rt+g MAXa {Qt (st+1,a)} - Qt (st ,at ) OFF POLICY: Q-Learning Maximization Operator!!!

  7. Learning - Model FreePolicy evaluation: TD(0) An online view: At state st we performed action at, received reward rtand moved to state st+1. Our “estimation error” isAt =rt+gVt(st+1)-Vt(st), The update: Vt +1(st) = Vt(st ) + a At No maximization over actions!

  8. Learning - Model FreeOptimal Control: on-policy Learn online the optimal Q* function. Qt+1 (st ,at ) = Qt (st ,at )+ a [ rt+g Qt (st+1,at+1) - Qt (st ,at )] ON-Policy:SARSA at+1 the e-greedy policy for Qt. The policy selects the action! Need to balance exploration and exploitation.

  9. Modified Notation • Rather than Q(s,a) have Qa(s) • Greedy(Q) = MAXa Qa(s) • Each action has a function Qa(s) • Learn eachQa(s)independently!

  10. Large state space • Reduce number of states • Symmetries (x-o) • Cluster states • Define attributes • Limited number of attributes • Some states will be identical • Action view of a state

  11. Example X-O • For each action (square) • Consider row/diagonal/column through it • The state will encode the status of “rows”: • Two X’s • Two O’s • Mixed (both X and O) • One X • One O • empty • Only Three types of squares/actions

  12. Clustering states • Need to create attributes • Attributes should be “game dependent” • Different “real” states - same representation • How do we differentiate states? • We estimate action value. • Consider only legal actions. • Play “best” action.

  13. Function Approximation • Use a limited model for Qa(s) • Have an attribute vector: • Each state s has a vector vec(s)=x1 ... xk • Normally k << |S| • Examples: • Neural Network • Decision tree • Linear Function • Weights  = 1 ... k • Value  ixi

  14. Gradient Decent • Minimize Squared Error • Square Error = ½  P(s) [V(s) – V(s)]2 • P(s) is sum weighting on the states • Algorithm: • (t+1) = (t) +  [V(st) – V(t)(st)] (t) V(t)(st) • (t) = partial derivatives • Replace V(st) by a sample • Monte Carlo: use Rt forV(st) • TD(0) use At for [V(st) – V(t)(st)]

  15. Linear Functions • Linear function:  ixi = < ,x > • Derivative (t) Vt(st) = vec(st) • Update Rule: • t+1 = t +  [V(st) – Vt(st)] vec(st) • MC: t+1 = t +  [ Rt – < t ,st>] vec(st) • TD: t+1 = t +  At vec(st)

  16. Example: 4 in a row • Select attributes for action (column): • 3 in a row (type X or type O) • 2 in a row (type X or O) and [blocked/ not] • Next location 3 in a row. • Next move might lose • Other “features” • RL will learn the weights. • Look ahead significantly helps • use max-min tree

  17. Bootstraping • Playing against a “good” player • Using .... • Self play • Start with a random player • play against one self. • Choose a starting point. • Max-Min tree with simple scoring function. • Add some simple guidance • add “compulsory” moves.

  18. Scoring Function • Checkers: • Number of pieces • Number of Queens • Chess • Weighted sum of pieces • Othello/Reversi • Difference in number of pieces • Can be used with Max-Min Tree • (,) pruning

  19. Example: Revesrsi (Othello) • Use a simple score functions: • difference in pieces • edge pieces • corner pieces • Use Max-Min Tree • RL: optimize weights.

  20. Advanced issues • Time constraints • fast and slow modes • Opening • can help • End game • many cases: few pieces, • can be solved efficiently • Train on a specific state • might be helpful/ not sure that its worth the effort.

  21. What is Next? • Create teams: • at least 2 students at most 3 students • Group size will influence our expectations! • Choose a game! • Give the names and game • GUI for game • Deadline Dec. 17, 2006

  22. Schedule (more) • System specification • Project outline • High level components planning • Jan. 21, 2007 • Build system • Project completion • April 29, 2007 • All supporting documents in html!

  23. Next week • GUI interface (using C++) • Afterwards: • Each groups works by itself

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