Decision Making in Intelligent Systems Lecture 9

1. Decision Making in Intelligent SystemsLecture 9 BSc course Kunstmatige Intelligentie 2008 Bram Bakker Intelligent Systems Lab Amsterdam Informatics Institute Universiteit van Amsterdam bram@science.uva.nl

2. Overview of this lecture • Last lecture! • Illustrate trade-offs and issues that arise in real applications • Illustrate use of domain knowledge • Describe some RL topics that UvA is working on

3. Final exam: mei 2007 • Tijd/plek nog onbekend (voor mij)! • Let op website: http://staff.science.uva.nl/~bram/DMIS/

4. Case study 1: TD Gammon Tesauro 1992, 1994, 1995, ... • White has just rolled a 5 and a 2 so can move one of his pieces 5 and one (possibly the same) 2 steps • Objective is to advance all pieces to points 19-24 • 30 pieces, 24 locations implies enormous number of configurations • Effective branching factor of 400

5. A Few Details • Reward: 0 at all times except those in which the game is won, when it is 1 • Episodic (game = episode), undiscounted • Gradient descent TD(l) with a multi-layer neural network • weights initialized to small random numbers • backpropagation of TD error • four input units for each point; unary encoding of number of white pieces, plus other features • Learning during self-play

6. Multi-layer Neural Network

7. Summary of TD-Gammon Results

8. Samuel’s Checkers Player Arthur Samuel 1959, 1967 • Minimax to determine “backed-up score” of a position • Rote learning: save each board config encountered together with backed-up score • Learning: similar to TD algorithm

9. Samuel’s Backups

10. The Basic Idea “. . . we are attempting to make the score, calculated for the current board position, look like that calculated for the terminal board positions of the chain of moves which most probably occur during actual play.” A. L. Samuel Some Studies in Machine Learning Using the Game of Checkers, 1959

11. More Samuel Details • Did not include explicit rewards • Instead used so-called “piece advantage” feature • No special treatment of terminal positions • Generalization method produced “better than average” play; “tricky but beatable” • Supervised mode: “book learning”

12. Spong 1994 The Acrobot

13. Acrobot Learning Curves for Sarsa(l)

14. Typical Acrobot Learned Behavior

15. Elevator Dispatching Crites and Barto 1996

16. Control Strategies • Zoning: divide building into zones; park in zone when idle. Robust in heavy traffic. • Search-based methods: greedy or non-greedy. Receding Horizon control. • Rule-based methods: expert systems/fuzzy logic; from human “experts” • Other heuristic methods: Longest Queue First (LQF), Highest Unanswered Floor First (HUFF), Dynamic Load Balancing (DLB) • Adaptive/Learning methods: NNs for prediction, parameter space search using simulation, DP on simplified model, non-sequential RL

17. The Elevator Model(from Lewis, 1991) Parameters: • Floor Time (time to move one floor at max speed): 1.45 secs. • Stop Time (time to decelerate, open and close doors, and accelerate again): 7.19 secs. • TurnTime (time needed by a stopped car to change directions): 1 sec. • Load Time (the time for one passenger to enter or exit a car): a random variable with range from 0.6 to 6.0 secs, mean of 1 sec. • Car Capacity: 20 passengers Discrete Event System: continuous time, asynchronous elevator operation Traffic Profile: • Poisson arrivals with rates changing every 5 minutes; down-peak

18. State Space • 18 hall call buttons: 2 combinations • positions and directions of cars: 18 (rounding to nearest floor) • motion states of cars (accelerating, moving, decelerating, stopped, loading, turning): 6 • 40 car buttons: 2 • Set of passengers waiting at each floor, each passenger's arrival time and destination: unobservable. However, 18 real numbers are available giving elapsed time since hall buttons pushed; we discretize these. • Set of passengers riding each car and their destinations: observable only through the car buttons 18 4 4 40 22 Conservatively about 10 states

19. Actions • When moving (halfway between floors): – stop at next floor – continue past next floor • When stopped at a floor: – go up – go down

20. Constraints • A car cannot pass a floor if a passenger wants to get off there • A car cannot change direction until it has serviced all onboard passengers traveling in the current direction • Don’t stop at a floor if another car is already stopping, or is stopped, there • Don’t stop at a floor unless someone wants to get off there • Given a choice, always move up standard special heuristic

21. Performance Criteria • Average wait time • Average system time (wait + travel time) • % waiting > T seconds (e.g., T = 60) • Average squared wait time (to encourage fast and fair service) Minimize:

22. Average Squared Wait Time Instantaneous cost: Define return as an integral rather than a sum (Bradtke and Duff, 1994): becomes

23. Algorithm

24. Neural Networks 47 inputs, 20 sigmoid hidden units, 1 or 2 output units • 9 binary: state of each hall down button • 9 real: elapsed time of hall down button if pushed • 16 binary: one on at a time: position and direction of car making decision • 10 real: location/direction of other cars: “footprint” • 1 binary: at highest floor with waiting passenger? • 1 binary: at floor with longest waiting passenger? • 1 bias unit  1 Inputs:

25. Elevator Results

26. Dynamic Channel Allocation Singh and Bertsekas 1997

27. Summary • RL can lead to successful applications • Background knowledge important • Learning directly in the real world is rarely possible • You need a more or less accurate simulation • Function approximation (e.g. neural networks) is important to deal with large state spaces

28. Frontier Dimensions • Smart function approximation • Non-Markov case: • Partially Observable MDPs (POMDPs) • Bayesian approach: belief states • construct state from sequence of observations • Modularity and hierarchies • Learning and planning at several different levels • Theory of options, MAXQ • Multi-agent RL

29. Adaptive resolution function approximation • Learn, in your state(-action) space • where you can generalize over many states (coarse-grained view) • where you must distinguish between states (fine-grained view) • Learn based on experienced rewards • Returns guide formation of boundaries between regions in state(-action) space

30. Frontier Dimensions • Smart function approximation • Non-Markov case: • Partially Observable MDPs (POMDPs) • Bayesian approach: belief states • construct state from sequence of observations • Modularity and hierarchies • Learning and planning at several different levels • Theory of options, MAXQ • Multi-agent RL

31. Architectures NNs fully observable MDPs Direct value function approximation Actor-critic

32. Architectures partially observable case Direct value function approximation Actor-critic

33. Long Short-Term Memory (LSTM) The memory cells can learn to remember relevant information from the timeseries of inputs for long periods of time (e.g. Hochreiter & Schmidhuber, 1997; Bakker, 2001)

34. Frontier Dimensions • Smart function approximation • Non-Markov case: • Partially Observable MDPs (POMDPs) • Bayesian approach: belief states • construct state from sequence of observations • Modularity and hierarchies • Learning and planning at several different levels • Theory of options, MAXQ • Multi-agent RL

35. Hierarchical methods policy HIGH overall task policy policy subtask subtask policy policy policy policy LOW subtask subtask subtask subtask

36. Frontier Dimensions • Smart function approximation • Non-Markov case: • Partially Observable MDPs (POMDPs) • Bayesian approach: belief states • construct state from sequence of observations • Modularity and hierarchies • Learning and planning at several different levels • Theory of options, MAXQ • Multi-agent RL

37. Multi-agent RL • Structure overall task such that team of agents (rather than single agent) can solve it • Task must be decomposible in this way • Find way of distributing rewards between agents • Agents must be rewarded for good contribution to overall team • Agents must not be rewarded for bad contribution or selfish behavior

38. Traffic simulator

39. Approach • Model-based multi-agent reinforcement learning • Traffic behavior model is estimated online (maximum likelihood model) • Value function/policy is estimated online using approximate real-time dynamic programming • Each traffic light junction makes locally optimal decision by using value function and sensing local cars around the junction • Recently an explicit coordination mechanism was added by means of coordination graphs and maxplus

40. 3D visualisation traffic simulator Thanks to Matthijs Amelink

41. Multi-agent example: Robocup simulation league • Kok & Vlassis (2002-2006)

42. Studying for final exam • Literature • Sutton & Barto (1998) book • Kaelbling, Littman, & Cassandra (1998): Planning and acting in partially observable stochastic domains, AI journal article. (website) Sections 1-3. • Questions will test: • General insight into important issues • Ability to apply the mathematics of RL • Use the slides! • Open book • Try answering some questions at the end of each chapter

43. Final exam: mei 2008 • ? mei • Plaats: ? • Deze informatie zal op de DMIS website staan: http://staff.science.uva.nl/~bram/DMIS/