1 / 54

Hierarchical Reinforcement Learning

Hierarchical Reinforcement Learning. Mausam. [A Survey and Comparison of HRL techniques]. The Outline of the Talk. MDPs and Bellman’s curse of dimensionality. RL: Simultaneous learning and planning. Explore avenues to speed up RL. Illustrate prominent HRL methods.

Download Presentation

Hierarchical Reinforcement Learning

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Hierarchical Reinforcement Learning Mausam [A Survey and Comparison of HRL techniques]

  2. The Outline of the Talk • MDPs and Bellman’s curse of dimensionality. • RL: Simultaneous learning and planning. • Explore avenues to speed up RL. • Illustrate prominent HRL methods. • Compare prominent HRL methods. • Discuss future research. • Summarise

  3. Environment What action next? Percept Action Decision Making Slide courtesy Dan Weld

  4. Personal Printerbot • States (S) :{loc,has-robot-printout, user-loc,has-user-printout},map • Actions (A) :{moven,moves,movee,movew, extend-arm,grab-page,release-pages} • Reward (R) : if h-u-po +20 else -1 • Goal (G) : All states with h-u-po true. • Start state: A state with h-u-po false.

  5. Episodic Markov Decision Process Episodic MDP ´ MDP with absorbing goals • hS, A, P, R, G, s0i • S : Set of environment states. • A: Set of available actions. • P: Probability Transition model. P(s’|s,a)* • R: Reward model. R(s)* • G: Absorbing goal states. • s0 : Start state. • : Discount factor**. * Markovian assumption. ** bounds R for infinite horizon.

  6. Goal of an Episodic MDP Find a policy (S!A), which: • maximises expected discounted reward for a • a fully observable* Episodic MDP. • if agent is allowed to execute for an indefinite horizon. * Non-noisy complete information perceptors

  7. Solution of an Episodic MDP • Define V*(s) : Optimal reward starting in state s. • Value Iteration : Start with an estimate of V*(s) and successively re-estimate it to converge to a fixed point.

  8. Complexity of Value Iteration • Each iteration – polynomial in |S| • Number of iterations – polynomial in |S| • Overall – polynomial in |S| • Polynomial in |S| -  |S| : exponential in number of features in the domain*. * Bellman’s curse of dimensionality

  9. The Outline of the Talk • MDPs and Bellman’s curse of dimensionality. • RL: Simultaneous learning and planning. • Explore avenues to speed up RL. • Illustrate prominent HRL methods. • Compare prominent HRL methods. • Discuss future research. • Summarise

  10. Gain knowledge • Gain understanding • Gain skills • Modification of behavioural tendency Learning Environment Data

  11. Gain knowledge • Gain understanding • Gain skills • Modification of behavioural tendency What action next? Decision Making while Learning* Environment Percepts Datum Action * Known as Reinforcement Learning

  12. Reinforcement Learning • Unknown Pand reward R. • Learning Component : Estimate the Pand R values via data observed from the environment. • Planning Component : Decide which actions to take that will maximise reward. • Exploration vs. Exploitation • GLIE (Greedy in Limit with Infinite Exploration)

  13. Learning • Model-based learning • Learn the model, and do planning • Requires less data, more computation • Model-free learning • Plan without learning an explicit model • Requires a lot of data, less computation

  14. Q-Learning • Instead of learning, P and R, learn Q* directly. • Q*(s,a) : Optimal reward starting in s, if the first action is a, and after that the optimal policy is followed. • Q* directly defines the optimal policy: Optimal policy is the action with maximum Q* value.

  15. Q-Learning • Given an experience tuple hs,a,s’,ri • Under suitable assumptions, and GLIE exploration Q-Learning converges to optimal. New estimate of Q value Old estimate of Q value

  16. Semi-MDP: When actions take time. • The Semi-MDP equation: • Semi-MDP Q-Learning equation: where experience tuple is hs,a,s’,r,Ni r = accumulated discounted reward while action a was executing.

  17. Printerbot • Paul G. Allen Center has 85000 sq ft space • Each floor ~ 85000/7 ~ 12000 sq ft • Discretise location on a floor: 12000 parts. • State Space (without map) : 2*2*12000*12000 --- very large!!!!! • How do humans do the decision making?

  18. The Outline of the Talk • MDPs and Bellman’s curse of dimensionality. • RL: Simultaneous learning and planning. • Explore avenues to speedup RL. • Illustrate prominent HRL methods. • Compare prominent HRL methods. • Discuss future research. • Summarise

  19. 1. The Mathematical PerspectiveA Structure Paradigm • S: Relational MDP • A: Concurrent MDP • P: Dynamic Bayes Nets • R: Continuous-state MDP • G: Conjunction of state variables • V: Algebraic Decision Diagrams • : Decision List (RMDP)

  20. 2. Modular Decision Making

  21. 2. Modular Decision Making • Go out of room • Walk in hallway • Go in the room

  22. 2. Modular Decision Making • Humans plan modularly at different granularities of understanding. • Going out of one room is similar to going out of another room. • Navigation steps do not depend on whether we have the print out or not.

  23. 3. Background Knowledge • Classical Planners using additional control knowledge can scale up to larger problems. • (E.g. : HTN planning, TLPlan) • What forms of control knowledge can we provide to our Printerbot? • First pick printouts, then deliver them. • Navigation – consider rooms, hallway, separately, etc.

  24. A mechanism that exploits all three avenues : Hierarchies • Way to add a special (hierarchical) structure on different parameters of an MDP. • Draws from the intuition and reasoning in human decision making. • Way to provide additional control knowledge to the system.

  25. The Outline of the Talk • MDPs and Bellman’s curse of dimensionality. • RL: Simultaneous learning and planning. • Explore avenues to speedup RL. • Illustrate prominent HRL methods. • Compare prominent HRL methods. • Discuss future research. • Summarise

  26. Hierarchy • Hierarchy of : Behaviour, Skill, Module, SubTask, Macro-action, etc. • picking the pages • collision avoidance • fetch pages phase • walk in hallway • HRL ´ RL with temporally extended actions

  27. Hierarchical Algos ´ Gating Mechanism • Hierarchical Learning • Learning the gating function • Learning the individual behaviours • Learning both * g is a gate bi is a behaviour *Can be a multi- level hierarchy.

  28. Option : Movee until end of hallway • Start : Any state in the hallway. • Execute : policy as shown. • Terminate : when s is end of hallway.

  29. Options [Sutton, Precup, Singh’99] • An option is a well defined behaviour. • o = hIo, o, oi • Io:Set of states (IoµS) in which o can be initiated. • o(s): Policy (S!A*) when o is executing. • o(s) : Probability that o terminates in s. *Can be a policy over lower level options.

  30. Learning • An option is temporally extended action with well defined policy. • Set of options (O) replaces the set of actions (A) • Learning occurs outside options. • Learning over options ´ Semi MDP Q-Learning.

  31. Movew Moven Moven Return Movew Moves Moves Return Machine: Movee + Collision Avoidance : End of hallway Call M1 Movee Choose Obstacle Call M2 End of hallway Return M1 M2

  32. Hierarchies of Abstract Machines[Parr, Russell’97] • A machine is a partial policy represented by a Finite State Automaton. • Node : • Execute a ground action. • Call a machine as a subroutine. • Choose the next node. • Return to the calling machine.

  33. Hierarchies of Abstract Machines • A machine is a partial policy represented by a Finite State Automaton. • Node : • Execute a ground action. • Call a machine as subroutine. • Choose the next node. • Return to the calling machine.

  34. Learning • Learning occurs within machines, as machines are only partially defined. • Flatten all machines out and consider states [s,m] where s is a world state, and m, a machine node ´MDP • reduce(SoM) : Consider only states where machine node is a choice node ´Semi-MDP. • Learning ¼ Semi-MDP Q-Learning

  35. Task Hierarchy: MAXQ Decomposition[Dietterich’00] Root Children of a task are unordered Fetch Deliver Take Give Navigate(loc) Extend-arm Grab Release Extend-arm Moven Moves Movew Movee

  36. MAXQ Decomposition • Augment the state s by adding the subtask i : [s,i]. • Define C([s,i],j) as the reward received in i after j finishes. • Q([s,Fetch],Navigate(prr)) = V([s,Navigate(prr)])+C([s,Fetch],Navigate(prr))* • Express V in terms of C • Learn C, instead of learning Q Reward received while navigating Reward received after navigation *Observe the context-free nature of Q-value

  37. The Outline of the Talk • MDPs and Bellman’s curse of dimensionality. • RL: Simultaneous learning and planning. • Explore avenues to speedup RL. • Illustrate prominent HRL methods. • Compare prominent HRL methods. • Discuss future research. • Summarise

  38. 1. State Abstraction • Abstract state : A state having fewer state variables; different world states maps to the same abstract state. • If we can reduce some state variables, then we can reduce on the learning time considerably! • We may use different abstract states for different macro-actions.

  39. State Abstraction in MAXQ • Relevance : Only some variables are relevant for the task. • Fetch : user-loc irrelevant • Navigate(printer-room) : h-r-po,h-u-po,user-loc • Fewer params for V of lower levels. • Funnelling : Subtask maps many states to smaller set of states. • Fetch : All states map to h-r-po=true, loc=pr.room. • Fewer params for C of higher levels.

  40. State Abstraction in Options, HAM • Options : Learning required only in states that are terminal states for some option. • HAM : Original work has no abstraction. • Extension: Three-way value decomposition*: Q([s,m],n) = V([s,n]) +C([s,m],n) + Cex([s,m]) • Similar abstractions are employed. *[Andre,Russell’02]

  41. 2. Optimality Hierarchical Optimality vs. Recursive Optimality

  42. Optimality • Options : Hierarchical • Use (A[O) : Global** • Interrupt options • HAM : Hierarchical* • MAXQ : Recursive* • Interrupt subtasks • Use Pseudo-rewards • Iterate! * Can define eqns for both optimalities **Adv. of using macro-actions maybe lost.

  43. 3. Language Expressiveness • Option • Can only input a complete policy • HAM • Can input a complete policy. • Can input a task hierarchy. • Can represent “amount of effort”. • Later extended to partial programs. • MAXQ • Cannot input a policy (full/partial)

  44. 4. Knowledge Requirements • Options • Requires complete specification of policy. • One could learn option policies – given subtasks. • HAM • Medium requirements • MAXQ • Minimal requirements

  45. 5. Models advanced • Options : Concurrency • HAM : Richer representation, Concurrency • MAXQ : Continuous time, state, actions; Multi-agents, Average-reward. • In general, more researchers have followed MAXQ • Less input knowledge • Value decomposition

  46. 6. Structure Paradigm • S: Options, MAXQ • A: All • P: None • R: MAXQ • G: All • V: MAXQ • : All

  47. The Outline of the Talk • MDPs and Bellman’s curse of dimensionality. • RL: Simultaneous learning and planning. • Explore avenues to speedup RL. • Illustrate prominent HRL methods. • Compare prominent HRL methods. • Discuss future research. • Summarise

  48. Directions for Future Research • Bidirectional State Abstractions • Hierarchies over other RL research • Model based methods • Function Approximators • Probabilistic Planning • Hierarchical P and Hierarchical R • Imitation Learning

  49. Directions for Future Research • Theory • Bounds (goodness of hierarchy) • Non-asymptotic analysis • Automated Discovery • Discovery of Hierarchies • Discovery of State Abstraction • Apply…

  50. P2 P1 D2 D1 Parts Ware-house Assemblies D3 D4 P3 P4 Applications • Toy Robot • Flight Simulator • AGV Scheduling • Keepaway soccer Images courtesy various sources

More Related