University Paderborn 16 January 2009 RG Knowledge Based Systems Hans Kleine Büning Reinforcement...

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Universi ty Paderbor n 16 January 2009 RG Knowledge Based Systems Hans Kleine Büning Reinforcement Learning

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Page 1: University Paderborn 16 January 2009 RG Knowledge Based Systems Hans Kleine Büning Reinforcement Learning.

UniversityPaderbor

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16 January 2009

RG Knowledge Based Systems

Hans Kleine Büning

Reinforcement LearningReinforcement Learning

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Reinforcement Learning Prof. Dr. Hans

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OutlineOutline

• Motivation• Applications• Markov Decision Processes• Q-learning• Examples

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Reinforcement Learning: The Idea

• A way of programming agents by reward and punishment without specifying how the task is to be achieved

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Learning to Ride a Bicycle

Environment

Environment

state

action

€€€€€€

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Learning to Ride a Bicycle

• States:– Angle of handle bars

– Angular velocity of handle bars

– Angle of bicycle to vertical

– Angular velocity of bicycle to vertical

– Acceleration of angle of bicycle to vertical

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Learning to Ride a Bicycle

Environment

Environment

state

action

€€€€€€

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Learning to Ride a Bicycle

• Actions:– Torque to be applied to the

handle bars

– Displacement of the center of mass from the bicycle’s plan (in cm)

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Learning to Ride a Bicycle

Environment

Environment

state

action

€€€€€€

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Angle of bicycle to vertical is greater

than 12°

Reward = 0

Reward = -1

no yes

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Learning To Ride a Bicycle

Reinforcement Learning

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Reinforcement Learning: Applications

• Board Games– TD-Gammon program, based on reinforcement learning, has

become a world-class backgammon player

• Mobile Robot Controlling– Learning to Drive a Bicycle– Navigation– Pole-balancing– Acrobot

• Sequential Process Controlling– Elevator Dispatching

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Key Features of Reinforcement Learning

• Learner is not told which actions to take• Trial and error search• Possibility of delayed reward:

– Sacrifice of short-term gains for greater long-term gains

• Explore/Exploit trade-off• Considers the whole problem of a goal-directed

agent interacting with an uncertain environment

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The Agent-Environment Interaction

• Agent and environment interact at discrete time steps: t = 0,1, 2, …– Agent observes state at step t :

st 2 S

– produces action at step t: at 2 A

– gets resulting reward : rt +1 2 ℜ

– and resulting next state: st +1 2 S

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The Agent’s Goal:

• Coarsely, the agent’s goal is to get as much reward as it

can over the long run

Policy is• a mapping from states to action s) = a

• Reinforcement learning methods specify how the agent changes its policy as a result of experience experience

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Deterministic Markov Decision Process

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Example

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Example: Corresponding MDP

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Example: Corresponding MDP

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Example: Corresponding MDP

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Example: Policy

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Value of Policy and Rewards

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Value of Policy and Agent’s Task

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Nondeterministic Markov Decision Process

P = 0

.8

P = 0.1

P = 0.1

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Nondeterministic Markov Decision Process

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Nondeterministic Markov Decision Process

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Example with South-Easten Wind

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Example with South-Easten Wind

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Methods

Dynamic Programming

ValueFunction

Approximation+

DynamicProgramming

ReinforcementLearning,

Monte Carlo Methods

ValuationFunction

Approximation+

ReinforcementLearning

continuousstates

discrete states discrete statescontinuous

states

Model (reward function and transitionprobabilities) is known

Model (reward function or transitionprobabilities) is unknown

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Q-learning Algorithm

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Q-learning Algorithm

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Example

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Example: Q-table Initialization

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Example: Episode 1

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Example: Episode 1

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Example: Episode 1

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Example: Episode 1

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Example: Episode 1

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Example: Q-table

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Example: Episode 1

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Episode 1

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Example: Q-table

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Example: Episode 2

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Example: Episode 2

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Example: Episode 2

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Example: Q-table after Convergence

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Example: Value Function after Convergence

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Example: Optimal Policy

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Example: Optimal Policy

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Q-learning

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Convergence of Q-learning

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Blackjack• Standard rules of blackjack hold• State space:

– element[0] - current value of player's hand (4-21)

– element[1] - value of dealer's face -up card (2-11)

– element[2] - player does not have usable ace (0/1)

• Starting states:– player has any 2 cards (uniformly

distributed), dealer has any 1 card (uniformly distributed)

• Actions: – HIT– STICK

• Rewards: – 1 for a loss– 0 for a draw– 1 for a win

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Blackjack: Optimal Policy

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Reinforcement Learning: Example

• States– Grids

• Actions– Left– Up– Right– Down

• Rewards– Bonus 20– Food 1– Predator -10– Empty grid -0.1

• Transition probabilities– 0.80 – agent goes where he

intends to go– 0.20 – to any other adjacent

grid or remains where it was (in case he is on the board of the grid world he goes to the other side)

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Reinforcement Learning: Example

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Reinforcement Learning: Example

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Reinforcement Learning: Example

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Reinforcement Learning: Example

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Reinforcement Learning: Example

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Reinforcement Learning: Example

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Reinforcement Learning: Example

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Reinforcement Learning: Example

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Reinforcement Learning: Example

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Reinforcement Learning: Example


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