Post on 21-Dec-2014
description
Encoding Robotic Sensor Statesfor Q-Learning using the
Self-Organizing Map
Gabriel J. FerrerDepartment of Computer Science
Hendrix College
Outline
Statement of Problem
Q-Learning
Self-Organizing Maps
Experiments
Discussion
Statement of Problem
Goal
Make robots do what we want
Minimize/eliminate programming
Proposed Solution: Reinforcement Learning
Specify desired behavior using rewards
Express rewards in terms of sensor states
Use machine learning to induce desired actions
Target Platform
Lego Mindstorms NXT
Robotic Platform
Experimental Task
Drive forward
Avoid hitting things
Q-Learning
Table of expected rewards (“Q-values”) Indexed by state and action
Algorithm steps Calculate state index from sensor values
Calculate the reward
Update previous Q-value
Select and perform an action
Q(s,a) = (1 - α) Q(s,a) + α (r + γ max(Q(s',a)))
Certain sensors provide continuous values
Sonar
Motor encoders
Q-Learning requires discrete inputs
Group continuous values into discrete “buckets”
[Mahadevan and Connell, 1992]
Q-Learning produces discrete actions
Forward
Back-left/Back-right
Q-Learning and Robots
Creating Discrete Inputs
Basic approach Discretize continuous values into sets
Combine each discretized tuple into a single index
Another approach Self-Organizing Map
Induces a discretization of continuous values
[Touzet 1997] [Smith 2002]
Self-Organizing Map (SOM)
2D Grid of Output Nodes Each output corresponds to an ideal input value
Inputs can be anything with a distance function
Activating an Output Present input to the network
Output with the closest ideal input is the “winner”
Applying the SOM
Each input is a vector of sensor values Sonar
Left/Right Bump Sensors
Left/Right Motor Speeds
Distance function is sum-of-squared-differences
SOM Unsupervised Learning
• Present an input to the network
• Find the winning output node
• Update ideal input for winner and neighbors
– weightij = weightij + (α * (inputij – weightij))
• Neighborhood function
2
2
2c
d
e
Experiments
Implemented in Java (LeJOS 0.85)
Each experiment 240 seconds (800 Q-Learning iterations)
36 States
Three actions Both motors forward Left motor backward, right motor stopped Left motor stopped, right motor backward
Rewards
Either bump sensor pressed: 0.0
Base reward: 1.0 if both motors are going forward
0.5 otherwise
Multiplier: Sonar value greater than 20 cm: 1
Otherwise, (sonar value) / 20
Parameters
Discount (γ): 0.5
Learning rate (α): 1/(1 + (t/100)), t is the current iteration (time step)
Used for both SOM and Q-Learning [Smith 2002]
Exploration/Exploitation Epsilon = α/4
Probability of random action Selected using weighted distribution
Experimental Controls
Q-Learning without SOM
Qa States Current action (1-3)
Current bumper states
Quantized sonar values (0-19 cm; 20-39; 40+)
Qb States Current bumper states
Quantized sonar values (9) (0-11 cm…; 84-95; 96+)
SOM Formulations
36 Output Nodes
Category “a”: Length-5 input vectors
Motor speeds, bumper values, sonar value
Category “b”: Length-3 input vectors
Bumper values, sonar value
All sensor values normalized to [0-100]
SOM Formulations
QSOM Based on [Smith 2002] Gaussian Neighborhood
Neighborhood size is one-half SOM width
QT Based on [Touzet 1997] Learning rate is fixed at 0.9 Neighborhood is immediate Manhattan neighbors
Neighbor learning rate is 0.4
Quantitative Results
Qa Qb QSOMa QSOMb QTa QTb
Mean 607.97 578.91 468.86 534.49 456.19 545.61
StDv 81.92 76.95 39.39 160.41 85.07 57.98
Median 608.75 667.5 485.11 587.64 442.62 560.77
Min 506.47 528.67 410.2 354.25 378.72 481.55
Max 723 540.55 495 661.59 547.22 594.5
Mean/It 0.76 0.72 0.59 0.67 0.57 0.68
StDv/It 0.1 0.1 0.05 0.2 0.11 0.07
Qualitative Results
QSOMa Motor speeds ranged from 2% to 50%
Sonar values stuck between 90% and 94%
QSOMb Sonar values range from 40% to 95%
Best two runs arguably the best of the bunch
Very smooth SOM values in both cases
Qualitative Results
QTa Sonar values ranged from 10% to 100%
Still a weak performer on average
Best performer similar to QTb
QTb Developed bump-sensor oriented behavior
Made little use of sonar
Highly uneven SOM values in both cases
Experimental Area
First Movie
QSOMb
Strong performer (Reward: 661.89)
Minimum sonar value: 43.35% (110 cm)
Second Movie
Also QSOMb
Typical bad performer (Reward: 451.6) Learns to avoid by always driving backwards
Baseline “not-forward” reward: 400.0
Minimum sonar value: 57.51% (146 cm) Hindered by small filming area
Discussion
Use of SOM on NXT can be effective More research needed to address shortcomings
Heterogeneity of sensors is a problem Need to try NXT experiments with multiple sonars
Previous work involved homogeneous sensors
Approachable by undergraduate students Technique taught in junior/senior AI course