Encoding Robotic Sensor States for Q-Learning using the Self-Organizing Map
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Transcript of Encoding Robotic Sensor States for Q-Learning using the Self-Organizing Map
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
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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