Download Supervised learning - TKK Automation Technology Laboratory

AS 84.4340 Automation Technology
Postgraduate Course
Supervised learning in robotics
Turo Keski-Jaskari
18.4.2008
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Contents
• Introduction
• Learning methods
• Classifiers
• Decision trees
• Support Vector Machines
• Neural nets
• Backpropagation
• Exercise
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Machine vs. Robot Learning
Machine Learning
Robot Learning
• Learning in “vacuum”
• Embedded learning
• Statistically well-behaved data
• Data distribution not homogeneous
• Mostly off-line
• Mostly on-line
• Informative feedback
• Qualitative and sparse feed-back
• Computational time not an issue
• Time is crucial
• Hardware does not matter
• Hardware is a priority
• Convergence proof
• Empirical proof
• Generalized statements, but there’s some truth behind them
http://www.nada.kth.se/kurser/kth/2D1431/02/index.html, lecture 12
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Supervised learning
• In supervised learning the “teacher signal” and corresponding
output signals are known
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vs. unsupervised learning, where only input is known
Signal can be made for teaching
Or recorded from successful runs
Or it could be from robot’s own complementary sensors
• Depending on the method, the learning system will build an internal
model based on the training input-output pairs, that then produces
reasonable results for unseen inputs too
• Usually used for minimization of error signals for problems that
have static input-output mappings
• Training can be used for example to learn the signal weights of a
neural network. Like teaching a child, only easier..
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In robotics
• “Naturalness” makes it a good approach for interacting with robots
• Natural teaching in human world is in essence supervised too
• Supervised learning can also be utilized for navigation, localization,
action control, or basically any task where a “correct” signal can be
shown to the robot
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Process
• The process of supervised machine
learning
• At first there is a problem, then the
required data is evaluated and preprocessed
• Algorithm selection is a critical point
• Result after iterative training rounds
is a classifier for the problem in
hand
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“Approaches and algorithms”
From Wikipedia: Supervised learning
• Analytical learning
• Artificial neural network
• Backpropagation
• Boosting
• Bayesian statistics
• Case-based reasoning
• Decision tree learning
• Inductive logic programming
• Gaussian process regression
• Learning Automata
• Minimum message length (decision trees, decision graphs, etc.)
• Naive bayes classifier
• Nearest Neighbor Algorithm
• Probably approximately correct learning (PAC) learning
• Ripple down rules, a knowledge acquisition methodology
• Symbolic machine learning algorithms
• Subsymbolic machine learning algorithms
• Support vector machines
• Random Forests
• Ensembles of Classifiers
• Ordinal Classification
• Data Pre-processing
• Handling imbalanced datasets
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Supervised learning methods
• Classifiers
• Decision trees
• Support Vector Machines
• Neural approaches fit well into this scope
• They can track errors over the learning steps, and adjust network weights
accordingly, thus learning even complex shapes (and the brain learns too)
• Reinforcement learning is close but not quite
• Handling of successful runs can be the same
• Difference is in handling of errors
• Basically in RL the learner knows it did wrong, but in supervised learning it
also gets to know where the goal was
• RL suits for problems with sequential dynamics, and optimizing a scalar
objective
• ”Further relatives”: Hebbian learning, Q-learning
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Basic classifier
•Reached hypothesis:
•Most specific & most general hypotheses
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Decision trees
• Trees that classify instances by sorting them based on feature
values
• “Leafs” are features, nodes are decisions, branches are values
• Root should be the one that best divides the group
Univariate
tree
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Multivariate trees
• Univariate trees use only one input dimension to split.
• Multivariate tree is more general, offering all input dimensions to be
used in the decision node
• Nonlinear versions even more effective
Cutting hyperplane
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Support Vector Machines
• Linear classifiers
• Also known as maximum margin classifiers
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Supervised actor-critic reinforcement learning
• Combining supervised learning with actor-critic RL
• Supervisor adds structure to a learning problem
• Like a parent’s comment for a child learning to bounce a ball
• Supervised learning makes that structure part of an actor critic
framework for reinforcement learning
“Value function”
“Control
policy”
Rosenstein & al.
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Practical experiment
• Example was replicated with real 7DoF whole arm manipulator
• Task to learn was peg insertion into a hole
• Two kind of sources for “criticism”, a feedback controller and a human operator
• Performance worsens first before the robot starts getting input from supervisor
• After 60 trials there is a significant difference for the supervisor only case
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Neuron
• Even a single neuron is a
hugely complicated machine
• In average 7000 links to
other cells in human brain..
• Try to model this!
• Considering these..
Caenorhabditis elegans
302 neurons
(fully mapped)
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Fruit fly
~300000 neurons
Human
~60 billion neurons
Neuron
• Back off a bit
• MISO-system
• Dendrites are inputs for a
neuron
• Axons transfer the output to
other neurons
• “Pulse coded” signals, traveling
one-way only
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Perceptron
• A simplified stochastic model of a neuron
• Invented 1957 at Cornell Aeronautical Laboratory
by Frank Rosenblatt
• Simplest kind of feedforward neural network
• m input signals (dendrites), weighted by weights
wk0 to wkm, and bk is the bias
• The perceptron (“neuron”) sums up the weighted
signals, and outputs a pulse if the threshold
function was fulfilled
• Ф can be a function or simply a threshold
• Output is selected by a threshold (usually
constant, but can be a function too)
 m

yk     wkj x j  bk 
 j 1

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Perceptron network
• All the inputs connect to every output
• Weights are adjustable -> learning
• Essentially perceptron also defines a hyperplane for data
classification, adding perceptrons and soon also layers increase the
representation capabilities
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Multilayer perceptrons
• One layer can only learn linear behaviors
• Multiple layers allow for nonlinear regression
• Usually output neurons have linear output, and hidden ones either
log-sigmoid or tan-sigmoid (normally preferable) activation functions
Log sigmoid function
[0 .. 1]
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Symmetric tanh
[-1 .. 1]
Multilayer perceptrons
• In larger networks every neuron in a layer is linked to every neuron
in the next layer, unidirectional in feed-forward nets
• In learning phase all the weights of these “synapses” are adjusted
gradually by iteration
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Layers and neurons
• Number of output layer neurons is normally the same as the
amount of desired output variables
• Amount of neurons in hidden layers is in practice usually selected
by trial and error, though experienced user can estimate something
from the input data variations too
• If the MLP network has only one hidden layer, its neurons seem to
“interact” with each other (improving one causes degrading in
another)
• For this reason, MLP networks are commonly designed with two
hidden layers
• The first hidden layer is responsible for extracting local features
• Second one extracts global features
• -> Leads to multi-level feature extraction like in the human visual cortex
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Training the net
•
Usually multi-layer perceptron networks learn (=estimate the
weights) by back-propagation technique
1. Present a training sample to the net
2. Compare output with the desired output, calculate error
3. Calculate local errors, i.e. error for each neuron
4. Adjust the weights of inputs of each neuron to lower the local error
5. Assign “blame” for the local error to neurons at the previous level (backpropagation step)
6. Repeat the steps above on the neurons at the previous level, using each
one’s “blame” as its error
•
Using the training samples once (one cycle through all layers) is
called an epoch in learning. Full learning cycle could utilize f.ex.
200 epochs. Normally an error goal criteria is also set.
Maths in Alpaydin, Chapter 11.7
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Training the net
• Online learning is more interesting in robotics than offline
• It saves memory
• Problem may be changing over time
• There may be physical changes in the system
• Gradient descent, minimize quadratic error
• And for multi-layer with back-propagation as before (non-linearity
added)
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Conclusions
• Multilayer perceptrons are a powerful tool to learn even nonlinear
behaviors
• Supervised learning is a natural way for teaching robots
• Combining supervised learning with other types (like RL) may be a
good idea, and also increases naturality
• Human supervisor corrects the little mistakes, preventing the robot to “bang
its head to the wall” for too long..
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References
• Ethem Alpaydin, “Introduction to machine learning”, The MIT Press
(Mainly chapters 2 & 9-11)
• S. Kotsiantis, Supervised Machine Learning: A Review of
Classification Techniques, Informatica Journal 31 (2007) 249-268
• Michael T. Rosenstein and Andrew G. Barto, Supervised Actor Critic
Reinforcement Learning, Department of Computer Science,
University of Massachusetts, Amherst
• A chapter in J. Si, A. Barto, W. Powell, and D. Wunsch, eds., Learning and
Approximate Dynamic Programming: Scaling Up to the Real World. John
Wiley & Sons, Inc., New York, 2004.
• +Misc links, like wikipedia..
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Exercise
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• Build and train a multilayer feedforward backpropagation neural network to
estimate optimal controls for a flying robot!
• Data (matrices P and T) is in “superdata.mat”
• Input data (P) is recorded from four successful runs through a certain zig-zag
route (Red Bull Air Race etc) using a simulator. First four rows of P are the rudder
angles, next four rows of P are the elevator angles of the same run. The first row
of T shows the rudder angles from a real run with the flying robot, and the second
row shows the corresponding elevator angles.
• Find a neural network model for the system by using feed-forward neural network
(Matlab ’doc newff’, Neural Network Toolbox). Choose a suitable number of
neurons and their layers, suitable transfer functions for neurons and train and
simulate the net. Plot the results. Comment on how well you can estimate the
rudder movements and how well the elevator.
• (Don’t worry, the results will not be utilized in a commercial airliner )
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