- Share my experience of traditional (not data driven) optimization. - Provide a slightly different angle to describe what machine learning does.

1. Machine Learning
Shaoqing Tan <tansq7@gmail.com>
vs
Traditional Optimization

2. Agenda
● Share my experience of traditional (not data driven) optimization.
● Provide a slightly different angle to describe what machine learning does.
● Demo with course project.

3. Machine Learning
● Helps predict behavior of new samples
● Learns data pattern with mathematics
● Minimizes the deviation from correct behavior
● Hyper parameters are not learned

4. Traditional Optimization
● Helps select parameters in engineering design
● Minimizes a loss function defined by
○ Safety factor
○ Monetary cost
○ Performance
● Often subject to constraints
● Loss function is evaluated via
○ Solid / fluidic mechanics simulation (FEA)
○ Electrical / electromagnetic simulation
○ Other logic / mathematics

5. Def of loss
Optimization
Design experiment
Evaluate loss
Check terminationKnowledge
Constraint
Initialization
Generically Speaking

6. Def of loss
Optimization
Design experiment
Evaluate loss
Check terminationKnowledge
Constraint
Initialization
Neural Network Training
NN loss
Training data
Gradient descent +
back propagation

7. Def of loss
Optimization
Design experiment
Evaluate loss
Check terminationKnowledge
Constraint
Initialization
Mechanical Design
Mech simulation
performance
Design constraints
Black box sampler

8. Def of loss
Optimization
Design experiment
Evaluate loss
Check terminationKnowledge
Constraint
Initialization
Neural Network Param Tuning
Cross validated
model performance
Design constraints
Black box sampler

9. Comparison
Def of loss Constraint Experiment Design
NN training NN loss Data Gradient descent +
back propagation
Mechanical
design
Mechanical simulation
performance
Design constraints Black box sampler
NN param
tuning
Cross validated model
performance
Design constraints Black box sampler

10. Black Box Sampling
● Gradient descent
○ Performs very well because it directly knows where it’s going!
○ Need derivative to function
● Black box means derivative is unavailable, such samplers include
○ Grid search: Brute force
○ Random search (Monti Carlo): Aimless
○ Quasi gradient descent: Susceptible to noise
○ Surrogate adaptive sampling - Models known points and sample new
points around the minimum of the sample
● Each one of these samplers will carry its own hyper parameters!

11. Surrogate Adaptive Sampling
● Surrogate models include
○ Bayesian
○ Radial basis function
○ Gaussian
○ Spline
○ Ensemble of the above
● Python libraries
○ https://github.com/HIPS/Spearmint
○ https://github.com/dme65/pySOT
● Google “global / black box optimization”

12. Demo & Questions