Using Bayesian Optimization to Tune Machine Learning Models
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USING BAYESIAN OPTIMIZATION TO TUNE MACHINE LEARNING MODELS Scott Clark Co-founder and CEO of SigOpt [email protected] @DrScottClark
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Transcript of Using Bayesian Optimization to Tune Machine Learning Models
USING BAYESIAN OPTIMIZATIONTO TUNE MACHINE LEARNING MODELS
Scott ClarkCo-founder and CEO of SigOpt
[email protected] @DrScottClark
TRIAL AND ERROR WASTES EXPERT TIME
Machine Learning is extremely powerful
Tuning Machine Learning systemsis extremely non-intuitive
UNRESOLVED PROBLEM IN ML
https://www.quora.com/What-is-the-most-important-unresolved-problem-in-machine-learning-3
What is the most important unresolved problem in machine learning?
“...we still don't really know why some configurations of deep neural networks work in some case and not others, let alone having a more or less automatic approach to determining the architectures and the hyperparameters.”
Xavier Amatriain, VP Engineering at Quora(former Director of Research at Netflix)
LOTS OF TUNABLE PARAMETERS
COMMON APPROACH
Random Search for Hyper-Parameter Optimization, James Bergstra et al., 2012
1. Random search or grid search2. Expert defined grid search near “good” points3. Refine domain and repeat steps - “grad student descent”
COMMON APPROACH
● Expert intensive● Computationally intensive● Finds potentially local optima● Does not fully exploit useful information
Random Search for Hyper-Parameter Optimization, James Bergstra et al., 2012
1. Random search or grid search2. Expert defined grid search near “good” points3. Refine domain and repeat steps - “grad student descent”
… the challenge of how to collect information as efficiently as possible, primarily for settings where collecting information is time consuming and expensive.
Prof. Warren Powell - Princeton
What is the most efficient way to collect information?Prof. Peter Frazier - Cornell
How do we make the most money, as fast as possible?Me - @DrScottClark
OPTIMAL LEARNING
● Optimize some Overall Evaluation Criterion (OEC)○ Loss, Accuracy, Likelihood, Revenue
● Given tunable parameters○ Hyperparameters, feature parameters
● In an efficient way○ Sample function as few times as possible○ Training on big data is expensive
BAYESIAN GLOBAL OPTIMIZATION
Details at https://sigopt.com/research
Grid Search Random Search
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GRID SEARCH SCALES EXPONENTIALLY
4D
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...... ... ...BAYESIAN OPT SCALES LINEARLY
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HOW DOES IT FIT IN THE STACK?
Big Data
Machine LearningModels
with tunable parameters
Optimally suggests new parameters
HOW DOES IT FIT IN THE STACK?
Objective Metric
New parameters
Big Data
Machine LearningModels
with tunable parameters
Optimally suggests new parameters
HOW DOES IT FIT IN THE STACK?
Objective Metric
New parameters
Better Models
Big Data
Machine LearningModels
with tunable parameters
QUICK EXAMPLES
Optimally suggests new parameters
Ex: LOAN CLASSIFICATION (xgboost)
Prediction Accuracy
New parameters
Better AccuracyLoan
Applications
Default Prediction
with tunableML parameters
● Income● Credit Score● Loan Amount
COMPARATIVE PERFORMANCE
● 8.2% Better Accuracy than baseline
● 100x faster than standard tuning methods
Accuracy
Cost
Grid Search
Random Search
IterationsA
UC
.698
.690
.683
.6751,00010,000100,000
EXAMPLE: ALGORITHMIC TRADING
Expected Revenue
New parameters
Higher Returns
Market Data
Trading Strategy
with tunableweights and thresholds
● Closing Prices● Day of Week● Market Volatility
Optimally suggests new parameters
COMPARATIVE PERFORMANCE
Standard Method
Expert
● 200% Higher model returns than expert
● 10x faster than standard methods
HOW BAYESIAN OPTIMIZATION WORKS
1. Build Gaussian Process (GP) with points sampled so far
2. Optimize the fit of the GP (covariance hyperparameters)
3. Find the point(s) of highest Expected Improvement within parameter domain
4. Return optimal next best point(s) to sample
HOW DOES IT WORK?
HOW DOES IT WORK?
1. User reports data
2. SigOpt builds statistical model (Gaussian Process)
3. SigOpt finds the points of highest Expected Improvement
4. SigOpt suggests best parameters to test next
5. User tests those parameters and reports results to SigOpt
6. Repeat
HOW DOES IT WORK?
1. User reports data
2. SigOpt builds statistical model (Gaussian Process)
3. SigOpt finds the points of highest Expected Improvement
4. SigOpt suggests best parameters to test next
5. User tests those parameters and reports results to SigOpt
6. Repeat
HOW DOES IT WORK?
1. User reports data
2. SigOpt builds statistical model (Gaussian Process)
3. SigOpt finds the points of highest Expected Improvement
4. SigOpt suggests best parameters to test next
5. User tests those parameters and reports results to SigOpt
6. Repeat
HOW DOES IT WORK?
1. User reports data
2. SigOpt builds statistical model (Gaussian Process)
3. SigOpt finds the points of highest Expected Improvement
4. SigOpt suggests best parameters to test next
5. User tests those parameters and reports results to SigOpt
6. Repeat
HOW DOES IT WORK?
1. User reports data
2. SigOpt builds statistical model (Gaussian Process)
3. SigOpt finds the points of highest Expected Improvement
4. SigOpt suggests best parameters to test next
5. User tests those parameters and reports results to SigOpt
6. Repeat
HOW DOES IT WORK?
1. User reports data
2. SigOpt builds statistical model (Gaussian Process)
3. SigOpt finds the points of highest Expected Improvement
4. SigOpt suggests best parameters to test next
5. User tests those parameters and reports results to SigOpt
6. Repeat
EXTENDED EXAMPLE:EFFICIENTLY BUILDING CONVNETS
● Classify house numbers with more training data and more sophisticated model
PROBLEM
● TensorFlow makes it easier to design DNN architectures, but what structure works best on a given dataset?
CONVNET STRUCTURE
● Per parameter adaptive SGD variants like RMSProp and Adagrad seem to work best
● Still require careful selection of learning rate (α), momentum (β), decay (γ) terms
STOCHASTIC GRADIENT DESCENT
● Comparison of several RMSProp SGD parametrizations
● Not obvious which configurations will work best on a given dataset without experimentation
STOCHASTIC GRADIENT DESCENT
RESULTS
● Avg Hold out accuracy after 5 optimization runs consisting of 80 objective evaluations
● Optimized single 80/20 CV fold on training set, ACC reported on test set as hold out
PERFORMANCE
SigOpt(TensorFlow CNN)
Rnd Search(TensorFlow CNN)
No Tuning (sklearn RF)
No Tuning(TensorFlow CNN)
Hold Out ACC 0.8130 (+315.2%) 0.5690 0.5278 0.1958
COST ANALYSIS
Model Performance (CV Acc. threshold)
Random Search Cost
SigOpt Cost
SigOpt Cost Savings
Potential Savings In Production (50 GPUs)
87 % $275 $42 84% $12,530
85 % $195 $23 88% $8,750
80 % $46 $21 55% $1,340
70 % $29 $21 27% $400
EXAMPLE: TUNING DNN CLASSIFIERS
CIFAR10 Dataset● Photos of objects
● 10 classes
● Metric: Accuracy○ [0.1, 1.0]
Learning Multiple Layers of Features from Tiny Images, Alex Krizhevsky, 2009.
● All convolutional neural network● Multiple convolutional and dropout layers● Hyperparameter optimization mixture of
domain expertise and grid search (brute force)
USE CASE: ALL CONVOLUTIONAL
http://arxiv.org/pdf/1412.6806.pdf
MANY TUNABALE PARAMETERS...
● epochs: “number of epochs to run fit” - int [1,∞]● learning rate: influence on current value of weights at each step - double (0, 1]● momentum coefficient: “the coefficient of momentum” - double (0, 1]● weight decay: parameter affecting how quickly weight decays - double (0, 1]● depth: parameter affecting number of layers in net - int [1, 20(?)]● gaussian scale: standard deviation of initialization normal dist. - double (0,∞] ● momentum step change: mul. amount to decrease momentum - double (0, 1]● momentum step schedule start: epoch to start decreasing momentum - int [1,∞]● momentum schedule width: epoch stride for decreasing momentum - int [1,∞]
...optimal values non-intuitive
COMPARATIVE PERFORMANCE
● Expert baseline: 0.8995○ (using neon)
● SigOpt best: 0.9011○ 1.6% reduction in
error rate○ No expert time
wasted in tuning
USE CASE: DEEP RESIDUAL
http://arxiv.org/pdf/1512.03385v1.pdf
● Explicitly reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions
● Variable depth● Hyperparameter optimization mixture of domain expertise and grid
search (brute force)
COMPARATIVE PERFORMANCE
Standard Method
● Expert baseline: 0.9339○ (from paper)
● SigOpt best: 0.9436○ 15% relative error
rate reduction○ No expert time
wasted in tuning
@DrScottClark
https://sigopt.com@SigOpt
TRY OUT SIGOPT FOR FREE
https://sigopt.com/getstarted
● Quick example and intro to SigOpt● No signup required● Visual and code examples
MORE EXAMPLES
https://github.com/sigopt/sigopt-examples Examples of using SigOpt in a variety of languages and contexts.
Tuning Machine Learning Models (with code)A comparison of different hyperparameter optimization methods.
Using Model Tuning to Beat Vegas (with code)Using SigOpt to tune a model for predicting basketball scores.
Learn more about the technology behind SigOpt athttps://sigopt.com/research
GPs: FUNCTIONAL VIEW
overfit good fit underfit
GPs: FITTING THE GP
USE CASE: CLASSIFICATION MODELSMachine Learning models have many non-intuitive tunable hyperparameters
Problem:
BeforeStandard methods use high
resources for low performance
AfterSigOpt finds better parameters
with 10x fewer evaluations than standard methods
USE CASE: SIMULATIONS
BETTER RESULTS+450% FASTER
Expensive simulations require high resources for every run
Problem:
BeforeBrute force tuning approach
prohibitively expensive
AfterSigOpt finds better results with
fewer required simulations
