BAYESIAN GLOBAL OPTIMIZATIONUsing Optimal Learning to Tune ML Models
Scott Clark
OUTLINE
1. Why is Tuning ML Models Hard?
2. Standard Tuning Methods
3. Bayesian Global Optimization
4. Comparing Optimizers
5. Real World Examples
Machine Learning is extremely powerful
Machine Learning is extremely powerful
Tuning Machine Learning systems is extremely non-intuitive
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)
Photo: Joe Ross
TUNABLE PARAMETERS IN DEEP LEARNING
TUNABLE PARAMETERS IN DEEP LEARNING
TUNABLE PARAMETERS IN DEEP LEARNING
Photo: Tammy Strobel
STANDARD METHODSFOR HYPERPARAMETER SEARCH
EXAMPLE: FRANKE FUNCTION
Grid Search Random Search
This slide’s GIF loops automatically
Predictive Models
PredictiveModels
TUNING MACHINE LEARNING MODELS
New parameters
Objective Metric
Better Models
Big Data
BAYESIAN GLOBAL OPTIMIZATION
… 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?Scott Clark - CEO, SigOpt
OPTIMAL LEARNING
● Optimize objective function○ Loss, Accuracy, Likelihood
● Given parameters○ Hyperparameters, feature parameters
● Find the best hyperparameters○ Sample function as few times as possible○ Training on big data is expensive
BAYESIAN GLOBAL OPTIMIZATION
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?
GAUSSIAN PROCESSES
GAUSSIAN PROCESSES
GAUSSIAN PROCESSES
GAUSSIAN PROCESSES
GAUSSIAN PROCESSES
GAUSSIAN PROCESSES
GAUSSIAN PROCESSES
GAUSSIAN PROCESSES
overfit good fit underfit
GAUSSIAN PROCESSES
EXPECTED IMPROVEMENT
EXPECTED IMPROVEMENT
EXPECTED IMPROVEMENT
EXPECTED IMPROVEMENT
EXPECTED IMPROVEMENT
EXPECTED IMPROVEMENT
EVALUATING THE OPTIMIZER
What is the best value found after optimization completes?
METRIC: BEST FOUND
BLUE RED
BEST_FOUND 0.7225 0.8949
How quickly is optimum found? (area under curve)
METRIC: AUC
BLUE RED
BEST_FOUND 0.9439 0.9435
AUC 0.8299 0.9358
● Optimization functions (eg Branin, Ackeley, Rosenbrock)● ML datasets (LIBSVM)
BENCHMARK SUITE
TEST FUNCTION TYPE COUNT
Continuous Params 184
Noisy Observations 188
Parallel Observations 45
Integer Params 34
Categorical Params / ML 47
Failure Observations 30
TOTAL 489
● On-demand cluster in AWS for parallel eval function optimization
● Full eval consists of
~10000 optimizations, taking ~4 hours
INFRASTRUCTURE
VIZ TOOL : BEST SEEN TRACES
METRICS: STOCHASTICITY
● Run each 20 times
● Mann-Whitney U test for significance
RANKING OPTIMIZERS● Alternate methods exist for black box optimization :
Spearmint, TPE, SMAC, PSO, RND Search, Grid Search
● Important to understand / track method performance disparity on high-level categories of functions
● For a given test function, want a partial ranking (allowing for ties) of method performance
RANKING OPTIMIZERS● First, Mann-Whitney U
tests using BEST_FOUND
● Tied results then partially ranked using AUC
● Any remaining ties, stay as ties for final ranking
RANKING AGGREGATION
● Aggregate partial rankings across all eval functions using Borda count (sum of methods ranked lower)
SHORT RESULTS SUMMARY
SIGOPT SERVICE
Predictive Models
PredictiveModels
HOW DOES SIGOPT INTEGRATE?
New parameters
Objective Metric
Better Models
Big Data
SIMPLIFIED MANAGEMENT
Before SigOpt
DISTRIBUTED MODEL TRAINING
● SigOpt serves as an AWS-ready distributed scheduler for training models across workers
● Each worker accesses the SigOpt API for the latest parameters to try
● Enables distributed training of non-distributed algorithms
INTEGRATIONS
REST API
@DrScottClark
https://sigopt.com@SigOpt
SHORT EXAMPLES
EXAMPLE: LOAN DATA
Loan Applications
Default Prediction
with tunableML parameters
● Income● Credit Score● Loan Amount
New parameters
Prediction Accuracy
Better Accuracy
COMPARATIVE PERFORMANCE
Accu
racy
Grid Search
Random Search
AU
C
.698
.690
.683
.675$1,000100 hrs
$10,0001,000 hrs
$100,00010,000 hrs
Cost
● Better: 22% fewer bad loans vs baseline
● Faster/Cheaper: 100x less time and AWS cost than standard tuning methods
EXAMPLE: ALGORITHMIC TRADING
Market Data
Trading Strategy
with tunableweights and thresholds
● Closing Prices● Day of Week● Market Volatility
New parameters
Expected Revenue
Higher Returns
COMPARATIVE PERFORMANCE
Standard Method
Expert
● Better: 200% Higher model returns than expert
● Faster/Cheaper: 10x faster than standard methods
1. SigOpt Live Demo
2. More Examplesa. Text Classification
b. Unsupervised + Supervised
c. Neural Nets with TensorFlow
ADDITIONAL TOPICS
AUTOMATICALLY TUNING TEXT SENTIMENT CLASSIFIER
● Automatically tune text sentiment classifier
● Amazon product review dataset (35K labels) eg : “This DVD is great. It brings back all the memories of the holidays as a young child.”
● Logistic regression is generally a good place to start
PROBLEM
● Maximize mean of k-fold cross-validation accuracies ● k = 5 folds, train and valid randomly split 70%, 30%
OBJECTIVE FUNCTION
● n-gram vocabulary selection parameters
● (min_n_gram, ngram_offset) determine which n-grams● (log_min_df, df_offset) filter for n-grams within df range
TEXT FEATURE PARAMETERS
Original Text “SigOpt optimizes any complicated system”
1-grams { “SigOpt”, “optimizes”, “any”, “complicated”, “system”}
2-grams { “SigOpt_optimizes”, “optimizes_any”, “any_complicated” … }
3-grams { “SigOpt_optimizes_any”, “optimizes_any_complicated” … }
● Logistic regression error cost parameters
M = number of training examples
θ = vector of weights the algorithm will learn for each n-gram in vocabulary
yi - training data label : {-1, 1} for our two class problem
xi - training data input vector: BOW vectors described in previous section
α - weight of regularization term (log_reg_coef in our experiment)
ρ - weight of l1 norm term (l1_coef in our experiment)
ERROR COST PARAMETERS
● 50 line python snippet to train and tune classifier with SigOpt
● 20 lines to define 6 parameter experiment and run optimization loop using SigOpt
PYTHON CODE
● E[f (λ)] after 20 runs, each run consisting of 60 function evaluations
● For Grid Search : 64 evenly spaced parameter configurations (order shuffled randomly)
● SigOpt statistical significance over grid and rnd (p = 0.0001, Mann-Whitney U test)
PERFORMANCE
SigOpt Rnd. Search Grid Search No Tuning (Baseline)
Best Found 0.8760 (+5.72%) 0.8673 (+4.67%) 0.8680 (+4.76%) 0.8286
EXPLOITING UNLABELLED DATA
● Classify house number digits with lack of labelled data
● Challenging digit variations, image clutter with neighboring digits
PROBLEM
● In general we’ll search for an optimized ML pipeline
OBJECTIVE
● Transform image patches into vectors of centroid distances, then pool to form final representation
● SigOpt optimizes selection of w, pool_r, K
UNSUPERVISED MODEL PARAMS
● Whitening transform often useful as image data pre-processing step, expose εZCA to SigOpt
UNSUPERVISED MODEL PARAMS
● Tune sparsity of centroid distance transform
● SigOpt optimizes threshold (active_p) selection
UNSUPERVISED MODEL PARAMS
● learning rate number of trees tree parameters (max_depth, sub_sample_sz), exposed to SigOpt
SUPERVISED MODEL PARAMS
METRIC OPTIMIZATION
● 20 optimization runs, each run consisting of 90 / 40 function evaluations for Unsup / Raw feature settings
● Optimized single CV fold on training set, ACC reported on test set as hold out
PERFORMANCE
SigOpt (Unsup Feats)
Rnd Search(Unsup Feats)
SigOpt (Raw Feats)
Rnd Search(Raw Feats)
No Tuning RF(Raw Feats)
Hold Out ACC 0.8708 (+51.4%) 0.8583 0.6844 0.6739 0.5751
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
METRIC OPTIMIZATION
● 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
https://sigopt.com/getstarted
Try it yourself!
MORE EXAMPLES
Automatically Tuning Text Classifiers (with code)A short example using SigOpt and scikit-learn to build and tune a text sentiment classifier.
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
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