BAYESIAN GLOBAL OPTIMIZATIONUsing Optimal Learning to Tune ML Models

Scott Clark

scott@sigopt.com

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

Questions?scott@sigopt.com

@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