Grid (Hyperparameter) Search

H2O supports two types of grid search – traditional (or “cartesian”) grid search and random grid search. In a cartesian grid search, users specify a set of values for each hyperparamter that they want to search over, and H2O will train a model for every combination of the hyperparameter values. This means that if you have three hyperparameters and you specify 5, 10 and 2 values for each, your grid will contain a total of 5*10*2 = 100 models.

In random grid search, the user specifies the hyperparamter space in the exact same way, except H2O will sample uniformly from the set of all possible hyperparamter value combinations. In random grid search, the user also specifies a stopping criterion, which controls when the random grid search is completed. The user can tell the random grid search to stop by specifying a maximum number of models or the maximum number of seconds allowed for the search. The user may also specify a performance-metric-based stopping criterion, which will stop the random grid search when the performance stops improving by a specified amount.

Once the grid search is complete, the user can query the grid object and sort the models by a particular performance metric (for example, “AUC”). All models are stored in the H2O cluster and are accessible by model id.

Examples of how to perform cartesian and random grid search in all of H2O’s APIs follow below. There are also longer grid search tutorials available for R and Python.

Quick Links

• Grid Search in R
• Grid Search in Python
• Java API
• REST API
• Supported Grid Search Hyperparameters
• Grid Testing
• Caveats/In Progress
• Additional Documentation

Grid Search in R

Grid search in R provides the following capabilities:

• H2OGrid class: Represents the results of the grid search
• h2o.getGrid(<grid_id>, sort_by, decreasing): Displays the specified grid
• h2o.grid(): Starts a new grid search parameterized by
  • model builder name (e.g., gbm)
  • model parameters (e.g., ntrees = 100)
  • hyper_parameters attribute for passing a list of hyper parameters (e.g., list(ntrees = c(1,100), learn_rate = c(0.1, 0.001)))
  • search_criteria optional attribute for specifying a more advanced search strategy

More about search_criteria:

This is a named list of control parameters for smarter hyperparameter search. The list can include values for: strategy, max_models, max_runtime_secs, stopping_metric, stopping_tolerance, stopping_rounds and seed. The default value for strategy, “Cartesian”, covers the entire space of hyperparameter combinations. If you want to use cartesian grid search, you can leave the search_criteria argument unspecified. Specify the “RandomDiscrete” strategy to perform a random search of all the combinations of your hyperparameters. RandomDiscrete should be usually combined with at least one early stopping criterion, max_models and/or max_runtime_secs. Some examples below:

list(strategy = "RandomDiscrete", max_models = 10, seed = 1)
list(strategy = "RandomDiscrete", max_runtime_secs = 3600)
list(strategy = "RandomDiscrete", max_models = 42, max_runtime_secs = 28800)
list(strategy = "RandomDiscrete", stopping_tolerance = 0.001, stopping_rounds = 10)
list(strategy = "RandomDiscrete", stopping_metric = "misclassification", stopping_tolerance = 0.0005, stopping_rounds = 5)

Grid Search Example in R

library(h2o)

h2o.init()

# Import a sample binary outcome dataset into H2O
data <- h2o.importFile("https://s3.amazonaws.com/erin-data/higgs/higgs_train_10k.csv")
test <- h2o.importFile("https://s3.amazonaws.com/erin-data/higgs/higgs_test_5k.csv")

# Identify predictors and response
y <- "response"
x <- setdiff(names(data), y)

# For binary classification, response should be a factor
data[,y] <- as.factor(data[,y])
test[,y] <- as.factor(test[,y])

# Split data into train & validation
ss <- h2o.splitFrame(data, seed = 1)
train <- ss[[1]]
valid <- ss[[2]]

# GBM hyperparamters
gbm_params1 <- list(learn_rate = c(0.01, 0.1),
                    max_depth = c(3, 5, 9),
                    sample_rate = c(0.8, 1.0),
                    col_sample_rate = c(0.2, 0.5, 1.0))

# Train and validate a cartesian grid of GBMs
gbm_grid1 <- h2o.grid("gbm", x = x, y = y,
                      grid_id = "gbm_grid1",
                      training_frame = train,
                      validation_frame = valid,
                      ntrees = 100,
                      seed = 1,
                      hyper_params = gbm_params1)

# Get the grid results, sorted by validation AUC
gbm_gridperf1 <- h2o.getGrid(grid_id = "gbm_grid1",
                             sort_by = "auc",
                             decreasing = TRUE)
print(gbm_gridperf1)

# Grab the top GBM model, chosen by validation AUC
best_gbm1 <- h2o.getModel(gbm_gridperf1@model_ids[[1]])

# Now let's evaluate the model performance on a test set
# so we get an honest estimate of top model performance
best_gbm_perf1 <- h2o.performance(model = best_gbm1,
                                  newdata = test)
h2o.auc(best_gbm_perf1)
# 0.7781779

# Look at the hyperparamters for the best model
print(best_gbm1@model[["model_summary"]])

Random Grid Search Example in R

# Use same data as above

# GBM hyperparamters (bigger grid than above)
gbm_params2 <- list(learn_rate = seq(0.01, 0.1, 0.01),
                    max_depth = seq(2, 10, 1),
                    sample_rate = seq(0.5, 1.0, 0.1),
                    col_sample_rate = seq(0.1, 1.0, 0.1))
search_criteria <- list(strategy = "RandomDiscrete", max_models = 36, seed = 1)

# Train and validate a random grid of GBMs
gbm_grid2 <- h2o.grid("gbm", x = x, y = y,
                      grid_id = "gbm_grid2",
                      training_frame = train,
                      validation_frame = valid,
                      ntrees = 100,
                      seed = 1,
                      hyper_params = gbm_params2,
                      search_criteria = search_criteria)

gbm_gridperf2 <- h2o.getGrid(grid_id = "gbm_grid2",
                             sort_by = "auc",
                             decreasing = TRUE)
print(gbm_gridperf2)

# Grab the top GBM model, chosen by validation AUC
best_gbm2 <- h2o.getModel(gbm_gridperf2@model_ids[[1]])

# Now let's evaluate the model performance on a test set
# so we get an honest estimate of top model performance
best_gbm_perf2 <- h2o.performance(model = best_gbm2,
                                  newdata = test)
h2o.auc(best_gbm_perf2)
# 0.7810757

# Look at the hyperparamters for the best model
print(best_gbm2@model[["model_summary"]])

For more information, refer to the R grid search tutorial, R grid search code, and runit_GBMGrid_airlines.R.

Grid Search in Python

• Class is H2OGridSearch
• <grid_name>.show(): Display a list of models (including model IDs, hyperparameters, and MSE) explored by grid search (where <grid_name> is an instance of an H2OGridSearch class)
• grid_search = H2OGridSearch(<model_type), hyper_params=hyper_parameters): Start a new grid search parameterized by:
  • model_type is the type of H2O estimator model with its unchanged parameters
  • hyper_params in Python is a dictionary of string parameters (keys) and a list of values to be explored by grid search (values) (e.g., {'ntrees':[1,100], 'learn_rate':[0.1, 0.001]}
  • search_criteria is the optional dictionary for specifying more a advanced search strategy

More about search_criteria:

This is a dictionary of control parameters for smarter hyperparameter search. The dictionary can include values for: strategy, max_models, max_runtime_secs, stopping_metric, stopping_tolerance, stopping_rounds and seed. The default value for strategy, “Cartesian”, covers the entire space of hyperparameter combinations. If you want to use cartesian grid search, you can leave the search_criteria argument unspecified. Specify the “RandomDiscrete” strategy to perform a random search of all the combinations of your hyperparameters. RandomDiscrete should be usually combined with at least one early stopping criterion, max_models and/or max_runtime_secs. Some examples below:

{'strategy': "RandomDiscrete", 'max_models': 10, 'seed': 1}
{'strategy': "RandomDiscrete", 'max_runtime_secs': 3600}
{'strategy': "RandomDiscrete", 'max_models': 42, 'max_runtime_secs': 28800}
{'strategy': "RandomDiscrete", 'stopping_tolerance': 0.001, 'stopping_rounds': 10}
{'strategy': "RandomDiscrete", 'stopping_metric': "misclassification", 'stopping_tolerance': 0.0005, 'stopping_rounds': 5}

Grid Search Example in Python

import h2o
from h2o.estimators.gbm import H2OGradientBoostingEstimator
from h2o.grid.grid_search import H2OGridSearch

h2o.init()

# Import a sample binary outcome dataset into H2O
data = h2o.import_file("https://s3.amazonaws.com/erin-data/higgs/higgs_train_10k.csv")
test = h2o.import_file("https://s3.amazonaws.com/erin-data/higgs/higgs_test_5k.csv")

# Identify predictors and response
x = data.columns
y = "response"
x.remove(y)

# For binary classification, response should be a factor
data[y] = data[y].asfactor()
test[y] = test[y].asfactor()

# Split data into train & validation
ss = data.split_frame(seed = 1)
train = ss[0]
valid = ss[1]

# GBM hyperparameters
gbm_params1 = {'learn_rate': [0.01, 0.1],
                'max_depth': [3, 5, 9],
                'sample_rate': [0.8, 1.0],
                'col_sample_rate': [0.2, 0.5, 1.0]}

# Train and validate a cartesian grid of GBMs
gbm_grid1 = H2OGridSearch(model=H2OGradientBoostingEstimator,
                          grid_id='gbm_grid1',
                          hyper_params=gbm_params1)
gbm_grid1.train(x=x, y=y,
                training_frame=train,
                validation_frame=valid,
                ntrees=100,
                seed=1)

# Get the grid results, sorted by validation AUC
gbm_gridperf1 = gbm_grid1.get_grid(sort_by='auc', decreasing=True)
gbm_gridperf1

# Grab the top GBM model, chosen by validation AUC
best_gbm1 = gbm_gridperf1.models[0]

# Now let's evaluate the model performance on a test set
# so we get an honest estimate of top model performance
best_gbm_perf1 = best_gbm1.model_performance(test)

best_gbm_perf1.auc()
# 0.7781778619721595

Random Grid Search Example in Python

# Use same data as above

# GBM hyperparameters
gbm_params2 = {'learn_rate': [i * 0.01 for i in range(1, 11)],
                'max_depth': list(range(2, 11)),
                'sample_rate': [i * 0.1 for i in range(5, 11)],
                'col_sample_rate': [i * 0.1 for i in range(1, 11)]}

# Search criteria
search_criteria = {'strategy': 'RandomDiscrete', 'max_models': 36, 'seed': 1}

# Train and validate a random grid of GBMs
gbm_grid2 = H2OGridSearch(model=H2OGradientBoostingEstimator,
                          grid_id='gbm_grid2',
                          hyper_params=gbm_params2,
                          search_criteria=search_criteria)
gbm_grid2.train(x=x, y=y,
                training_frame=train,
                validation_frame=valid,
                ntrees=100,
                seed=1)

# Get the grid results, sorted by validation AUC
gbm_gridperf2 = gbm_grid2.get_grid(sort_by='auc', decreasing=True)
gbm_gridperf2

# Grab the top GBM model, chosen by validation AUC
best_gbm2 = gbm_gridperf2.models[0]

# Now let's evaluate the model performance on a test set
# so we get an honest estimate of top model performance
best_gbm_perf2 = best_gbm2.model_performance(test)

best_gbm_perf2.auc()
# 0.7810757307013204

For more information, refer to the Python grid search tutorial, Python grid search code, and pyunit_benign_glm_grid.py.

Grid Search Java API

Each parameter exposed by the schema can specify if it is supported by grid search by including the attribute gridable=true in the schema @API annotation. In any case, the Java API does not restrict the parameters supported by grid search.

There are two core entities: Grid and GridSearch. GridSeach is a job-building Grid object and is defined by the user’s model factory and the hyperspace walk strategy. The model factory must be defined for each supported model type (DRF, GBM, DL, and K-means). The hyperspace walk strategy specifies how the user-defined space of hyperparameters is traversed. The space definition is not limited. For each point in hyperspace, model parameters of the specified type are produced.

The implementation supports a simple cartesian grid search as well as random search with several different stopping criteria. Grid build triggers a new model builder job for each hyperspace point returned by the walk strategy. If the model builder job fails, the resulting model is ignored; however, it can still be tracked in the job list, and errors are returned in the grid build result.

Model builder jobs are run serially in sequential order. More advanced job scheduling schemes are under development. Note that in cases of true big data, sequential scheduling will yield the highest performance. It is only with a large cluster and small data that concurrent scheduling will improve performance.

The grid object contains the results of the grid search: a list of model keys produced by the grid search as well as any errors, and a table of metrics for each succesful model. The grid object publishes a simple API to get the models.

Launch the grid search by specifying:

• the common model hyperparameters (parameter values that will be common across all models in the search)
• the search hyperparameters (a map <parameterName, listOfValues> that defines the parameter spaces to traverse)
• optionally, search criteria (an instance of HyperSpaceSearchCriteria)

The Java API can grid search any parameters defined in the model parameter’s class (e.g., GBMParameters). Paramters that are appropriate for gridding are marked by the @API parameter, but this is not enforced by the framework.

Additional methods are available in the model builder to support creation of model parameters and configuration. This eliminates the requirement of the previous implementation where each gridable value was represented as a double. This also allows users to specify different building strategies for model parameters. For example, the REST layer uses a builder that validates parameters against the model parameter’s schema, where the Java API uses a simple reflective builder. Additional reflections support is provided by PojoUtils (methods setField, getFieldValue).

Example

HashMap<String, Object[]> hyperParms = new HashMap<>();
hyperParms.put("_ntrees", new Integer[]{1, 2});
hyperParms.put("_distribution", new DistributionFamily[]{DistributionFamily.multinomial});
hyperParms.put("_max_depth", new Integer[]{1, 2, 5});
hyperParms.put("_learn_rate", new Float[]{0.01f, 0.1f, 0.3f});

// Setup common model parameters
GBMModel.GBMParameters params = new GBMModel.GBMParameters();
params._train = fr._key;
params._response_column = "cylinders";
// Trigger new grid search job, block for results and get the resulting grid object
GridSearch gs =
 GridSearch.startGridSearch(params, hyperParms, GBM_MODEL_FACTORY, new HyperSpaceSearchCriteria.CartesianSearchCriteria());
Grid grid = (Grid) gs.get();

Exposing grid search end-point for a new algorithm

In the following example, the PCA algorithm has been implemented, and we would like to expose the algorithm via REST API. The following aspects are assumed:

• The PCA model builder is called PCA
• The PCA parameters are defined in a class called PCAParameters
• The PCA parameters schema is called PCAParametersV3

To add support for PCA grid search:

1. Add the PCA model build factory into the hex.grid.ModelFactories class:

class ModelFactories {
 /* ... */
 public static ModelFactory<PCAModel.PCAParameters>
   PCA_MODEL_FACTORY =
   new ModelFactory<PCAModel.PCAParametners>() {
     @Override
     public String getModelName() {
       return "PCA";
     }
     @Override
     public ModelBuilder buildModel(PCAModel.PCAParameters params) {
       return new PCA(params);
     }
  };
}

2. Add the PCA REST end-point schema:

public class PCAGridSearchV99 extends GridSearchSchema<PCAGridSearchHandler.PCAGrid,
 PCAGridSearchV99,
 PCAModel.PCAParameters,
 PCAV3.PCAParametersV3> {
}

3. Add the PCA REST end-point handler:

   public class PCAGridSearchHandler
    extends GridSearchHandler<PCAGridSearchHandler.PCAGrid,
    PCAGridSearchV99,
    PCAModel.PCAParameters,
    PCAV3.PCAParametersV3> {
   
      public PCAGridSearchV99 train(int version, PCAGridSearchV99 gridSearchSchema) {
        return super.do_train(version, gridSearchSchema);
      }
   
      @Override
      protected ModelFactory<PCAModel.PCAParameters> getModelFactory() {
        return ModelFactories.PCA_MODEL_FACTORY;
      }
   
      @Deprecated
      public static class PCAGrid extends Grid<PCAModel.PCAParameters> {
   
        public PCAGrid() {
          super(null, null, null, null);
        }
      }
   }
   

4. Register the REST end-point in the register factory hex.api.Register:

public class Register extends AbstractRegister {
  @Override
  public void register() {
    // ...
    H2O.registerPOST("/99/Grid/pca", PCAGridSearchHandler.class, "train", "Run grid search for PCA model.");
    // ...
  }
}

REST API

The current implementation of the grid search REST API exposes the following endpoints:

• GET /<version>/Grids: List available grids, with optional parameters to sort the list by model metric such as MSE
• GET /<version>/Grids/<grid_id>: Return specified grid
• POST /<version>/Grids/<algo_name>: Start a new grid search
  • <algo_name>: Supported algorithm values are {glm, gbm, drf, kmeans, deeplearning}

Endpoints accept model-specific parameters (e.g., GBMParametersV3) and an additional parameter called hyper_parameters, which contains a dictionary of the hyperparameters that will be searched. In this dictionary, an array of values is specified for each searched hyperparameter.

{
  "ntrees":[1,5],
  "learn_rate":[0.1,0.01]
}

An optional search_criteria dictionary specifies options for controlling more advanced search strategies. Currently, full Cartesian is the default. RandomDiscrete allows a random search over the hyperparameter space with three ways of specifying when to stop the search: max number of models, max time, and metric-based early stopping (e.g., stop if MSE hasn’t improved by 0.0001 over the 5 best models). An example is:

{
  "strategy": "RandomDiscrete",
  "max_runtime_secs": 600,
  "max_models": 100,
  "stopping_metric": "AUTO",
  "stopping_tolerance": 0.00001,
  "stopping_rounds": 5,
  "seed": 123456
}

With grid search, each model is built sequentially, allowing users to view each model as it is built.

Example

Invoke a new GBM model grid search by POSTing the following request to /99/Grid/gbm:

parms:{hyper_parameters={"ntrees":[1,5],"learn_rate":[0.1,0.01]}, training_frame="filefd41fe7ac0b_csv_1.hex_2", grid_id="gbm_grid_search", response_column="Species"", ignored_columns=[""]}

Supported Grid Search Hyperparameters

The following hyperparameters are supported by grid search.

Common Hyperparameters

• weights_column
• offset_column
• fold_column
• fold_assignment
• stopping_rounds
• max_runtime_secs
• stopping_metric
• stopping_tolerance

Shared Tree Hyperparameters

Note: The Shared Tree hyperparameters apply to DRF and GBM.

• balance_classes
• class_sampling_factors
• max_after_balance_size
• ntrees
• max_depth
• min_rows
• nbins
• nbins_top_level
• nbins_cats
• seed
• sample_rate
• sample_rate_per_class
• col_sample_rate_per_tree
• col_sample_rate_change_per_level
• min_split_improvement
• histogram_type

DRF Hyperparameters

• mtries
• categorical_encoding

GBM Hyperparameters

• learn_rate
• learn_rate_annealing
• col_sample_rate
• max_abs_leafnode_pred
• pred_noise_bandwidth
• distribution
• tweedie_power
• quantile_alpha
• huber_alpha
• categorical_encoding

Isolation Forest Hyperparameters

• mtries
• ntrees
• max_depth
• min_rows
• categorical_encoding
• sample_size
• sample_rate

K-Means Hyperparameters

• max_iterations
• standardize
• seed
• init
• estimate_k
• k
• categorical_encoding

GLM Hyperparameters

• seed
• tweedie_variance_power
• tweedie_link_power
• alpha
• lambda
• missing_values_handling
• standardize

GLRM Hyperparameters

• transform
• k
• loss
• multi_loss
• loss_by_col
• period
• regularization_x
• regularization_y
• gamma_x
• gamma_y
• max_iterations
• max_updates
• init_step_size
• min_step_size
• seed
• init
• svd_method

Naïve Bayes Hyperparameters

• laplace
• min_sdev
• eps_sdev
• min_prob
• eps_prob
• compute_metrics
• seed

PCA Hyperparameters

• transform
• k
• max_iterations

Deep Learning Hyperparameters

• balance_classes
• class_sampling_factors
• max_after_balance_size
• activation
• hidden
• epochs
• train_samples_per_iteration
• target_ratio_comm_to_comp
• seed
• adaptive_rate
• rho
• epsilon
• rate
• rate_annealing
• rate_decay
• momentum_start
• momentum_ramp
• momentum_stable
• nesterov_accelerated_gradient
• input_dropout_ratio
• hidden_dropout_ratios
• l1
• l2
• max_w2
• initial_weight_distribution
• initial_weight_scale
• initial_weights
• initial_biases
• loss
• distribution
• tweedie_power
• quantile_alpha
• score_interval
• score_training_samples
• score_validation_samples
• score_duty_cycle
• classification_stop
• regression_stop
• quiet_mode
• score_validation_sampling
• overwrite_with_best_model
• use_all_factor_levels
• standardize
• variable_importances
• fast_mode
• force_load_balance
• replicate_training_data
• single_node_mode
• shuffle_training_data
• missing_values_handling
• sparse
• col_major
• average_activation
• sparsity_beta
• max_categorical_features
• reproducible
• elastic_averaging
• elastic_averaging_moving_rate
• elastic_averaging_regularization
• categorical_encoding

Aggregator Hyperparameters

• radius_scale
• transform
• pca_method
• k
• max_iterations

XGBoost Hyperparameters

• ntrees
• max_depth
• min_rows
• seed
• sample_rate
• subsample
• col_sample_rate
• col_sample_by_level
• col_sample_rate_per tree
• colsample_bytree
• min_split_improvement
• gamma
• learn_rate
• eta
• max_abs_leafnode_pred
• max_delta_step
• distribution
• tweedie_power
• categorical_encoding
• tree_method
• num_leaves
• min_sum_hessian_in_leaf
• min_data_in_leaf
• grow_policy
• booster
• reg_lambda
• sample_type
• normalize_type
• rate_drop
• one_drop
• skip_drop

AutoML Hyperparameters

• keep_cross_validation_models

Grid Testing

The current test infrastructure includes:

R Tests

• GBM grids using wine, airlines, and iris datasets verify the consistency of results
• DL grid using the hidden parameter verifying the passing of structured parameters as a list of values
• Minor R testing support verifying equality of the model’s parameters against a given list of hyper parameters.

JUnit Test

• Basic tests verifying consistency of the results for DRF, GBM, and KMeans
• JUnit test assertions for grid results

There are tests for the RandomDiscrete search criteria in runit_GBMGrid_airlines.R and pyunit_benign_glm_grid.py.

Caveats/In Progress

• Currently, the schema system requires specific classes instead of parameterized classes. For example, the schema definition Grid<GBMParameters> is not supported unless your define the class GBMGrid extends Grid<GBMParameters>.
• Grid Job scheduler is sequential only; schedulers for concurrent builds are under development. Note that in cases of true big data sequential scheduling will yield the highest performance. It is only with a large cluster and small data that concurrent scheduling will improve performance.
• The model builder job and grid jobs are not associated.
• There is no way to list the hyper space parameters that caused a model builder job failure.
• The h2o.get_grid() (Python) or h2o.getGrid() (R) function can be called to retrieve a grid search instance. If neither cross-validation nor a validation frame is used in the grid search, then the training metrics will display in the “get grid” output. If a validation frame is passed to the grid, and nfolds = 0, then the validation metrics will display. However, if nfolds > 1, then cross-validation metrics will display even if a validation frame is provided.

Additional Documentation

• H2O Core Java Developer Documentation: The definitive Java API guide for the core components of H2O.
• H2O Algos Java Developer Documentation: The definitive Java API guide for the algorithms used by H2O.
• Hyperparameter Optimization in H2O: A guide to Grid Search and Random Search in H2O.