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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 hyperparameter 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 hyperparameter space in the exact same way, except H2O will sample uniformly from the set of all possible hyperparameter 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. Longer grid search tutorials are also available for R and Python.

Grid Search in R and Python​

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 (for example, gbm)
    • model parameters (for example, ntrees = 100)
    • hyper_parameters attribute for passing a list of hyper parameters (for example, list(ntrees = c(1,100), learn_rate = c(0.1, 0.001)))
    • search_criteria optional attribute for specifying a more advanced search strategy
    • parallelism The number of models to build in parallel. Parallelism allows the leader node to search the hyperspace and build models in a parallel way, which ultimately speeds up grid search on small data. A value of 1 (default) specifies sequential building. Specify 0 for adaptive parallelism, which is decided by H2O. Any number >1 sets the exact number of models built in parallel.

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 is Cartesian, which 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. You can also use Sequential, which goes through the specified parameters in sequence and requires the specified parameter lists to have the same length. The Sequential strategy exposes the early_stopping parameter (defaults to TRUE) that can be used to disable early stopping while still obeying the max_models and 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)

list(strategy = "Sequential", max_runtime_secs = 3600)
list(strategy = "Sequential", max_models = 42, max_runtime_secs = 28800)
list(strategy = "Sequential", stopping_tolerance = 0.001, stopping_rounds = 10)
list(strategy = "Sequential", early_stopping = FALSE)
list(strategy = "Sequential", early_stopping = FALSE, max_models = 42, max_runtime_secs = 28800)

Grid Search Examples​

library(h2o)

h2o.init()

# Import a sample binary outcome dataset into H2O
data <- h2o.importFile("https://s3.amazonaws.com/h2o-public-test-data/smalldata/higgs/higgs_train_10k.csv")
test <- h2o.importFile("https://s3.amazonaws.com/h2o-public-test-data/smalldata/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 hyperparameters
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 hyperparameters for the best model
print(best_gbm1@model[["model_summary"]])

Random Grid Search Examples​

# Use same data as previous example

# GBM hyperparameters (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 hyperparameters 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 the GBM grid airlines test.

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

H2O supports saving and loading grids even after a cluster wipe or complete cluster restart. The save_grid function will export a grid and its models into a given folder while the load_grid function loads a previously saved grid and all its models from the given folder.

Two modes are available to save a grid (in both R and Python):

  • Use auto-checkpointing and supply the export_checkpoints_dir parameter
  • Call the function h2o.save_grid for manual export

Checkpointing Example​

Using the Grid Search example through the hyperparameters section, run the following additional commands to retrieve the checkpointed saved grid.

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

# Identify the grid_id and model_ids
grid_id <- gbm_grid1@grid_id
gbm_grid_model_count <- length(gbm_grid1@model_ids)

# Wipe the cloud to simulate cluster restart 
#(the models will no longer be available)
h2o.removeAll()

# Retrieve the saved grid
grid <- h2o.loadGrid(paste0(tempdir(), "/", grid_id))
grid

Manual Export Example​

Using the Grid Search example through the hyperparameters section, run the following additional commands to retrieve the manually exported saved grid.

# 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)

# Identify the grid_id and model_ids
grid_id <- gbm_grid1@grid_id
gbm_grid1_model_count <- length(gbm_grid1@model_ids)

# Save the grid
saved_path <- h2o.saveGrid(grid_directory = tempdir(), grid_id = grid_id)

# Wipe the cloud to simulate cluster restart 
#(the models will no longer be available)
h2o.removeAll()

# Retrieve the saved grid
grid <- h2o.loadGrid(saved_path)
grid

H2O supports progress recovery should the cluster fail during grid training. The recovery_dir parameter will cause the grid to save all its inputs and outputs into the given directory, and should the training fail, the grid progress can be resumed from the last model that was successfully trained.

iris <- h2o.importFile(
    "https://s3.amazonaws.com/h2o-public-test-data/smalldata/iris/iris.csv", 
    destination_frame="iris"
)
hyper_parameters <- list(
    learn_rate=c(0.01, 0.02, 0.03, 0.04),
    ntrees=c(100, 120, 130, 140)
)
# train a cartesian grid of GBMs
gbm_grid <- h2o.grid(
    "gbm", x=1:4, y=5, 
    grid_id="gbm_grid", training_frame=iris, 
    hyper_params=hyper_parameters,
    recovery_dir="s3://my-bucket/gbm_grid_recovery"
)

# on a new cluster recover grid
# this will load the training frame and any other objects required for training
h2o.loadGrid(
    "s3://my-bucket/gbm_grid_recovery/gbm_grid", # append grid ID to the recovery_dir 
    load_params_references=TRUE
)
iris <- h2o.getFrame("iris") # get reference to re-loaded training frame
# continue grid training, same grid id will cause H2O to resume progress
grid <- h2o.grid(
    "gbm", grid_id="gbm_grid", x=1:4, y=5,
    training_frame=iris, 
    hyper_params=hyper_parameters # use original hyper-parameters
)

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.

The two core entities are 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 (for example, 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);
}
};
}
  1. Add the PCA REST end-point schema:
public class PCAGridSearchV99 extends GridSearchSchema<PCAGridSearchHandler.PCAGrid,
PCAGridSearchV99,
PCAModel.PCAParameters,
PCAV3.PCAParametersV3> {
}

  1. 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);
         }
       }
    }

  2. 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 (for example, 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 (for example, 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.

Supervised Algorithms​

AutoML Hyperparameters​

No available hyperparameters.

CoxPH Hyperparameters​

  • use_all_factor_levels

Deep Learning Hyperparameters​

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

DRF Hyperparameters​

  • balance_classes
  • class_sampling_factors
  • distribution
  • max_after_balance_size
  • seed

GLM Hyperparameters​

  • alpha
  • dispersion_learning_rate
  • init_dispersion_parameter
  • lambda (lambda_)
  • rand_family
  • rand_link
  • startval
  • theta
  • tweedie_variance_power
  • tweedie_link_power

Isotonic Regression Hyperparameters​

No available hyperparameters.

ModelSelection Hyperparameters​

  • alpha
  • lambda (lambda_)
  • missing_values_handling
  • nparallelism
  • rand_family
  • seed
  • startval
  • tweedie_variance_power

GAM Hyperparameters​

  • alpha
  • balance_classes
  • bs
  • gam_columns
  • lambda (lambda_)
  • missing_values_handling
  • num_knots
  • rand_family
  • scale
  • seed
  • splines_non_negative
  • spline_order
  • startval
  • theta
  • tweedie_variance_power

GBM Hyperparameters​

  • balance_classes
  • class_sampling_factors
  • distribution
  • max_after_balance_size
  • seed

Naïve Bayes Hyperparameters​

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

Rulefit Hyperparameters​

  • seed

Stacked Ensemble Hyperparameters​

  • seed

SVM Hyperparameters​

  • gamma
  • hyper_param
  • rank_ratio
  • seed

Uplift DRF Hyperparameters​

  • balance_classes
  • class_sampling_factors
  • max_after_balance_size
  • seed

XGBoost Hyperparameters​

  • backend
  • booster
  • colsample_bylevel
  • colsample_bynode
  • colsample_bytree
  • distribution
  • dmatrix_type
  • eta
  • gamma
  • grow_policy
  • max_bins
  • max_delta_step
  • max_leaves
  • min_child_weight
  • normalize_type
  • one_drop
  • rate_drop
  • reg_alpha
  • reg_lambda
  • sample_type
  • scale_pos_weight
  • seed
  • skip_drop
  • subsample
  • tree_method

Unsupervised Hyperparameters​

Aggregator Hyperparameters​

  • k
  • max_iterations
  • pca_method
  • rel_tol_num_exemplars
  • target_num_exemplars
  • transform
  • use_all_factor_levels

GLRM Hyperparameters​

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

PCA Hyperparameters​

  • k
  • max_iterations
  • transform

K-Means Hyperparameters​

  • estimate_k
  • init
  • max_iterations
  • seed
  • standardize

Isolation Forest Hyperparameters​

  • seed

Extended Isolation Forest Hyperparameters​

  • seed

Shared Tree Hyperparameters​

Shared Tree HyperparametersGBMDRFXGBoostIsolation ForestExtended Isolation ForestUplift DRF
col_sample_rateYesNoYesNoNoNo
col_sample_rate_change_per_levelYesYesYesYesYesYes
col_sample_rate_per_treeYesYesYesYesYesYes
histogram_typeYesYesYesYesNoYes
learn_rateYesNoYesNoNoNo
max_abs_leafnode_predYesNoYesNoNoNo
max_depthYesYesYesYesYesYes
min_rowsYesYesYesYesYesYes
min_split_improvementYesYesYesYesYesYes
mtriesNoYesNoYesNoYes
nbinsYesYesYesYesYesYes
nbins_catsYesYesYesYesYesYes
nbins_top_levelYesYesYesYesYesYes
ntreesYesYesYesYesYesYes
sample_rateYesYesYesYesNoYes
sample_rate_per_classYesYesYesYesYesYes
sample_sizeNoNoNoYesYesNo
seedYesYesYesYesYesYes
learn_rate_annealingYesNoNoNoNoNo
pred_noise_bandwidthYesNoNoNoNoNo

Stopping and Runtime Controls​

The following parameters apply to all supervised algorithms and are marked Hyperparameter: yes on their individual pages. They control early stopping and total runtime rather than model structure, so fix them once per grid rather than varying them across models:

Set these on search_criteria or on the per-model parameters to cap total runtime or stop individual models early.

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

Tests for the RandomDiscrete search criteria are in the GBM grid airlines test 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.
  • No mechanism exists to list the hyperspace parameters that caused a model builder job failure.
  • Call h2o.get_grid() in Python or h2o.getGrid() in R 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​

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