CAVE

Meta Data

Meta data, i.e. number of instances and parameters as well as configuration budget. Statistics apply to the best run, if multiple configurator runs are compared.

General

General information about the optimization scenario.

# aggregated parallel BOHB runs 10
# parameters 7
Deterministic target algorithm True
Optimized run objective quality
Run-Specific

Information to specific runs (if there are multiple runs). Interesting for parallel optimizations or usage of budgets/fidelities.

budget 1 budget 3 budget 9
Total time spent evaluating configurations 255454.91 sec 458507.82 sec 1153603.02 sec
Average time per configuration (mean / std) 66.01 sec (± 57.30) 177.72 sec (± 138.02) 544.15 sec (± 396.82)
# evaluated configurations 3870 2580 2120
# changed parameters (default to incumbent) 7 7 7
Configuration origins Acquisition Function : 2438, Random : 1432 Acquisition Function : 2012, Random : 568 Acquisition Function : 1617, Random : 503
Incumbents Over Budgets

Show the incumbents for each budget (i.e. the best configuration by kernel-estimation using data from that budget).

budget 1 budget 3 budget 9
batch_size 10 10 8
discount 0.958445 0.958445 0.990177
entropy_regularization 0.219758 0.219758 0.206025
learning_rate 0.00267234 0.00267234 0.00136828
likelihood_ratio_clipping 0.949068 0.949068 0.922201
n_units_1 84 84 126
n_units_2 111 111 121
Cost 123.0 140.0 179.889
BOHB Learning Curves

Visualizing the learning curves of all individual HyperBand-iterations. Model-based picks are marked with a cross. The config-id tuple denotes (iteration, stage, id_within_stage), where the iteration is the hyperband iteration and the stage is the index of the budget in which the configuration was first sampled (should be 0). The third index is just a sequential enumeration. This id can be interpreted as a nested index-identifier.

Budget Correlation

Use spearman correlation to get a correlation-value and a p-value for every pairwise combination of budgets. First value is the correlation, second is the p-value (the p-value roughly estimates the likelihood to obtain this correlation coefficient with uncorrelated datasets). This can be used to estimate how well a budget approximates the function to be optimized.

Configurators Behavior
Configurator Footprint

Analysis of the iteratively sampled configurations during the optimization procedure. Multi-dimensional scaling (MDS) is used to reduce dimensionality of the search space and plot the distribution of evaluated configurations. The larger the dot, the more often the configuration was evaluated on instances from the set. Configurations that were incumbents at least once during optimization are marked as red squares. Configurations acquired through local search are marked with a 'x'. The downward triangle denotes the final incumbent, whereas the orange upward triangle denotes the default configuration. The heatmap and the colorbar correspond to the predicted performance in that part of the search space.

Interactive
Static
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Cost Over Time

Depicts the average cost of the best so far found configuration (using all trajectory data) over the time spent by the configurator (including target algorithm runs and the overhead generated by the configurator) If the curve flattens out early, it indicates that too much time was spent for the configurator run; whereas a curve that is still improving at the end of the budget indicates that one should increase the configuration budget. The plotted standard deviation gives the uncertainty over multiple configurator runs.

Parallel Coordinates

Previously used by Golovin et al. to study the frequency of chosen parameter settings in black-box-optimization. Each line corresponds to one configuration in the runhistory and shows the parameter settings and the corresponding (estimated) average cost. To handle large configuration spaces with hundreds of parameters, the (at most) 10 most important parameters based on a fANOVA parameter importance analysis are plotted. To emphasize better configurations, the performance is encoded in the color of each line, ranging from blue to red. These plots provide insights into whether the configurator focused on specific parameter values and how these correlate to their costs. NOTE: the given runhistory should contain only optimization and no validation to analyze the explored parameter-space.

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Parameter Importance

Parameter Importance analysis to determine which of the parameters most influence the analysed algorithms performance.

Importance Table

Parameters are initially sorted by average. Only parameters with an importance greater than 5 in any of the methods are shown. Note, that the values of the used methods are not directly comparable. For more information on the metrics, see respective tooltips.

fANOVA

fANOVA (functional analysis of variance) computes the fraction of the variance in the cost space explained by changing a parameter by marginalizing over all other parameters, for each parameter (or for pairs of parameters). Parameters with high importance scores will have a large impact on the performance. To this end, a random forest is trained as an empirical performance model on the available empirical data from the available runhistories.

Importance
-------------------- Single importance: -------------------- --------------------
discount 20.4606 +/- 11.784
batch_size 5.4967 +/- 3.8915
learning_rate 3.4615 +/- 3.026
entropy_regularization 1.6406 +/- 1.8142
n_units_1 0.7475 +/- 0.9433
likelihood_ratio_clipping 0.7267 +/- 0.6724
n_units_2 0.5735 +/- 0.4222
-------------------- Pairwise importance: -------------------- --------------------
discount & batch_size 6.6184 +/- 5.4168
discount & learning_rate 5.6498 +/- 3.9109
discount & entropy_regularization 3.6442 +/- 3.265
batch_size & learning_rate 3.0571 +/- 2.0302
discount & n_units_1 2.3893 +/- 3.2305
learning_rate & entropy_regularization 0.8282 +/- 1.6415
batch_size & entropy_regularization 0.8039 +/- 0.5902
batch_size & n_units_1 0.4626 +/- 0.4853
learning_rate & n_units_1 0.1925 +/- 0.2415
entropy_regularization & n_units_1 0.1666 +/- 0.2919
Marginals
discount
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batch_size
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learning_rate
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entropy_regularization
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n_units_1
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likelihood_ratio_clipping
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n_units_2
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Pairwise Marginals
discount & batch_size
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discount & learning_rate
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discount & entropy_regularization
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batch_size & learning_rate
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discount & n_units_1
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learning_rate & entropy_regularization
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batch_size & entropy_regularization
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batch_size & n_units_1
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learning_rate & n_units_1
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entropy_regularization & n_units_1
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Importance
-------------------- Single importance: -------------------- --------------------
discount 13.9079 +/- 8.9614
batch_size 7.9511 +/- 5.432
entropy_regularization 4.6757 +/- 6.288
learning_rate 3.9117 +/- 2.6278
likelihood_ratio_clipping 3.8846 +/- 7.9333
n_units_1 2.8052 +/- 4.8185
n_units_2 0.6493 +/- 0.8385
-------------------- Pairwise importance: -------------------- --------------------
discount & batch_size 7.1254 +/- 3.291
discount & likelihood_ratio_clipping 6.3741 +/- 5.6589
discount & learning_rate 4.387 +/- 2.6596
discount & entropy_regularization 3.2372 +/- 3.3237
batch_size & learning_rate 2.5406 +/- 1.2372
batch_size & likelihood_ratio_clipping 0.8555 +/- 0.5317
batch_size & entropy_regularization 0.8151 +/- 0.7631
entropy_regularization & likelihood_ratio_clipping 0.7775 +/- 1.8244
learning_rate & likelihood_ratio_clipping 0.7425 +/- 0.787
entropy_regularization & learning_rate 0.428 +/- 0.4925
Marginals
discount
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batch_size
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entropy_regularization
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learning_rate
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likelihood_ratio_clipping
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n_units_1
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n_units_2
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Pairwise Marginals
discount & batch_size
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discount & likelihood_ratio_clipping
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discount & learning_rate
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discount & entropy_regularization
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batch_size & learning_rate
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batch_size & likelihood_ratio_clipping
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batch_size & entropy_regularization
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entropy_regularization & likelihood_ratio_clipping
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learning_rate & likelihood_ratio_clipping
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entropy_regularization & learning_rate
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Importance
-------------------- Single importance: -------------------- --------------------
discount 19.317 +/- 8.7635
batch_size 15.7729 +/- 9.1154
learning_rate 3.7046 +/- 5.6795
likelihood_ratio_clipping 3.3983 +/- 3.9136
n_units_1 1.8647 +/- 3.1457
entropy_regularization 1.2473 +/- 1.949
n_units_2 0.3915 +/- 0.5608
-------------------- Pairwise importance: -------------------- --------------------
discount & batch_size 10.4271 +/- 5.1149
discount & likelihood_ratio_clipping 4.8495 +/- 4.4263
discount & learning_rate 4.4318 +/- 5.9691
batch_size & learning_rate 3.0992 +/- 1.8549
discount & n_units_1 2.987 +/- 4.4374
batch_size & likelihood_ratio_clipping 2.4033 +/- 2.5565
likelihood_ratio_clipping & n_units_1 0.5867 +/- 1.3872
batch_size & n_units_1 0.5747 +/- 0.553
learning_rate & likelihood_ratio_clipping 0.4292 +/- 0.4297
learning_rate & n_units_1 0.2549 +/- 0.6863
Marginals
discount
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batch_size
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learning_rate
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likelihood_ratio_clipping
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n_units_1
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entropy_regularization
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n_units_2
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Pairwise Marginals
discount & batch_size
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discount & likelihood_ratio_clipping
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discount & learning_rate
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batch_size & learning_rate
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discount & n_units_1
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batch_size & likelihood_ratio_clipping
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likelihood_ratio_clipping & n_units_1
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batch_size & n_units_1
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learning_rate & likelihood_ratio_clipping
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learning_rate & n_units_1
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Local Parameter Importance (LPI)

Using an empirical performance model, performance changes of a configuration along each parameter are calculated. To quantify the importance of a parameter value, the variance of all cost values by changing that parameter are predicted and then the fraction of all variances is computed. This analysis is inspired by the human behaviour to look for improvements in the neighborhood of individual parameters of a configuration.

learning_rate
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discount
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batch_size
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likelihood_ratio_clipping
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entropy_regularization
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n_units_1
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n_units_2
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learning_rate
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discount
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batch_size
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likelihood_ratio_clipping
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n_units_1
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entropy_regularization
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n_units_2
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discount
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learning_rate
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batch_size
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likelihood_ratio_clipping
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n_units_1
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entropy_regularization
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n_units_2
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