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Hyper Parameter Optimization Comparison

Posted by Anonymous Author

Comparison of Hyperparameter Optimization (HPO) algorithms on several problems.

Hyperparameter Optimization algorithms are list below:

All algorithms run in NNI local environment.

Machine Environment：

OS: Linux Ubuntu 16.04 LTS
CPU: Intel(R) Xeon(R) CPU E5-2690 v3 @ 2.60GHz 2600 MHz
Memory: 112 GB
NNI Version: v0.7
NNI Mode(local|pai|remote): local
Python version: 3.6
Is conda or virtualenv used?: Conda
is running in docker?: no

AutoGBDT Example

Problem Description

Nonconvex problem on the hyper-parameter search of AutoGBDT example.

Search Space

{
  "num_leaves": {
    "_type": "choice",
    "_value": [10, 12, 14, 16, 18, 20, 22, 24, 28, 32, 48, 64, 96, 128]
  },
  "learning_rate": {
    "_type": "choice",
    "_value": [0.00001, 0.0001, 0.001, 0.01, 0.05, 0.1, 0.2, 0.5]
  },
  "max_depth": {
    "_type": "choice",
    "_value": [-1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 28, 32, 48, 64, 96, 128]
  },
  "feature_fraction": {
    "_type": "choice",
    "_value": [0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2]
  },
  "bagging_fraction": {
    "_type": "choice",
    "_value": [0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2]
  },
  "bagging_freq": {
    "_type": "choice",
    "_value": [1, 2, 4, 8, 10, 12, 14, 16]
  }
}

The total search space is 1,204,224, we set the number of maximum trial to 1000. The time limitation is 48 hours.

Results

Algorithm Best loss Average of Best 5 Losses Average of Best 10 Losses
Random Search 0.418854 0.420352 0.421553
Random Search 0.417364 0.420024 0.420997
Random Search 0.417861 0.419744 0.420642
Grid Search 0.498166 0.498166 0.498166
Evolution 0.409887 0.409887 0.409887
Evolution 0.413620 0.413875 0.414067
Evolution 0.409887 0.409887 0.409887
Anneal 0.414877 0.417289 0.418281
Anneal 0.409887 0.409887 0.410118
Anneal 0.413683 0.416949 0.417537
Metis 0.416273 0.420411 0.422380
Metis 0.420262 0.423175 0.424816
Metis 0.421027 0.424172 0.425714
TPE 0.414478 0.414478 0.414478
TPE 0.415077 0.417986 0.418797
TPE 0.415077 0.417009 0.418053
SMAC 0.408386 0.408386 0.408386
SMAC 0.414012 0.414012 0.414012
SMAC 0.408386 0.408386 0.408386
BOHB 0.410464 0.415319 0.417755
BOHB 0.418995 0.420268 0.422604
BOHB 0.415149 0.418072 0.418932
HyperBand 0.414065 0.415222 0.417628
HyperBand 0.416807 0.417549 0.418828
HyperBand 0.415550 0.415977 0.417186
GP 0.414353 0.418563 0.420263
GP 0.414395 0.418006 0.420431
GP 0.412943 0.416566 0.418443

In this example, all the algorithms are used with default parameters. For Metis, there are about 300 trials because it runs slowly due to its high time complexity O(n^3) in Gaussian Process.

RocksDB Benchmark 'fillrandom' and 'readrandom'

Problem Description

DB_Bench is the main tool that is used to benchmark RocksDB's performance. It has so many hapermeter to tune.

The performance of DB_Bench is associated with the machine configuration and installation method. We run the DB_Benchin the Linux machine and install the Rock in shared library.

Machine configuration

RocksDB:    version 6.1
CPU:        6 * Intel(R) Xeon(R) CPU E5-2690 v4 @ 2.60GHz
CPUCache:   35840 KB
Keys:       16 bytes each
Values:     100 bytes each (50 bytes after compression)
Entries:    1000000

Storage performance

Latency: each IO request will take some time to complete, this is called the average latency. There are several factors that would affect this time including network connection quality and hard disk IO performance.

IOPS: IO operations per second, which means the amount of read or write operations that could be done in one seconds time.

IO size: the size of each IO request. Depending on the operating system and the application/service that needs disk access it will issue a request to read or write a certain amount of data at the same time.

**Throughput (in MB/s) = Average IO size x IOPS **

IOPS is related to online processing ability and we use the IOPS as the metric in my experiment.

Search Space

{
  "max_background_compactions": {
    "_type": "quniform",
    "_value": [1, 256, 1]
  },
  "block_size": {
    "_type": "quniform",
    "_value": [1, 500000, 1]
  },
  "write_buffer_size": {
    "_type": "quniform",
    "_value": [1, 130000000, 1]
  },
  "max_write_buffer_number": {
    "_type": "quniform",
    "_value": [1, 128, 1]
  },
  "min_write_buffer_number_to_merge": {
    "_type": "quniform",
    "_value": [1, 32, 1]
  },
  "level0_file_num_compaction_trigger": {
    "_type": "quniform",
    "_value": [1, 256, 1]
  },
  "level0_slowdown_writes_trigger": {
    "_type": "quniform",
    "_value": [1, 1024, 1]
  },
  "level0_stop_writes_trigger": {
    "_type": "quniform",
    "_value": [1, 1024, 1]
  },
  "cache_size": {
    "_type": "quniform",
    "_value": [1, 30000000, 1]
  },
  "compaction_readahead_size": {
    "_type": "quniform",
    "_value": [1, 30000000, 1]
  },
  "new_table_reader_for_compaction_inputs": {
    "_type": "randint",
    "_value": [1]
  }
}

The search space is enormous (about 10^40) and we set the maximum number of trial to 100 to limit the computation resource.

Results

fillrandom' Benchmark

Model Best IOPS (Repeat 1) Best IOPS (Repeat 2) Best IOPS (Repeat 3)
Random 449901 427620 477174
Anneal 461896 467150 437528
Evolution 436755 389956 389790
TPE 378346 482316 468989
SMAC 491067 490472 491136
Metis 444920 457060 454438

Figure:

'readrandom' Benchmark

Model Best IOPS (Repeat 1) Best IOPS (Repeat 2) Best IOPS (Repeat 3)
Random 2276157 2285301 2275142
Anneal 2286330 2282229 2284012
Evolution 2286524 2283673 2283558
TPE 2287366 2282865 2281891
SMAC 2270874 2284904 2282266
Metis 2287696 2283496 2277701

Figure: