19.5. Asynchronous Successive Halving¶ Open the notebook in SageMaker Studio Lab
As we have seen in Section 19.3, we can accelerate HPO by distributing the evaluation of hyperparameter configurations across either multiple instances or multiples CPUs / GPUs on a single instance. However, compared to random search, it is not straightforward to run successive halving (SH) asynchronously in a distributed setting. Before we can decide which configuration to run next, we first have to collect all observations at the current rung level. This requires to synchronize workers at each rung level. For example, for the lowest rung level \(r_{\text{min}}\), we first have to evaluate all \(N = \eta^K\) configurations, before we can promote the \(\frac{1}{\eta}\) of them to the next rung level.
In any distributed system, synchronization typically implies idle time for workers. First, we often observe high variations in training time across hyperparameter configurations. For example, assuming the number of filters per layer is a hyperparameter, then networks with less filters finish training faster than networks with more filters, which implies idle worker time due to stragglers. Moreover, the number of slots in a rung level is not always a multiple of the number of workers, in which case some workers may even sit idle for a full batch.
Figure Fig. 19.5.1 shows the scheduling of synchronous SH with \(\eta=2\) for four different trials with two workers. We start with evaluating Trial-0 and Trial-1 for one epoch and immediately continue with the next two trials once they are finished. We first have to wait until Trial-2 finishes, which takes substantially more time than the other trials, before we can promote the best two trials, i.e., Trial-0 and Trial-3 to the next rung level. This causes idle time for Worker-1. Then, we continue with Rung 1. Also, here Trial-3 takes longer than Trial-0, which leads to an additional ideling time of Worker-0. Once, we reach Rung-2, only the best trial, Trial-0, remains which occupies only one worker. To avoid that Worker-1 idles during that time, most implementaitons of SH continue already with the next round, and start evaluating new trials (e.g Trial-4) on the first rung.
Fig. 19.5.1 Synchronous successive halving with two workers.¶
Asynchronous successive halving (ASHA) (Li et al., 2018) adapts SH to the asynchronous parallel scenario. The main idea of ASHA is to promote configurations to the next rung level as soon as we collected at least \(\eta\) observations on the current rung level. This decision rule may lead to suboptimal promotions: configurations can be promoted to the next rung level, which in hindsight do not compare favourably against most others at the same rung level. On the other hand, we get rid of all synchronization points this way. In practice, such suboptimal initial promotions have only a modest impact on performance, not only because the ranking of hyperparameter configurations is often fairly consistent across rung levels, but also because rungs grow over time and reflect the distribution of metric values at this level better and better. If a worker is free, but no configuration can be promoted, we start a new configuration with \(r = r_{\text{min}}\), i.e the first rung level.
Fig. 19.5.2 shows the scheduling of the same configurations for ASHA. Once Trial-1 finishes, we collect the results of two trials (i.e Trial-0 and Trial-1) and immediately promote the better of them (Trial-0) to the next rung level. After Trial-0 finishes on rung 1, there are too few trials there in order to support a further promotion. Hence, we continue with rung 0 and evaluate Trial-3. Once Trial-3 finishes, Trial-2 is still pending. At this point we have 3 trials evaluated on rung 0 and one trial evaluated already on rung 1. Since Trial-3 performs worse than Trial-0 at rung 0, and \(\eta=2\), we cannot promote any new trial yet, and Worker-1 starts Trial-4 from scratch instead. However, once Trial-2 finishes and scores worse than Trial-3, the latter is promoted towards rung 1. Afterwards, we collected 2 evaluations on rung 1, which means we can now promote Trial-0 towards rung 2. At the same time, Worker-1 continues with evaluating new trials (i.e., Trial-5) on rung 0.
Fig. 19.5.2 Asynchronous successive halving (ASHA) with two workers.¶
import logging
from d2l import torch as d2l
logging.basicConfig(level=logging.INFO)
import matplotlib.pyplot as plt
from syne_tune import StoppingCriterion, Tuner
from syne_tune.backend.python_backend import PythonBackend
from syne_tune.config_space import loguniform, randint
from syne_tune.experiments import load_experiment
from syne_tune.optimizer.baselines import ASHA
INFO:root:SageMakerBackend is not imported since dependencies are missing. You can install them with
pip install 'syne-tune[extra]'
AWS dependencies are not imported since dependencies are missing. You can install them with
pip install 'syne-tune[aws]'
or (for everything)
pip install 'syne-tune[extra]'
AWS dependencies are not imported since dependencies are missing. You can install them with
pip install 'syne-tune[aws]'
or (for everything)
pip install 'syne-tune[extra]'
INFO:root:Ray Tune schedulers and searchers are not imported since dependencies are missing. You can install them with
pip install 'syne-tune[raytune]'
or (for everything)
pip install 'syne-tune[extra]'
19.5.1. Objective Function¶
We will use Syne Tune with the same objective function as in Section 19.3.
def hpo_objective_lenet_synetune(learning_rate, batch_size, max_epochs):
from syne_tune import Reporter
from d2l import torch as d2l
model = d2l.LeNet(lr=learning_rate, num_classes=10)
trainer = d2l.HPOTrainer(max_epochs=1, num_gpus=1)
data = d2l.FashionMNIST(batch_size=batch_size)
model.apply_init([next(iter(data.get_dataloader(True)))[0]], d2l.init_cnn)
report = Reporter()
for epoch in range(1, max_epochs + 1):
if epoch == 1:
# Initialize the state of Trainer
trainer.fit(model=model, data=data)
else:
trainer.fit_epoch()
validation_error = trainer.validation_error().cpu().detach().numpy()
report(epoch=epoch, validation_error=float(validation_error))
We will also use the same configuration space as before:
min_number_of_epochs = 2
max_number_of_epochs = 10
eta = 2
config_space = {
"learning_rate": loguniform(1e-2, 1),
"batch_size": randint(32, 256),
"max_epochs": max_number_of_epochs,
}
initial_config = {
"learning_rate": 0.1,
"batch_size": 128,
}
19.5.2. Asynchronous Scheduler¶
First, we define the number of workers that evaluate trials concurrently. We also need to specify how long we want to run random search, by defining an upper limit on the total wall-clock time.
n_workers = 2 # Needs to be <= the number of available GPUs
max_wallclock_time = 12 * 60 # 12 minutes
The code for running ASHA is a simple variation of what we did for asynchronous random search.
mode = "min"
metric = "validation_error"
resource_attr = "epoch"
scheduler = ASHA(
config_space,
metric=metric,
mode=mode,
points_to_evaluate=[initial_config],
max_resource_attr="max_epochs",
resource_attr=resource_attr,
grace_period=min_number_of_epochs,
reduction_factor=eta,
)
INFO:syne_tune.optimizer.schedulers.fifo:max_resource_level = 10, as inferred from config_space
INFO:syne_tune.optimizer.schedulers.fifo:Master random_seed = 1667793106
Here, metric and resource_attr specify the key names used with
the report callback, and max_resource_attr denotes which input
to the objective function corresponds to \(r_{\text{max}}\).
Moreover, grace_period provides \(r_{\text{min}}\), and
reduction_factor is \(\eta\). We can run Syne Tune as before
(this will take about 12 minutes):
trial_backend = PythonBackend(
tune_function=hpo_objective_lenet_synetune,
config_space=config_space,
)
stop_criterion = StoppingCriterion(max_wallclock_time=max_wallclock_time)
tuner = Tuner(
trial_backend=trial_backend,
scheduler=scheduler,
stop_criterion=stop_criterion,
n_workers=n_workers,
print_update_interval=int(max_wallclock_time * 0.6),
)
tuner.run()
INFO:syne_tune.tuner:results of trials will be saved on /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031
INFO:root:Detected 8 GPUs
INFO:root:running subprocess with command: /home/d2l-worker/miniconda3/envs/d2l-en-release-0/bin/python /home/d2l-worker/miniconda3/envs/d2l-en-release-0/lib/python3.9/site-packages/syne_tune/backend/python_backend/python_entrypoint.py --learning_rate 0.1 --batch_size 128 --max_epochs 10 --tune_function_root /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/tune_function --tune_function_hash 6c8e36c199e084d1b6182e90bb4929ca --st_checkpoint_dir /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/0/checkpoints
INFO:syne_tune.tuner:(trial 0) - scheduled config {'learning_rate': 0.1, 'batch_size': 128, 'max_epochs': 10}
INFO:root:running subprocess with command: /home/d2l-worker/miniconda3/envs/d2l-en-release-0/bin/python /home/d2l-worker/miniconda3/envs/d2l-en-release-0/lib/python3.9/site-packages/syne_tune/backend/python_backend/python_entrypoint.py --learning_rate 0.07083800234912864 --batch_size 164 --max_epochs 10 --tune_function_root /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/tune_function --tune_function_hash 6c8e36c199e084d1b6182e90bb4929ca --st_checkpoint_dir /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/1/checkpoints
INFO:syne_tune.tuner:(trial 1) - scheduled config {'learning_rate': 0.07083800234912864, 'batch_size': 164, 'max_epochs': 10}
INFO:syne_tune.tuner:Trial trial_id 0 completed.
INFO:syne_tune.tuner:Trial trial_id 1 completed.
INFO:root:running subprocess with command: /home/d2l-worker/miniconda3/envs/d2l-en-release-0/bin/python /home/d2l-worker/miniconda3/envs/d2l-en-release-0/lib/python3.9/site-packages/syne_tune/backend/python_backend/python_entrypoint.py --learning_rate 0.03307323415999148 --batch_size 143 --max_epochs 10 --tune_function_root /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/tune_function --tune_function_hash 6c8e36c199e084d1b6182e90bb4929ca --st_checkpoint_dir /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/2/checkpoints
INFO:syne_tune.tuner:(trial 2) - scheduled config {'learning_rate': 0.03307323415999148, 'batch_size': 143, 'max_epochs': 10}
INFO:root:running subprocess with command: /home/d2l-worker/miniconda3/envs/d2l-en-release-0/bin/python /home/d2l-worker/miniconda3/envs/d2l-en-release-0/lib/python3.9/site-packages/syne_tune/backend/python_backend/python_entrypoint.py --learning_rate 0.3278827763026901 --batch_size 196 --max_epochs 10 --tune_function_root /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/tune_function --tune_function_hash 6c8e36c199e084d1b6182e90bb4929ca --st_checkpoint_dir /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/3/checkpoints
INFO:syne_tune.tuner:(trial 3) - scheduled config {'learning_rate': 0.3278827763026901, 'batch_size': 196, 'max_epochs': 10}
INFO:root:running subprocess with command: /home/d2l-worker/miniconda3/envs/d2l-en-release-0/bin/python /home/d2l-worker/miniconda3/envs/d2l-en-release-0/lib/python3.9/site-packages/syne_tune/backend/python_backend/python_entrypoint.py --learning_rate 0.010646658248085899 --batch_size 255 --max_epochs 10 --tune_function_root /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/tune_function --tune_function_hash 6c8e36c199e084d1b6182e90bb4929ca --st_checkpoint_dir /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/4/checkpoints
INFO:syne_tune.tuner:(trial 4) - scheduled config {'learning_rate': 0.010646658248085899, 'batch_size': 255, 'max_epochs': 10}
INFO:root:running subprocess with command: /home/d2l-worker/miniconda3/envs/d2l-en-release-0/bin/python /home/d2l-worker/miniconda3/envs/d2l-en-release-0/lib/python3.9/site-packages/syne_tune/backend/python_backend/python_entrypoint.py --learning_rate 0.29027789545213717 --batch_size 41 --max_epochs 10 --tune_function_root /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/tune_function --tune_function_hash 6c8e36c199e084d1b6182e90bb4929ca --st_checkpoint_dir /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/5/checkpoints
INFO:syne_tune.tuner:(trial 5) - scheduled config {'learning_rate': 0.29027789545213717, 'batch_size': 41, 'max_epochs': 10}
INFO:syne_tune.tuner:Trial trial_id 3 completed.
INFO:root:running subprocess with command: /home/d2l-worker/miniconda3/envs/d2l-en-release-0/bin/python /home/d2l-worker/miniconda3/envs/d2l-en-release-0/lib/python3.9/site-packages/syne_tune/backend/python_backend/python_entrypoint.py --learning_rate 0.8219530011711292 --batch_size 73 --max_epochs 10 --tune_function_root /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/tune_function --tune_function_hash 6c8e36c199e084d1b6182e90bb4929ca --st_checkpoint_dir /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/6/checkpoints
INFO:syne_tune.tuner:(trial 6) - scheduled config {'learning_rate': 0.8219530011711292, 'batch_size': 73, 'max_epochs': 10}
INFO:syne_tune.tuner:Trial trial_id 6 completed.
INFO:root:running subprocess with command: /home/d2l-worker/miniconda3/envs/d2l-en-release-0/bin/python /home/d2l-worker/miniconda3/envs/d2l-en-release-0/lib/python3.9/site-packages/syne_tune/backend/python_backend/python_entrypoint.py --learning_rate 0.2750859826101329 --batch_size 62 --max_epochs 10 --tune_function_root /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/tune_function --tune_function_hash 6c8e36c199e084d1b6182e90bb4929ca --st_checkpoint_dir /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/7/checkpoints
INFO:syne_tune.tuner:(trial 7) - scheduled config {'learning_rate': 0.2750859826101329, 'batch_size': 62, 'max_epochs': 10}
INFO:syne_tune.tuner:Trial trial_id 5 completed.
INFO:root:running subprocess with command: /home/d2l-worker/miniconda3/envs/d2l-en-release-0/bin/python /home/d2l-worker/miniconda3/envs/d2l-en-release-0/lib/python3.9/site-packages/syne_tune/backend/python_backend/python_entrypoint.py --learning_rate 0.023276597762652115 --batch_size 217 --max_epochs 10 --tune_function_root /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/tune_function --tune_function_hash 6c8e36c199e084d1b6182e90bb4929ca --st_checkpoint_dir /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/8/checkpoints
INFO:syne_tune.tuner:(trial 8) - scheduled config {'learning_rate': 0.023276597762652115, 'batch_size': 217, 'max_epochs': 10}
INFO:syne_tune.tuner:tuning status (last metric is reported)
trial_id status iter learning_rate batch_size max_epochs epoch validation_error worker-time
0 Completed 10 0.100000 128 10 10 0.272152 93.415593
1 Completed 10 0.070838 164 10 10 0.396901 91.280133
2 Stopped 2 0.033073 143 10 2 0.900040 21.134821
3 Completed 10 0.327883 196 10 10 0.246272 87.031827
4 Stopped 4 0.010647 255 10 4 0.899109 40.460765
5 Completed 10 0.290278 41 10 10 0.138099 214.133559
6 Completed 10 0.821953 73 10 10 0.136102 122.203708
7 InProgress 7 0.275086 62 10 7 0.180451 88.313845
8 InProgress 3 0.023277 217 10 3 0.900867 27.230914
2 trials running, 7 finished (5 until the end), 436.45s wallclock-time
INFO:root:running subprocess with command: /home/d2l-worker/miniconda3/envs/d2l-en-release-0/bin/python /home/d2l-worker/miniconda3/envs/d2l-en-release-0/lib/python3.9/site-packages/syne_tune/backend/python_backend/python_entrypoint.py --learning_rate 0.042908333506354195 --batch_size 189 --max_epochs 10 --tune_function_root /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/tune_function --tune_function_hash 6c8e36c199e084d1b6182e90bb4929ca --st_checkpoint_dir /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/9/checkpoints
INFO:syne_tune.tuner:(trial 9) - scheduled config {'learning_rate': 0.042908333506354195, 'batch_size': 189, 'max_epochs': 10}
INFO:syne_tune.tuner:Trial trial_id 7 completed.
INFO:root:running subprocess with command: /home/d2l-worker/miniconda3/envs/d2l-en-release-0/bin/python /home/d2l-worker/miniconda3/envs/d2l-en-release-0/lib/python3.9/site-packages/syne_tune/backend/python_backend/python_entrypoint.py --learning_rate 0.08269681669102813 --batch_size 214 --max_epochs 10 --tune_function_root /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/tune_function --tune_function_hash 6c8e36c199e084d1b6182e90bb4929ca --st_checkpoint_dir /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/10/checkpoints
INFO:syne_tune.tuner:(trial 10) - scheduled config {'learning_rate': 0.08269681669102813, 'batch_size': 214, 'max_epochs': 10}
INFO:root:running subprocess with command: /home/d2l-worker/miniconda3/envs/d2l-en-release-0/bin/python /home/d2l-worker/miniconda3/envs/d2l-en-release-0/lib/python3.9/site-packages/syne_tune/backend/python_backend/python_entrypoint.py --learning_rate 0.012997240331087727 --batch_size 164 --max_epochs 10 --tune_function_root /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/tune_function --tune_function_hash 6c8e36c199e084d1b6182e90bb4929ca --st_checkpoint_dir /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/11/checkpoints
INFO:syne_tune.tuner:(trial 11) - scheduled config {'learning_rate': 0.012997240331087727, 'batch_size': 164, 'max_epochs': 10}
INFO:root:running subprocess with command: /home/d2l-worker/miniconda3/envs/d2l-en-release-0/bin/python /home/d2l-worker/miniconda3/envs/d2l-en-release-0/lib/python3.9/site-packages/syne_tune/backend/python_backend/python_entrypoint.py --learning_rate 0.011328707678415345 --batch_size 255 --max_epochs 10 --tune_function_root /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/tune_function --tune_function_hash 6c8e36c199e084d1b6182e90bb4929ca --st_checkpoint_dir /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/12/checkpoints
INFO:syne_tune.tuner:(trial 12) - scheduled config {'learning_rate': 0.011328707678415345, 'batch_size': 255, 'max_epochs': 10}
INFO:root:running subprocess with command: /home/d2l-worker/miniconda3/envs/d2l-en-release-0/bin/python /home/d2l-worker/miniconda3/envs/d2l-en-release-0/lib/python3.9/site-packages/syne_tune/backend/python_backend/python_entrypoint.py --learning_rate 0.22009050759642151 --batch_size 82 --max_epochs 10 --tune_function_root /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/tune_function --tune_function_hash 6c8e36c199e084d1b6182e90bb4929ca --st_checkpoint_dir /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/13/checkpoints
INFO:syne_tune.tuner:(trial 13) - scheduled config {'learning_rate': 0.22009050759642151, 'batch_size': 82, 'max_epochs': 10}
INFO:root:running subprocess with command: /home/d2l-worker/miniconda3/envs/d2l-en-release-0/bin/python /home/d2l-worker/miniconda3/envs/d2l-en-release-0/lib/python3.9/site-packages/syne_tune/backend/python_backend/python_entrypoint.py --learning_rate 0.020413725054654552 --batch_size 237 --max_epochs 10 --tune_function_root /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/tune_function --tune_function_hash 6c8e36c199e084d1b6182e90bb4929ca --st_checkpoint_dir /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/14/checkpoints
INFO:syne_tune.tuner:(trial 14) - scheduled config {'learning_rate': 0.020413725054654552, 'batch_size': 237, 'max_epochs': 10}
INFO:root:running subprocess with command: /home/d2l-worker/miniconda3/envs/d2l-en-release-0/bin/python /home/d2l-worker/miniconda3/envs/d2l-en-release-0/lib/python3.9/site-packages/syne_tune/backend/python_backend/python_entrypoint.py --learning_rate 0.6784587461954453 --batch_size 203 --max_epochs 10 --tune_function_root /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/tune_function --tune_function_hash 6c8e36c199e084d1b6182e90bb4929ca --st_checkpoint_dir /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/15/checkpoints
INFO:syne_tune.tuner:(trial 15) - scheduled config {'learning_rate': 0.6784587461954453, 'batch_size': 203, 'max_epochs': 10}
INFO:syne_tune.tuner:Trial trial_id 13 completed.
INFO:root:running subprocess with command: /home/d2l-worker/miniconda3/envs/d2l-en-release-0/bin/python /home/d2l-worker/miniconda3/envs/d2l-en-release-0/lib/python3.9/site-packages/syne_tune/backend/python_backend/python_entrypoint.py --learning_rate 0.43108540040153104 --batch_size 125 --max_epochs 10 --tune_function_root /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/tune_function --tune_function_hash 6c8e36c199e084d1b6182e90bb4929ca --st_checkpoint_dir /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/16/checkpoints
INFO:syne_tune.tuner:(trial 16) - scheduled config {'learning_rate': 0.43108540040153104, 'batch_size': 125, 'max_epochs': 10}
INFO:syne_tune.tuner:Trial trial_id 15 completed.
INFO:root:running subprocess with command: /home/d2l-worker/miniconda3/envs/d2l-en-release-0/bin/python /home/d2l-worker/miniconda3/envs/d2l-en-release-0/lib/python3.9/site-packages/syne_tune/backend/python_backend/python_entrypoint.py --learning_rate 0.6157267539635003 --batch_size 55 --max_epochs 10 --tune_function_root /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/tune_function --tune_function_hash 6c8e36c199e084d1b6182e90bb4929ca --st_checkpoint_dir /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031/17/checkpoints
INFO:syne_tune.tuner:(trial 17) - scheduled config {'learning_rate': 0.6157267539635003, 'batch_size': 55, 'max_epochs': 10}
INFO:syne_tune.stopping_criterion:reaching max wallclock time (720), stopping there.
INFO:syne_tune.tuner:Stopping trials that may still be running.
INFO:syne_tune.tuner:Tuning finished, results of trials can be found on /home/d2l-worker/syne-tune/python-entrypoint-2023-02-10-04-25-46-031
--------------------
Resource summary (last result is reported):
trial_id status iter learning_rate batch_size max_epochs epoch validation_error worker-time
0 Completed 10 0.100000 128 10 10 0.272152 93.415593
1 Completed 10 0.070838 164 10 10 0.396901 91.280133
2 Stopped 2 0.033073 143 10 2 0.900040 21.134821
3 Completed 10 0.327883 196 10 10 0.246272 87.031827
4 Stopped 4 0.010647 255 10 4 0.899109 40.460765
5 Completed 10 0.290278 41 10 10 0.138099 214.133559
6 Completed 10 0.821953 73 10 10 0.136102 122.203708
7 Completed 10 0.275086 62 10 10 0.156755 128.145663
8 Stopped 4 0.023277 217 10 4 0.900867 34.682456
9 Stopped 2 0.042908 189 10 2 0.899992 20.798310
10 Stopped 2 0.082697 214 10 2 0.899948 21.235815
11 Stopped 2 0.012997 164 10 2 0.899995 22.458586
12 Stopped 4 0.011329 255 10 4 0.901248 36.187555
13 Completed 10 0.220091 82 10 10 0.217100 139.510096
14 Stopped 4 0.020414 237 10 4 0.900652 36.855564
15 Completed 10 0.678459 203 10 10 0.178764 84.944084
16 InProgress 8 0.431085 125 10 8 0.192300 72.108503
17 InProgress 2 0.615727 55 10 2 0.345099 35.291729
2 trials running, 16 finished (8 until the end), 723.03s wallclock-time
validation_error: best 0.13610213994979858 for trial-id 6
--------------------
Note that we are running a variant of ASHA where underperforming trials
are stopped early. This is different to our implementation in
Section 19.4.1, where each training job is started with a
fixed max_epochs. In the latter case, a well-performing trial which
reaches the full 10 epochs, first needs to train 1, then 2, then 4, then
8 epochs, each time starting from scratch. This type of pause-and-resume
scheduling can be implemented efficiently by checkpointing the training
state after each epoch, but we avoid this extra complexity here. After
the experiment has finished, we can retrieve and plot results.
d2l.set_figsize()
e = load_experiment(tuner.name)
e.plot()
WARNING:matplotlib.legend:No artists with labels found to put in legend. Note that artists whose label start with an underscore are ignored when legend() is called with no argument.
19.5.3. Visualize the Optimization Process¶
Once more, we visualize the learning curves of every trial (each color in the plot represents a trial). Compare this to asynchronous random search in Section 19.3. As we have seen for successive halving in Section 19.4, most of the trials are stopped at 1 or 2 epochs (\(r_{\text{min}}\) or \(\eta * r_{\text{min}}\)). However, trials do not stop at the same point, because they require different amount of time per epoch. If we ran standard successive halving instead of ASHA, we would need to synchronize our workers, before we can promote configurations to the next rung level.
d2l.set_figsize([6, 2.5])
results = e.results
for trial_id in results.trial_id.unique():
df = results[results["trial_id"] == trial_id]
d2l.plt.plot(
df["st_tuner_time"],
df["validation_error"],
marker="o"
)
d2l.plt.xlabel("wall-clock time")
d2l.plt.ylabel("objective function")
Text(0, 0.5, 'objective function')
19.5.4. Summary¶
Compared to random search, successive halving is not quite as trivial to run in an asynchronous distributed setting. To avoid synchronisation points, we promote configurations as quickly as possible to the next rung level, even if this means promoting some wrong ones. In practice, this usually does not hurt much, and the gains of asynchronous versus synchronous scheduling are usually much higher than the loss of the suboptimal decision making.