A N A LGORITHM -A GNOSTIC NAS B ENCHMARK
Anonymous authors
Paper under double-blind review
A BSTRACT
Neural architecture search (NAS) has achieved breakthrough success in a great number of applications in the past few years.
It could be time to take a step back and analyze the good and bad aspects in the ﬁeld of NAS.
A variety of algorithms search architectures under different search space.
These searched architectures are trained using different setups, e.g., hyper-parameters, data augmentation, regularization.
This raises a comparability problem when comparing the performance of various NAS algorithms.
In this work, we propose an Algorithm-Agnostic NAS
Benchmark ( AA-NAS-Bench ) with a ﬁxed search space, which provides a uniﬁed benchmark for almost any up-to-date NAS algorithms.
The design of our search space is inspired from that used in the most popular cell-based searching algorithms, where a cell is represented as a directed acyclic graph.
Each edge here is associated with an operation selected from a predeﬁned operation set.
For it to be applicable for all NAS algorithms, the search space deﬁned in AA-NAS-Bench includes 4 nodes and 5 associated operation options, which generates 15,625 neural cell candidates in total.
The training log using the same setup and performance for each architecture candidate are provided for three datasets.
This allows researchers to avoid unnecessary repetitive training for selected architecture and focus solely on the search algorithm itself.
The training time saved for every architecture also largely improves the efﬁciency of most NAS algorithms and presents a more computational cost friendly NAS community for a broader range of researchers.
The diagnostic information such as ﬁne-grained loss and accuracy is also provided, which can give inspirations to new designs of NAS algorithms.
We demonstrate the applicability of the proposed AA-NAS-Bench via benchmarking many recent NAS algorithms.
I NTRODUCTION
The deep learning community is undergoing a transition from hand-designed neural architecture (He et al., 2016; Krizhevsky et al., 2012; Szegedy et al., 2015) to automatically designed neural architecture (Zoph & Le, 2017; Pham et al., 2018; Real et al., 2019; Dong & Yang, 2019b; Liu et al., 2019).
In its early era, the great success of deep learning was promoted by novel neural architectures, such as ResNet (He et al., 2016), Inception (Szegedy et al., 2015), VGGNet (Simonyan &
Zisserman, 2015), and Transformer (Vaswani et al., 2017).
However, manually designing one architecture requires human experts to try numerous different operation and connection choices (Zoph & Le, 2017).
In contrast to architectures that are manually designed, those automatically found by neural architecture search (NAS) algorithms require much less human interaction and expert effort.
These NAS-generated architectures have shown promising results in many domains, such as image recognition (Zoph & Le, 2017; Pham et al., 2018;
Real et al., 2019), sequence modeling (Pham et al., 2018; Dong & Yang, 2019b; Liu et al., 2019), etc.
Recently, a variety of NAS algorithms have been increasingly proposed.
While these NAS methods are methodically designed and show promising improvements, many setups in their algorithms are different.
(1) Different search space is utilized, e.g., different macro skeletons of the whole architecture (Zoph et al., 2018;
Cai et al., 2019) and a different operation set for the micro cell within the skeleton (Pham et al., 2018), etc.
(2) After a good architecture is selected, various strategies can be employed to train this architecture and report the performance, e.g., different data augmentation (Ghiasi et al., 2018; Zhang et al., 2018), different regularization (Zoph et al., 2018), different scheduler (Loshchilov & Hutter, 2017), and different selections of hyper-parameters (Liu et al.,
[Figure]
residual block (stride=2) residual block (stride=2) global average pool cell  N × cell  N × architecture zeroize skip-connect 1  1 conv 3  3 conv 3  3 avg pool ××× predeﬁned operation set
[Figure]
; Dong & Yang, 2019a).
The validation set for testing the performance of the selected architecture is not split in the same way (Liu et al., 2019; Pham et al., 2018).
These discrepancies raise a comparability problem when comparing the performance of various NAS algorithms, making it difﬁcult to conclude their contributions.
In response to this problem, we propose the AA-NAS-Bench with a ﬁxed cell search space.
We are inspired by the search space used in the most popular neural cell-based searching algorithms (Zoph et al., 2018;
Liu et al., 2019).
As shown in Figure 1, each architecture consists of a predeﬁned skeleton with a stack of the searched cell.
In this way, architecture search is transformed into the problem of searching a good cell.
Each cell is represented as a densely-connected directed acyclic graph (DAG) as shown in the bottom section of Figure 1.
Here the node represents the sum of the feature maps and each edge is associated with an operation transforming the feature maps from the source node to the target node.
The size of the search space is related to the number of nodes deﬁned for the DAG and the size of the operation set.
In AA-NAS-Bench , we choose 4 nodes and 5 representative operation candidates for the operation set, which generates a total search space of 15,625 cells/architectures.
Each architecture is trained multiple times on three different datasets.
The training log and performance of each architecture are provided for each run.
The training accuracy/test accuracy/training loss/test loss after every training epoch for each architecture plus the number of parameters and ﬂoating point operations (FLOPs) are accessible.
All code, data, and architecture information are publicly available.
The AA-NAS-Bench has shown its value in the ﬁeld of NAS research.
(1) It provides a uniﬁed benchmark for most up-to-date NAS algorithms including all cell-based NAS methods.
With AANAS-Bench , researchers can focus on designing robust searching algorithm while avoiding tedious hyper-parameter tuning of the searched architecture.
Thus, AA-NAS-Bench provides a relatively fair benchmark for the comparison of different NAS algorithms.
(2) We provide the full training log of each architecture.
Unnecessary repetitive training procedure of each selected architecture can be avoided (Liu et al., 2018;
Zoph & Le, 2017) so that researchers can target on the essence of NAS, i.e., search algorithm.
Another beneﬁt is that the validation time for NAS largely decreases when testing in AA-NAS-Bench , which provides a computational power friendly environment for more participations in NAS.
(3) It is the ﬁrst NAS benchmark that provides results of each architecture on multiple datasets.
The model transferability can be thoroughly evaluated for most NAS algorithms.
(4) In AA-NAS-Bench , we provide systematic analysis of the proposed search space.
We also evaluate many recent advanced NAS algorithms including reinforcement learning (RL)-based methods, evolutionary strategy (ES)-based methods, differentiable-based methods, etc.
We hope our empirical analysis can bring some insights to the future designs of NAS algorithms.
A LGORITHM -A GNOSTIC NAS B ENCHMARK
Our AA-NAS-Bench is algorithm-agnostic.
Put simply, it is applicable to almost any up-to-date NAS algorithms.
In this section, we will brieﬂy introduce our AA-NAS-Bench .
The search space of AANAS-Bench is inspired by cell-based NAS algorithms (Section 2.1).
AA-NAS-Bench evaluates each architecture on three different datasets (Section 2.2).
All implementation details of AA-NAS-Bench are introduced in Section 2.3.
AA-NAS-Bench also provides some diagnostic information which can be used for potentially better designs of future NAS algorithms (discussed in Section 2.4).
2. A RCHITECTURES IN THE S EARCH S PACE
Macro Skeleton .
Our search space follows the design of its counterpart as used in the recent neural cell-based NAS algorithms (Liu et al., 2019; Zoph et al., 2018; Pham et al., 2018).
As shown in the top of Figure 1, the skeleton is initiated with one 3-by-3 convolution with 16 output channels and a batch normalization layer (Ioffe & Szegedy, 2015).
The main body of the skeleton includes three stacks of cells, connected by a residual block.
Each cell is stacked N = 5 times, with the number of output channels as 16, 32 and 64 for the ﬁrst, second and third stages, respectively.
The intermediate residual block is the basic residual block with a stride of 2 (He et al., 2016), which serves to downsample the spatial size and double the channels of an input feature map.
The shortcut path in this residual block consists of a 2-by-2 average pooling layer with stride of 2 and a 1-by-1 convolution.
The skeleton ends up with a global average pooling layer to ﬂatten the feature map into a feature vector.
Classiﬁcation uses a fully connected layer with a softmax layer to transform the feature vector into the ﬁnal prediction.
Searched Cell .
Each cell in the search space is represented as a densely connected DAG.
The densely connected DAG is obtained by assigning a direction from the i -th node to the j -th node ( i < j ) for each edge in an undirected complete graph.
Each edge in this DAG is associated with an operation transforming the feature map from the source node to the target node.
All possible operations are selected from a predeﬁned operation set, as shown in Figure 1(bottom-right).
In our
AA-NAS-Bench , the predeﬁned operation set
O has L = 5 representative operations: (1) zeroize, (2) skip connection, (3) 1-by-1 convolution, (4) 3-by-3 convolution, and (5) 3-by-3 average pooling layer.
The convolution in this operation set is an abbreviation of an operation sequence of ReLU, convolution, and batch normalization.
The DAG has V = 4 nodes, where each node represents the sum of all feature maps transformed through the associated operations of the edges pointing to this node.
We choose V = 4 to allow the search space to contain basic residual block-like cells, which requires 4 nodes.
Densely connected DAG does not restrict the searched topology of the cell to be densely connected, since we include zeroize in the operation set, which is an operation of dropping the associated edge.
Besides, since we do not impose the constraint on the maximum number of edges (Ying et al., 2019), our search space is applicable to most NAS algorithms, including all cell-based NAS algorithms.
2. D ATASETS
We train and evaluate each architecture on CIFAR-10, CIFAR-100 (Krizhevsky et al., 2009), and
ImageNet-16-120 (Chrabaszcz et al., 2017).
We choose these three datasets because CIFAR and
ImageNet (Deng et al., 2009) are the most popular image classiﬁcation datasets.
We split each dataset into training, validation and test sets to provide a consistent training and evaluation settings for previous NAS algorithms (Liu et al., 2019).
Most NAS methods use the validation set to evaluate architectures after the architecture is optimized on the training set.
The validation performance of the architectures serves as supervision signals to update the searching algorithm.
The test set is to evaluate the performance of each searching algorithm by comparing the indicators (e.g., accuracy, model size, speed) of their selected architectures.
Previous methods use different splitting strategies, which may result in various searching costs and unfair comparisons.
We hope to use the proposed splits to unify the training, validation and test sets for a fairer comparison.
CIFAR-10 :
This is the standard image classiﬁcation dataset.
It consists of 60,000 32 × 32 colour images in 10 classes.
The original training set contains 50,000 images, with 5,000 images per class.
The original test set contains 10,000 images, with 1000 images per class.
Due to the need of validation set, we split all 50,000 training images in CIFAR-10 into two groups.
Each group contains 25,000 images with 10 classes.
We regard the ﬁrst group as the new training set and the second group as the validation set.
CIFAR-100 : This dataset is just like the CIFAR-10.
It has the same images as CIFAR-10 but categorizes each image into 100 ﬁne-grained classes.
The original training set on CIFAR-100 has
50,000 images, and the original test set has 10,000 images.
We randomly split the original test set into two group of equal size — 5,000 images per group.
One group is regarded as the validation set, and another one is regarded as the new test set.
ImageNet-16-120 : We build ImageNet-16-120 from the down-sampled variant of ImageNet (ImageNet16 × 16).
As indicated in Chrabaszcz et al.
(2017), down-sampling images in ImageNet can largely reduce the computation costs for optimal hyper-parameters of some classical models while maintaining similar searching results.
Chrabaszcz et al.
(2017) down-sampled the original
ImageNet to 16 × 16 pixels to form ImageNet16 × 16, from which we select all images with label ∈ [1 , 120] to construct ImageNet-16-120.
In sum, ImageNet-16-120 contains 151,700 training images, 3,000 validation images, and 3,000 test images with 120 classes.
2. A RCHITECTURE P ERFORMANCE
Training Architectures.
In order to unify the performance of every architecture, we give the performance of every architecture in our search space.
In our AA-NAS-Bench , we follow previous
[Table]
literature to set up the hyper-parameters and training strategies (Zoph et al., 2018; Loshchilov &
Hutter, 2017; He et al., 2016).
We train each architecture with the same strategy, which is shown in Table 1.
For simpliﬁcation, we denote all hyperparameters for training a model as a set H , and we use H † to denote the values of hyper-parameter that we use.
Speciﬁcally, we train each architecture via
Nesterov momentum SGD, using the cross-entropy loss for 200 epochs in total.
We set the weight decay as 0.0005 and decay the learning rate from 0.1 to 0 with a cosine annealing (Loshchilov &
Hutter, 2017).
We use the same H † on different datasets, except for the data augmentation which is slightly different due to the image resolution.
On CIFAR, we use the random ﬂip with probability of 0.5, the random crop 32 × 32 patch with 4 pixels padding on each border, and the normalization over RGB channels.
On ImageNet-16-120, we use a similar strategy but random crop 16 × 16 patch with 2 pixels padding on each border.
All codes are implemented with with PyTorch (Paszke et al., 2017).
Metrics .
We train each architecture with different random seeds on different datasets 1 .
We evaluate each architecture A after every training epoch.
AA-NAS-Bench provides the training, validation,
[Table]
[Table]
and test loss as well as accuracy.
We show the supported metrics on different datasets in Table 2.
Users can easily use ( A , i ) to query the results of the i -th run of A , which has negligible computational costs.
In this way, researchers could signiﬁcantly speed up their searching algorithm on these datasets and focus solely on the essence of NAS.
We list the training/test loss/accuracies over different split sets on four datasets in Table 2.
On CIFAR-10, we train the model on the training set and evaluate it on the validation set.
We also train the model on the training and validation set and evaluate it on the test set.
These two paradigm follow the typical experimental setup on CIFAR-10 in previous literature (Liu et al., 2018; Zoph et al., 2018; Liu et al., 2018; Pham et al., 2018).
On CIFAR-100 and ImageNet-16-120, we train the model on the training set and evaluate it on both validation and test sets.
2. D IAGNOSTIC I NFORMATION
Validation accuracy is a commonly used supervision signal for NAS.
However, considering the expensive computational costs for evaluating the architecture, the signal is too sparse.
In our AA-
[Table]
NAS-Bench , we also provide some training involves no cost but may provide platform-aware NAS (Tan al mutation-
Architecture Computational Costs: AA-NAS-Bench provides three computation metrics for each architecture — the number of parameters, FLOPs, and latency.
Algorithms that target on searching architectures with computational constraints, such as models on edge devices, can use these metrics directly in their algorithm designs without extra calculations.
Fine-grained [Table] and evaluation information.
AA-NAS-Bench tracks the changes in loss and accuracy of every architecture after every training epochs.
These ﬁne-grained training and evaluation information shows the tendency of the architecture performance and could indicate some attributes of the model, such as the speed of convergence, the stability, the over-ﬁtting or under-ﬁtting levels, etc.
These attributes may beneﬁt the designs of NAS algorithms.
Besides, some methods learn to predict the ﬁnal accuracy of an architecture based on the results of few early training epochs (Baker et al., 2018).
These algorithm can be trained faster and the performance of the accuracy prediction can be evaluated using the ﬁne-grained evaluation information.
Parameters of optimized architecture.
Our AA-NAS-Bench releases the trained parameters for each architecture.
This can provide ground truth label for hypernetwork-based NAS methods (Zhang et al., 2019; Brock et al., 2018), which learn to generate parameters of an architecture.
Other methods mutate an architecture to become another one (Real et al., 2019; Cai et al., 2018).
With AA-NASBench , researchers could directly use the off-the-shelf parameters instead of training from scratch and analyze how to transfer parameters from one architecture to another.
D IFFERENCE WITH NAS-B ENCH -
To the best of our knowledge, NAS-Bench-101 (Ying et al., 2019) is the only existing architecture dataset.
Similar to AA-NAS-Bench , NAS-Bench-101 also transforms the problem of architecture search into the problem of searching neural cells, represented as a DAG.
Differently, NAS-Bench101 deﬁnes operation candidates on the node, whereas we associate operations on the edge as inspired from (Liu et al., 2019; Dong & Yang, 2019b; Zoph et al., 2018).
We summarize characteristics of our AA-NAS-Bench and NAS-Bench-101 in Table 3.
The main highlights of our AA-NAS-Bench is (1) AA-NAS-Bench is algorithm-agnostic while NAS-Bench-101 is only applicable to selected algorithms.
The original complete search space, based on the nodes in NAS-Bench-101, is extremely huge.
So, it is exceedingly difﬁcult to efﬁciently traverse the training of all architectures.
To trade off the computational cost and the size of the search space, they constrain the maximum number of edges in the DAG.
However, it is difﬁcult to incorporate this constraint in all NAS algorithms, such as NAS algorithms based on parameter-sharing (Liu et al., 2019; Pham et al., 2018).
Therefore, many NAS algorithms cannot be directly evaluated on NAS-Bench-101.
Our AA-NAS-Bench solves this problem by sacriﬁcing the number of nodes and including all possible edges so that our search space is algorithm-agnostic.
(2) We provide extra diagnostic information, such as architecture computational cost, ﬁne-grained training and evaluation time, etc., which give inspirations to better and efﬁcient designs of NAS algorithms utilizing these diagnostic information.
A NALYSIS OF AA-NAS-B ENCH
An overview of architecture performance.
The performance of each architecture is shown in
Figure 2.
We show the test accuracy of every architecture in our search space in the left column of Figure 2.
The training, validation and test accuracy with respect to the number of parameters
[Figure]
are shown in the rest three columns, respectively.
Results show that a different number of parameters will affect the performance of the architectures, which indicates that the choices of operations are essential in NAS.
We also observe that the performance of the architecture can vary even when the number of parameters stays the same.
This observation indicates the importance of how the operations/cells are connected.
We compare the architectures with a classical human-designed architecture (ResNet) in all cases, which is indicated by an orange star mark.
ResNet shows competitive performance in three datasets, however, it still has room to improve, i.e., about 2% compared to the best architecture in CIFAR-100 and ImageNet16-120, about 1% compared to the best one with the same amount of parameters in CIFAR-100 and ImageNet
Architecture ranking on three datasets.
The ranking of every architecture in our search space is shown in Figure 3, where the architecture ranked in CIFAR-10 (x-axis) is ranked as in y-axis in CIFAR-100 and ImageNet-16-120, indicated by green and red markers respectively.
The performance of the architectures shows a generally consistent ranking over the three datasets with slightly different variance, which serves to test the generality of the searching algorithm.
Correlations of validation and test accuracies.
We visualize the correlation between the validation and test accuracy within one dataset and across datasets in Figure 4.
The correlation within one dataset is high compared to cross-dataset correlation.
The correlation dramatically decreases as we
[Figure]
only pick the top performing architectures.
When we directly transfer the best architecture in one dataset to another (a vanilla strategy), it can not 100% secure a good performance.
This phenomena is a call for better transferable NAS algorithms instead of vanilla strategy.
Dynamic ranking of architectures.
We show the ranking of the performance of all architectures in different time stamps in Figure 5.
The ranking based on the validation set (y axis) gradually converges to the ranking based on the ﬁnal test accuracy (x axis).
B ENCHMARK
In this section, we evaluate some recent searching methods on our AA-NAS-Bench , which can serve as baselines for future NAS algorithms in our dataset.
Speciﬁcally, we evaluate typical NAS algorithms in Table 4: (I) Random Search algorithms, e.g., random search (RS) (Bergstra & Bengio, 2012), random search with parameter sharing (RSPS) (Li & Talwalkar, 2019).
(II) ES methods, e.g.,
REA (Real et al., 2019). (III) RL algorithms, e.g., REINFORCE (Williams, 1992), ENAS (Pham et al., 2018). (IV) Differentiable algorithms.
e.g., ﬁrst order DARTS (DARTS-V1)
(Liu et al.,
Method test accuracy (%
[Table]
on
[Table]
[Table]
ImageNet
[Table]
trial [Table] trial [Table]
trial
[Table]
average valid test valid test
RS 94. RSPS 90.
DARTS-V 39.
DARTS-V 39.
GDAS 92.
SETN 92.
REA 93.
REINFORCE 93.
[Table]
, second order DARTS (DARTS-V2), GDAS (Dong & Yang, 2019b), and SETN (Dong & Yang, 2019a). (V) HPO methods, e.g., BOHB (Falkner et al., 2018). All algorithms use the training and validation set of CIFAR-10 to search architectures.
We report the test accuracy of the searched architectures plus the optimal architecture on three datasets. We make the following observations: (1) REA and REINFORCE perform best but costs much more computational time to train and evaluate each architecture (about 10 hours vs 3 hours). In our setup, they traverse 10015625 = 0 . 0064 of our search space in total.
(2) Methods with parameter sharing are efﬁcient. However, the validation performance obtained from the shared parameters cannot lead a good relative ranking of each architecture.
(3) DARTS-V1 and DARTS-V2 quickly converge to ﬁnd the architecture whose edges are all skip connection.
A possible reason is that the original hyperparameters of DARTS are chosen for their search space instead of ours.
(4) Using our ﬁne-grained information, REA, REINFORCE and RS can be ﬁnished in seconds which could signiﬁcantly reduce the search costs and let researchers focus solely on the search algorithm itself.
Clariﬁcation.
We have tried our best to implement each method.
However, still, some algorithms might obtain non-optimal results since their hyper-parameters might not ﬁt our AA-NAS-Bench . If researchers can provide better results with different hyper-parameters, we are happy to update results according to the new experimental results.
We also welcome more NAS algorithms to test on our dataset and would include them accordingly.
D ISCUSSION
How to avoid over-ﬁtting on AA-NAS-Bench ?
Our AA-NAS-Bench provides a benchmark for
NAS algorithms, aiming to provide a fair and computational cost-friendly environment to the NAS community.
The trained architecture and the easy-to-access performance of each architecture might provide some insidious ways for designing algorithms to over-ﬁt the best architecture in our AANAS-Bench .
Thus, we propose some rules which we wish the users will follow to achieve the original intention of AA-NAS-Bench , a fair and efﬁcient benchmark.
No regularization for a speciﬁc operation.
Since the best architecture is known in our benchmark, speciﬁc designs to ﬁt the structural attributes of the best performed architecture are insidious ways to ﬁt our AA-NAS-Bench .
For example, as mentioned in Section 5, we found that the best architecture with the same amount of parameters for CIFAR10 on AA-NAS-Bench is ResNet.
Restrictions on the number of residual connections is a way to over-ﬁt the CIFAR10 benchmark.
While this can give a good result on this benchmark, the searching algorithm might not generalize to other benchmarks.
Use the provided performance.
The training strategy affects the performance of the architecture.
We suggest the users stick to the performance provided in our benchmark even if it is feasible to use other H to get a better performance.
This provides a fair comparison with other algorithms.
Report results of multiple searching runs.
Since our benchmark can help to largely decrease the computational cost for a number of algorithms.
Multiple searching runs give a stable results of the searching algorithm with acceptable time cost.
Limitation regarding to hyper-parameter optimization (HPO).
The performance of an architecture depends on the hyper-parameters H for its training and the optimal conﬁguration of H may vary for different architectures.
In AA-NAS-Bench , we use the same conﬁguration for all architectures, which may bring biases to the performance of some architectures.
One related solution is HPO, which aims to search the optimal hyper-parameter conﬁguration.
However, searching the optimal hyper-parameter conﬁgurations and the architecture in one shot is too computationally expensive and still is an open problem.
Potential designs using diagnostic information in AA-NAS-Bench .
As pointed in Section 2.4, different kinds of diagnostic information are provided.
We hope that more insights about NAS could be found by analyzing these diagnostic information and further motivate potential solutions for NAS.
For example, parameter sharing (Pham et al., 2018) is the crucial technique to improve the searching efﬁciency, but the shared parameter would sacriﬁce the accuracy of each architecture.
Could we ﬁnd a better way to share parameters of each architecture from the learned 15,625 models’ parameters?
C ONCLUSION & F UTURE W ORK
In this paper we introduce the ﬁrst algorithm-agnostic benchmark for neural architecture search ( AA-NAS-Bench ), whereby almost any NAS algorithms can be directly evaluated.
We train and evaluate 15,625 architecture on three different datasets and we provide results regarding different metrics.
We comprehensively analyze our dataset and test some recent NAS algorithms on AA-NASBench to serve as baselines for future works.
In future, we will (1) consider HPO and NAS together and (2) much larger search space.
We welcome researchers to try their NAS algorithms on our
AA-NAS-Bench
and would update the paper to include their results
A I MPLEMENTATION D ETAILS
Based on the publicly available codes, we re-implement all algorithms by ourselves to search architectures on our AA-NAS-Bench .
We provide the implementation details of each searching algorithm below.
Random search (RS) (Bergstra & Bengio, 2012).
We randomly select 100 architectures.
We use the validation accuracy after 25 training epochs, which can be used directly in our AA-NAS-Bench as discussed in Section 2.4.
The architecture with the highest validation accuracy is selected as the ﬁnal searched architecture.
Random search with parameter sharing (RSPS) (Li & Talwalkar, 2019).
We train the shared parameters via Nesterov momentum SGD, using the cross-entropy loss for 150 epochs in total.
We set weight decay as 0.0005 and momentum of 0.9.
We decay the learning rate from 0.025 to 0.001 via cosine learning rate scheduler and clip the gradient by 5.
We use the batch size ofand randomly sample one architecture in each batch training.
Each architecture uses the training mode during training and evaluation mode during evaluation (Paszke et al., 2017).
After training the shared parameters, we evaluate 100 randomly selected architectures on the validation set and choose the one with highest validation accuracy.
The ﬁrst order and second order DARTS (DARTS-V1 and DARTS-V2)
(Liu et al., 2019).
We use the hyper-parameters as that of RSPS.
Differently, we train the algorithm in 50 epochs in total.
We train the architecture encoding via Adam with the learning rate of 0.0003 and the weight decay of 0.001.
Gradient-based search using differentiable architecture sampler (GDAS)
(Dong & Yang, 2019b).
We use the most hyper-parameters as that of DARTS but train in 240 epochs in total.
Self-Evaluated Template Network (SETN) (Dong & Yang, 2019a).
We use the most hyperparameters as that of DARTS but train in 400 epochs in total.
After training the shared parameters, we evaluate 100 randomly selected architectures on the validation set and select the one with highest validation accuracy.
Regularized evolution for image classiﬁer architecture search (REA) (Real et al., 2019).
We set the initial population size as 10, the number of cycles as 30, and the sample size of 3.
When using these hyper-parameters, there will be 100 architectures to be evaluated during the evolutionary procedure.
We use the validation accuracy after 25 training epochs as the ﬁtness.
REINFORCE (Williams, 1992).
We follow (Ying et al., 2019) to use the REINFORCE algorithm as a baseline RL method.
We use an architecture encoding to parameterize each candidate in our search space as (Liu et al., 2019; Dong & Yang, 2019b).
We use the validation accuracy aftertraining epochs as the reward in REINFORCE.
The architecture encoding is optimized via Adam with a learning rate of 0.001.
We ﬁnish the training in 100 episodes.
ENAS (Pham et al., 2018).
We use a two layer LSTM as the controller with the hidden size of 32.
We use the temperature of 5 and the tanh constant of 2.5 for the sampling logits Following (Pham et al., 2018), we also add the the controller’s sample entropy to the reward, weighted by 0.0001.
We optimize the controller with Adam using the constant learning rate of 0.001.
We optimizing the network weights with SGD following the learning rate scheduler as the original paper.
We did not impose any penalty to a speciﬁc operation.
BOHB (Falkner et al., 2018).
We choose to use BOHB as an HPO algorithm on our dataset.
We follow (Ying et al., 2019) to set up the hyper-parameters for BOHB.
To fairly compare with other
NAS algorithms, we change the number of samples for the acquisition function as 3 and the num- and in way
BOHB can only traverse architectures