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Title: On the Tunability of Optimizers in Deep Learning

Paper content:
There is no consensus yet on the question whether adaptive gradient methods like Adam are easier to use than non-adaptive optimization methods like SGD.
In this work, we fill in the important, yet ambiguous concept of ‘ease-of-use’ by defining an optimizer’s tunability:  How easy is it to find good hyperparameter configurations using automatic random hyperparameter search?
We propose a practical and universal quantitative measure for optimizer tunability that can form the basis for a fair optimizer benchmark.
Evaluating a variety of optimizers on an extensive set of standard datasets and architectures, we find  that Adam is the most tunable for the majority of problems, especially with a low budget for hyperparameter tuning.
With the ubiquity of deep learning in various applications, a multitude of first-order stochastic optimizers (Robbins & Monro, 1951) have been in vogue.
They have varying algorithmic components like momentum (Sutskever et al., 2013 ) and adaptive learning rates (Tieleman & Hinton, 2012; Duchi et al., 2011; Kingma & Ba, 2015) .
With all these choices, picking the optimizer is among the most important design decisions for machine learning practitioners.
For this decision, the best possible generalization performance is certainly an important characteristic to be taken into account.
However, we argue that in practice, an even more important characteristic is whether the best possible performance can be reached with the available resources.
The performance of optimizers strongly depends on the choice of hyperparameter values such as the learning rate.
In the machine learning research community, the sensitivity of models to hyperparameters has been of great debate recently, where in multiple cases, reported model advances did not stand the test of time because they can be explained by better hyperparameter tuning (Lucic et al., 2018; Melis et al., 2018; Henderson et al., 2018) .
This has led to calls for using automatic hyperparameter optimization methods with a fixed budget for a fairer comparison of models (Sculley et al., 2018; Feurer & Hutter, 2019; Eggensperger et al., 2019) .
For industrial applications, automated machine learning (AutoML, , which has automatic hyperparameter optimization as one of its key concepts, is becoming increasingly more important.
In both cases, an optimization algorithm that achieves good performances with relatively little tuning effort is arguably substantially more useful than an optimization algorithm that achieves top performances, but reaches it only with a lot of careful tuning effort.
Hence, we advocate that the performance obtained by an optimizer is not only the best performance obtained when using that optimizer, but also has to account for the cost of tuning its hyperparameters to obtain that performance, thus being dichotomous.
We term this concept tunability in this paper.
Despite the importance of this concept, there is no standard way of measuring tunability.
Works that propose optimization techniques show their performance on various tasks as depicted in Table 1 .
It is apparent that the experimental settings, as well as the network architectures tested, widely vary, hindering a fair comparison.
The introduction of benchmarking suites like DEEPOBS (Schneider et al., 2019) have standardized the tested architectures, however, this does not fix the problem of selecting the hyperparameters themselves, and the effort expended in doing so.
Previous studies treat tunability to be the best performance obtained on varying a hyperparameter (Schneider et al., 2019) or by measuring the improvement in performance by tuning a hyperparameter (Probst et al., 2019 ), but do not take any cognizance to the intermediate performance during the tuning process.
Table 1 : Experimental settings shown in the original papers of popular optimizers.
The large differences in test problems and tuning methods make them difficult to compare.
γ denotes learning rate, µ denotes momentum, λ is the weight decay coefficient.
Our work proposes a new notion of tunability for optimizers that takes into account the tuning efforts of an HPO.
The results of our experiments support the hypothesis that adaptive gradient methods are easier to tune than non-adaptive methods: In a setting with low budget for hyperparameter tuning, tuning only Adam optimizer's learning rate is likely to be a very good choice; it doesn't guarantee the best possible performance, but it is evidently the easiest to find well-performing hyperparameter configurations for.
While SGD yields the best performance in some cases, its best configuration is tedious to find, and Adam often performs close to it.
We, thus, state that the substantial value of the adaptive gradient methods, specifically Adam, is its amenability to hyperparameter search.
This is in contrast to the findings of Wilson et al. (2017) who observe no advantage in tunabilty for adaptive gradient methods, and thus deem them to be of 'marginal value'.
Unlike them, we base our experiments on a standard hyperparameter optimization method that allows for an arguably fairer comparison.
Our study is certainly not exhaustive: We do not study the effect of the inclusion of a learning rate schedule, or using a different HPO algorithm on the results.
However, their inclusion would result in a large increase the number of experiments, and constitutes our future work.
We hope that this paper encourages other researchers to conduct future studies on the performance of optimizers from a more holistic perspective, where the cost of the hyperparameter search is included.

assistant: text: This paper introduces a simple measure of tunability that allows to compare optimizers under resource constraints, finding that tuning Adam optimizers' learning rate is easiest to find well-performing hyperparameter configurations.