Self-Tuning Networks: Bilevel Optimization of Hyperparameters using Structured Best-Response Functions
Hyperparameter optimization can be formulated as a bilevel optimization problem, where the optimal parameters on the training set depend on the hyperparameters. We aim to adapt regularization hyperparameters for neural networks by fitting compact approximations to the best-response function, which maps hyperparameters to optimal weights and biases. We show how to construct scalable best-response approximations for neural networks by modeling the best-response as a single network whose hidden units are gated conditionally on the regularizer. We justify this approximation by showing the exact best-response for a shallow linear network with L2-regularized Jacobian can be represented by a similar gating mechanism. We fit this model using a gradient-based hyperparameter optimization algorithm which alternates between approximating the best-response around the current hyperparameters and optimizing the hyperparameters using the approximate best-response function. Unlike other gradient-based approaches, we do not require differentiating the training loss with respect to the hyperparameters, allowing us to tune discrete hyperparameters, data augmentation hyperparameters, and dropout probabilities. Because the hyperparameters are adapted online, our approach discovers hyperparameter schedules that can outperform fixed hyperparameter values. Empirically, our approach outperforms competing hyperparameter optimization methods on large-scale deep learning problems. We call our networks, which update their own hyperparameters online during training, Self-Tuning Networks (STNs).
 The paper proposes a bilevel optimization approach for hyperparameter tuning. This idea is not new having been proposed in works prior to the current resurgence of deep learning (e.g., Do et al., 2007, Domke 2012, and Kunisch & Pock, 2013). However, the combination of bilevel optimization for hyperparameter tuning with approximation is interesting. Moreover, the proposed approach readily handles discrete parameters. Experiments are run on small scale problems, namely, CIFAR-10 and PTB. Results are encouraging but not stellar. More work would need to be done to validate the utility of the proposed approach on larger scale problems.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Self-Tuning Networks: Bilevel Optimization of Hyperparameters using Structured Best-Response Functions
Hyperparameter optimization can be formulated as a bilevel optimization problem, where the optimal parameters on the training set depend on the hyperparameters. We aim to adapt regularization hyperparameters for neural networks by fitting compact approximations to the best-response function, which maps hyperparameters to optimal weights and biases. We show how to construct scalable best-response approximations for neural networks by modeling the best-response as a single network whose hidden units are gated conditionally on the regularizer. We justify this approximation by showing the exact best-response for a shallow linear network with L2-regularized Jacobian can be represented by a similar gating mechanism. We fit this model using a gradient-based hyperparameter optimization algorithm which alternates between approximating the best-response around the current hyperparameters and optimizing the hyperparameters using the approximate best-response function. Unlike other gradient-based approaches, we do not require differentiating the training loss with respect to the hyperparameters, allowing us to tune discrete hyperparameters, data augmentation hyperparameters, and dropout probabilities. Because the hyperparameters are adapted online, our approach discovers hyperparameter schedules that can outperform fixed hyperparameter values. Empirically, our approach outperforms competing hyperparameter optimization methods on large-scale deep learning problems. We call our networks, which update their own hyperparameters online during training, Self-Tuning Networks (STNs).
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 The paper proposes a bilevel optimization approach for hyperparameter tuning. This idea is not new having been proposed in works prior to the current resurgence of deep learning (e.g., Do et al., 2007, Domke 2012, and Kunisch & Pock, 2013). However, the combination of bilevel optimization for hyperparameter tuning with approximation is interesting. Moreover, the proposed approach readily handles discrete parameters. Experiments are run on small scale problems, namely, CIFAR-10 and PTB. Results are encouraging but not stellar. More work would need to be done to validate the utility of the proposed approach on larger scale problems.
assistant
 The paper proposes a bilevel optimization approach for hyperparameter tuning. This idea is not new having been proposed in works prior to the current resurgence of deep learning (e.g., Do et al., 2007, Domke 2012, and Kunisch & Pock, 2013). However, the combination of bilevel optimization for hyperparameter tuning with approximation is interesting. Moreover, the proposed approach readily handles discrete parameters. Experiments are run on small scale problems, namely, CIFAR-10 and PTB. Results are encouraging but not stellar. More work would need to be done to validate the utility of the proposed approach on larger scale problems.