The Living Thing / Notebooks :

AutoML

hyperparameter selection with the use of yet more hyperparameters

Usefulness: 🔧
Novelty: 💡
Uncertainty: 🤪 🤪 🤪
Incompleteness: 🚧 🚧 🚧

The sub-field of optimisation that specifically aims to automate model selection in machine learning. (and also occasionally ensemble construction)

Quoc Le & Barret Zoph weigh in for google:

Typically, our machine learning models are painstakingly designed by a team of engineers and scientists. This process of manually designing machine learning models is difficult because the search space of all possible models can be combinatorially large — a typical 10-layer network can have ~1010 candidate networks! […]

To make this process of designing machine learning models much more accessible, we’ve been exploring ways to automate the design of machine learning models. […] in this blog post, we’ll focus on our reinforcement learning approach and the early results we’ve gotten so far.

In our approach (which we call “AutoML”), a controller neural net can propose a “child” model architecture, which can then be trained and evaluated for quality on a particular task. That feedback is then used to inform the controller how to improve its proposals for the next round.

Should you bother getting fancy about this? Ben Recht argues no, that random search is competitive with highly tuned Bayesian methods in hyperparameter tuning. Let’s ignore him for a moment though and sniff in the hype.

Differentiable hyperparameter optimisation

MaDA15:

Hyperparameter optimization by gradient descent

Each meta-iteration runs an entire training run of stochastic gradient de- scent to optimize elementary parameters (weights 1 and 2). Gradients of the validation loss with respect to hyperparameters are then computed by propagating gradients back through the elementary training iterations. Hyperparameters (in this case, learning rate and momentum schedules) are then updated in the direction of this hypergradient. … The last remaining parameter to SGD is the initial parameter vector. Treating this vector as a hyperparameter blurs the distinction between learning and meta-learning. In the extreme case where all elementary learning rates are set to zero, the training set ceases to matter and the meta-learning procedure exactly reduces to elementary learning on the validation set. Due to philosophical vertigo, we chose not to optimize the initial parameter vector.

Their implementation, hypergrad, is cool, but no longer maintained.

Bayesian/surrogate optimisation

See Bayesian optimisation

Implementations

Refs

Abdel-Gawad, Ahmed, and Simon Ratner. 2007. “Adaptive Optimization of Hyperparameters in L2-Regularised Logistic Regression.” http://cs229.stanford.edu/proj2007/AbdelGawadRatner-AdaptiveHyperparameterOptimization.pdf.

Bengio, Yoshua. 2000. “Gradient-Based Optimization of Hyperparameters.” Neural Computation 12 (8): 1889–1900. https://doi.org/10.1162/089976600300015187.

Bergstra, James S., Rémi Bardenet, Yoshua Bengio, and Balázs Kégl. 2011. “Algorithms for Hyper-Parameter Optimization.” In Advances in Neural Information Processing Systems, 2546–54. Curran Associates, Inc. http://papers.nips.cc/paper/4443-algorithms-for-hyper-parameter-optimization.

Domke, Justin. 2012. “Generic Methods for Optimization-Based Modeling.” In International Conference on Artificial Intelligence and Statistics, 318–26. http://machinelearning.wustl.edu/mlpapers/paper_files/AISTATS2012_Domke12.pdf.

Eggensperger, Katharina, Matthias Feurer, Frank Hutter, James Bergstra, Jasper Snoek, Holger H. Hoos, and Kevin Leyton-Brown. n.d. “Towards an Empirical Foundation for Assessing Bayesian Optimization of Hyperparameters.” Accessed August 21, 2017. http://www.automl.org/papers/13-BayesOpt_EmpiricalFoundation.pdf.

Eigenmann, R., and J. A. Nossek. 1999. “Gradient Based Adaptive Regularization.” In Neural Networks for Signal Processing IX: Proceedings of the 1999 IEEE Signal Processing Society Workshop (Cat. No.98TH8468), 87–94. https://doi.org/10.1109/NNSP.1999.788126.

Feurer, Matthias, Aaron Klein, Katharina Eggensperger, Jost Springenberg, Manuel Blum, and Frank Hutter. 2015. “Efficient and Robust Automated Machine Learning.” In Advances in Neural Information Processing Systems 28, edited by C. Cortes, N. D. Lawrence, D. D. Lee, M. Sugiyama, and R. Garnett, 2962–70. Curran Associates, Inc. http://papers.nips.cc/paper/5872-efficient-and-robust-automated-machine-learning.pdf.

Foo, Chuan-sheng, Chuong B. Do, and Andrew Y. Ng. 2008. “Efficient Multiple Hyperparameter Learning for Log-Linear Models.” In Advances in Neural Information Processing Systems 20, edited by J. C. Platt, D. Koller, Y. Singer, and S. T. Roweis, 377–84. Curran Associates, Inc. http://papers.nips.cc/paper/3286-efficient-multiple-hyperparameter-learning-for-log-linear-models.pdf.

Fu, Jie, Hongyin Luo, Jiashi Feng, Kian Hsiang Low, and Tat-Seng Chua. 2016. “DrMAD: Distilling Reverse-Mode Automatic Differentiation for Optimizing Hyperparameters of Deep Neural Networks.” In PRoceedings of IJCAI, 2016. http://arxiv.org/abs/1601.00917.

Gelbart, Michael A., Jasper Snoek, and Ryan P. Adams. 2014. “Bayesian Optimization with Unknown Constraints.” In Proceedings of the Thirtieth Conference on Uncertainty in Artificial Intelligence, 250–59. UAI’14. Arlington, Virginia, United States: AUAI Press. http://hips.seas.harvard.edu/files/gelbart-constrained-uai-2014.pdf.

Grünewälder, Steffen, Jean-Yves Audibert, Manfred Opper, and John Shawe-Taylor. 2010. “Regret Bounds for Gaussian Process Bandit Problems.” In, 9:273–80. https://hal-enpc.archives-ouvertes.fr/hal-00654517/document.

Hutter, Frank, Holger H. Hoos, and Kevin Leyton-Brown. 2011. “Sequential Model-Based Optimization for General Algorithm Configuration.” In Learning and Intelligent Optimization, 6683:507–23. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25566-3_40.

Hutter, Frank, Holger Hoos, and Kevin Leyton-Brown. 2013. “An Evaluation of Sequential Model-Based Optimization for Expensive Blackbox Functions.” In Proceedings of the 15th Annual Conference Companion on Genetic and Evolutionary Computation, 1209–16. GECCO ’13 Companion. New York, NY, USA: ACM. https://doi.org/10.1145/2464576.2501592.

Li, Lisha, Kevin Jamieson, Giulia DeSalvo, Afshin Rostamizadeh, and Ameet Talwalkar. 2016. “Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization,” March. http://arxiv.org/abs/1603.06560.

Liu, Hanxiao, Karen Simonyan, and Yiming Yang. 2018. “DARTS: Differentiable Architecture Search,” June. http://arxiv.org/abs/1806.09055.

Maclaurin, Dougal, David K. Duvenaud, and Ryan P. Adams. 2015. “Gradient-Based Hyperparameter Optimization Through Reversible Learning.” In ICML, 2113–22. http://www.jmlr.org/proceedings/papers/v37/maclaurin15.pdf.

Močkus, J. 1975. “On Bayesian Methods for Seeking the Extremum.” In Optimization Techniques IFIP Technical Conference, edited by Prof Dr G. I. Marchuk, 400–404. Lecture Notes in Computer Science. Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-662-38527-2_55.

Salimans, Tim, Diederik Kingma, and Max Welling. 2015. “Markov Chain Monte Carlo and Variational Inference: Bridging the Gap.” In Proceedings of the 32nd International Conference on Machine Learning (ICML-15), 1218–26. ICML’15. Lille, France: JMLR.org. http://proceedings.mlr.press/v37/salimans15.html.

Snoek, Jasper, Hugo Larochelle, and Ryan P. Adams. 2012. “Practical Bayesian Optimization of Machine Learning Algorithms.” In Advances in Neural Information Processing Systems, 2951–9. Curran Associates, Inc. http://papers.nips.cc/paper/4522-practical-bayesian-optimization-of-machine-learning-algorithms.

Snoek, Jasper, Kevin Swersky, Rich Zemel, and Ryan Adams. 2014. “Input Warping for Bayesian Optimization of Non-Stationary Functions.” In Proceedings of the 31st International Conference on Machine Learning (ICML-14), 1674–82. http://www.jmlr.org/proceedings/papers/v32/snoek14.pdf.

Srinivas, Niranjan, Andreas Krause, Sham M. Kakade, and Matthias Seeger. 2012. “Gaussian Process Optimization in the Bandit Setting: No Regret and Experimental Design.” IEEE Transactions on Information Theory 58 (5): 3250–65. https://doi.org/10.1109/TIT.2011.2182033.

Swersky, Kevin, Jasper Snoek, and Ryan P Adams. 2013. “Multi-Task Bayesian Optimization.” In Advances in Neural Information Processing Systems 26, edited by C. J. C. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K. Q. Weinberger, 2004–12. Curran Associates, Inc. http://papers.nips.cc/paper/5086-multi-task-bayesian-optimization.pdf.

Thornton, Chris, Frank Hutter, Holger H. Hoos, and Kevin Leyton-Brown. 2013. “Auto-WEKA: Combined Selection and Hyperparameter Optimization of Classification Algorithms.” In Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 847–55. KDD ’13. New York, NY, USA: ACM. https://doi.org/10.1145/2487575.2487629.