Learned Optimizers that Scale and Generalize

Learning to learn has emerged as an important direction for achieving artificial intelligence. Two of the primary barriers to its adoption are an inability to scale to larger problems and a limited ability to generalize to new tasks. We introduce a learned gradient descent optimizer that generalizes well to new tasks, and which has significantly reduced memory and computation overhead. We achieve this by introducing a novel hierarchical RNN architecture, with minimal per-parameter overhead, augmented with additional architectural features that mirror the known structure of optimization tasks. We also develop a meta-training ensemble of small, diverse, optimization tasks capturing common properties of loss landscapes. The optimizer learns to outperform RMSProp/ADAM on problems in this corpus. More importantly, it performs comparably or better when applied to small convolutional neural networks, despite seeing no neural networks in its meta-training set. Finally, it generalizes to train Inception V3 and ResNet V2 architectures on the ImageNet dataset for thousands of steps, optimization problems that are of a vastly different scale than those it was trained on.

[1]  Lewis B. Ward Reminiscence and rote learning. , 1937 .

[2]  H. Harlow,et al.  The formation of learning sets. , 1949, Psychological review.

[3]  Y. Nesterov A method for solving the convex programming problem with convergence rate O(1/k^2) , 1983 .

[4]  E. Kehoe A layered network model of associative learning: learning to learn and configuration. , 1988, Psychological review.

[5]  Yoshua Bengio,et al.  Learning a synaptic learning rule , 1991, IJCNN-91-Seattle International Joint Conference on Neural Networks.

[6]  Richard J. Mammone,et al.  Meta-neural networks that learn by learning , 1992, [Proceedings 1992] IJCNN International Joint Conference on Neural Networks.

[7]  Richard S. Sutton,et al.  Adapting Bias by Gradient Descent: An Incremental Version of Delta-Bar-Delta , 1992, AAAI.

[8]  Paul Tseng,et al.  An Incremental Gradient(-Projection) Method with Momentum Term and Adaptive Stepsize Rule , 1998, SIAM J. Optim..

[9]  Sebastian Thrun,et al.  Learning to Learn , 1998, Springer US.

[10]  Magnus Thor Jonsson,et al.  Evolution and design of distributed learning rules , 2000, 2000 IEEE Symposium on Combinations of Evolutionary Computation and Neural Networks. Proceedings of the First IEEE Symposium on Combinations of Evolutionary Computation and Neural Networks (Cat. No.00.

[11]  Sepp Hochreiter,et al.  Learning to Learn Using Gradient Descent , 2001, ICANN.

[12]  Samy Bengio,et al.  On the search for new learning rules for ANNs , 1995, Neural Processing Letters.

[13]  Yoshua Bengio,et al.  On the Optimization of a Synaptic Learning Rule , 2007 .

[14]  Geoffrey E. Hinton,et al.  ImageNet classification with deep convolutional neural networks , 2012, Commun. ACM.

[15]  Yoshua Bengio,et al.  On the Properties of Neural Machine Translation: Encoder–Decoder Approaches , 2014, SSST@EMNLP.

[16]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[17]  Yoshua Bengio,et al.  Neural Machine Translation by Jointly Learning to Align and Translate , 2014, ICLR.

[18]  Sergey Ioffe,et al.  Rethinking the Inception Architecture for Computer Vision , 2015, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[19]  Marcin Andrychowicz,et al.  Learning to learn by gradient descent by gradient descent , 2016, NIPS.

[20]  Misha Denil,et al.  Learning to Learn for Global Optimization of Black Box Functions , 2016, ArXiv.

[21]  Joshua B. Tenenbaum,et al.  Building machines that learn and think like people , 2016, Behavioral and Brain Sciences.

[22]  Jian Sun,et al.  Identity Mappings in Deep Residual Networks , 2016, ECCV.

[23]  Demis Hassabis,et al.  Mastering the game of Go with deep neural networks and tree search , 2016, Nature.

[24]  Peter L. Bartlett,et al.  RL$^2$: Fast Reinforcement Learning via Slow Reinforcement Learning , 2016, ArXiv.

[25]  Bartunov Sergey,et al.  Meta-Learning with Memory-Augmented Neural Networks , 2016 .

[26]  Zeb Kurth-Nelson,et al.  Learning to reinforcement learn , 2016, CogSci.

[27]  Hugo Larochelle,et al.  Optimization as a Model for Few-Shot Learning , 2016, ICLR.

[28]  Quoc V. Le,et al.  Neural Architecture Search with Reinforcement Learning , 2016, ICLR.

[29]  Jitendra Malik,et al.  Learning to Optimize , 2016, ICLR.