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DARTS without a Validation Set: Optimizing the Marginal Likelihood

arXiv.org Artificial Intelligence

The success of neural architecture search (NAS) has historically been limited by excessive compute requirements. While modern weight-sharing NAS methods such as DARTS are able to finish the search in single-digit GPU days, extracting the final best architecture from the shared weights is notoriously unreliable. Training-Speed-Estimate (TSE), a recently developed generalization estimator with a Bayesian marginal likelihood interpretation, has previously been used in place of the validation loss for gradient-based optimization in DARTS. This prevents the DARTS skip connection collapse, which significantly improves performance on NASBench-201 and the original DARTS search space. We extend those results by applying various DARTS diagnostics and show several unusual behaviors arising from not using a validation set. Furthermore, our experiments yield concrete examples of the depth gap and topology selection in DARTS having a strongly negative impact on the search performance despite generally receiving limited attention in the literature compared to the operations selection.


Structured Evolution with Compact Architectures for Scalable Policy Optimization

arXiv.org Machine Learning

We present a new method of blackbox optimization via gradient approximation with the use of structured random orthogonal matrices, providing more accurate estimators than baselines and with provable theoretical guarantees. We show that this algorithm can be successfully applied to learn better quality compact policies than those using standard gradient estimation techniques. The compact policies we learn have several advantages over unstructured ones, including faster training algorithms and faster inference. These benefits are important when the policy is deployed on real hardware with limited resources. Further, compact policies provide more scalable architectures for derivative-free optimization (DFO) in high-dimensional spaces. We show that most robotics tasks from the OpenAI Gym can be solved using neural networks with less than 300 parameters, with almost linear time complexity of the inference phase, with up to 13x fewer parameters relative to the Evolution Strategies (ES) algorithm introduced by Salimans et al. (2017). We do not need heuristics such as fitness shaping to learn good quality policies, resulting in a simple and theoretically motivated training mechanism.


Autoencoders Learn Generative Linear Models

arXiv.org Machine Learning

Recent progress in learning theory has led to the emergence of provable algorithms for training certain families of neural networks. Under the assumption that the training data is sampled from a suitable generative model, the weights of the trained networks obtained by these algorithms recover (either exactly or approximately) the generative model parameters. However, the large majority of these results are only applicable to supervised learning architectures. In this paper, we complement this line of work by providing a series of results for unsupervised learning with neural networks. Specifically, we study the familiar setting of shallow autoencoder architectures with shared weights. We focus on three generative models for the data: (i) the mixture-of-gaussians model, (ii) the sparse coding model, and (iii) the non-negative sparsity model. All three models are widely studied in the machine learning literature. For each of these models, we rigorously prove that under suitable choices of hyperparameters, architectures, and initialization, the autoencoder weights learned by gradient descent % -based training can successfully recover the parameters of the corresponding model. To our knowledge, this is the first result that rigorously studies the dynamics of gradient descent for weight-sharing autoencoders. Our analysis can be viewed as theoretical evidence that shallow autoencoder modules indeed can be used as unsupervised feature training mechanisms for a wide range of datasets, and may shed insight on how to train larger stacked architectures with autoencoders as basic building blocks.


On the Role of Weight Sharing During Deep Option Learning

arXiv.org Machine Learning

The options framework is a popular approach for building temporally extended actions in reinforcement learning. In particular, the option-critic architecture provides general purpose policy gradient theorems for learning actions from scratch that are extended in time. However, past work makes the key assumption that each of the components of option-critic has independent parameters. In this work we note that while this key assumption of the policy gradient theorems of option-critic holds in the tabular case, it is always violated in practice for the deep function approximation setting. We thus reconsider this assumption and consider more general extensions of option-critic and hierarchical option-critic training that optimize for the full architecture with each update. It turns out that not assuming parameter independence challenges a belief in prior work that training the policy over options can be disentangled from the dynamics of the underlying options. In fact, learning can be sped up by focusing the policy over options on states where options are actually likely to terminate. We put our new algorithms to the test in application to sample efficient learning of Atari games, and demonstrate significantly improved stability and faster convergence when learning long options.


UnICORNN: A recurrent model for learning very long time dependencies

arXiv.org Machine Learning

The design of recurrent neural networks (RNNs) to accurately process sequential inputs with long-time dependencies is very challenging on account of the exploding and vanishing gradient problem. To overcome this, we propose a novel RNN architecture which is based on a structure preserving discretization of a Hamiltonian system of second-order ordinary differential equations that models networks of oscillators. The resulting RNN is fast, invertible (in time), memory efficient and we derive rigorous bounds on the hidden state gradients to prove the mitigation of the exploding and vanishing gradient problem. A suite of experiments are presented to demonstrate that the proposed RNN provides state of the art performance on a variety of learning tasks with (very) long time-dependencies.