Fast Adaptation with Linearized Neural Networks

The inductive biases of trained neural networks are difficult to understand and, consequently, to adapt to new settings. We study the inductive biases of linearizations of neural networks, which we show to be surprisingly good summaries of the full network functions. Inspired by this finding, we propose a technique for embedding these inductive biases into Gaussian processes through a kernel designed from the Jacobian of the network. In this setting, domain adaptation takes the form of interpretable posterior inference, with accompanying uncertainty estimation. This inference is analytic and free of local optima issues found in standard techniques such as fine-tuning neural network weights to a new task. We develop significant computational speed-ups based on matrix multiplies, including a novel implementation for scalable Fisher vector products. Our experiments on both image classification and regression demonstrate the promise and convenience of this framework for transfer learning, compared to neural network fine-tuning. Code is available at https://github.com/amzn/xfer/tree/master/finite_ntk.

Tomographic Auto-Encoder: Unsupervised Bayesian Recovery of Corrupted Data

We propose a new probabilistic method for unsupervised recovery of corrupted data. Given a large ensemble of degraded samples, our method recovers accurate posteriors of clean values, allowing the exploration of the manifold of possible reconstructed data and hence characterising the underlying uncertainty. In this setting, direct application of classical variational methods often gives rise to collapsed densities that do not adequately explore the solution space. Instead, we derive our novel reduced entropy condition approximate inference method that results in rich posteriors. We test our model in a data recovery task under the common setting of missing values and noise, demonstrating superior performance to existing variational methods for imputation and de-noising with different real data sets. We further show higher classification accuracy after imputation, proving the advantage of propagating uncertainty to downstream tasks with our model.

Empirical Bayes Transductive Meta-Learning with Synthetic Gradients

We propose a meta-learning approach that learns from multiple tasks in a transductive setting, by leveraging the unlabeled query set in addition to the support set to generate a more powerful model for each task. To develop our framework, we revisit the empirical Bayes formulation for multi-task learning. The evidence lower bound of the marginal log-likelihood of empirical Bayes decomposes as a sum of local KL divergences between the variational posterior and the true posterior on the query set of each task. We derive a novel amortized variational inference that couples all the variational posteriors via a meta-model, which consists of a synthetic gradient network and an initialization network. Each variational posterior is derived from synthetic gradient descent to approximate the true posterior on the query set, although where we do not have access to the true gradient. Our results on the Mini-ImageNet and CIFAR-FS benchmarks for episodic few-shot classification outperform previous state-of-the-art methods. Besides, we conduct two zero-shot learning experiments to further explore the potential of the synthetic gradient.

Online Constrained Model-based Reinforcement Learning

Applying reinforcement learning to robotic systems poses a number of challenging problems. A key requirement is the ability to handle continuous state and action spaces while remaining within a limited time and resource budget. Additionally, for safe operation, the system must make robust decisions under hard constraints. To address these challenges, we propose a model based approach that combines Gaussian Process regression and Receding Horizon Control. Using sparse spectrum Gaussian Processes, we extend previous work by updating the dynamics model incrementally from a stream of sensory data. This results in an agent that can learn and plan in real-time under non-linear constraints. We test our approach on a cart pole swing-up environment and demonstrate the benefits of online learning on an autonomous racing task. The environment's dynamics are learned from limited training data and can be reused in new task instances without retraining.

Similarity of Neural Networks with Gradients

A suitable similarity index for comparing learnt neural networks plays an important role in understanding the behaviour of the highly-nonlinear functions, and can provide insights on further theoretical analysis and empirical studies. We define two key steps when comparing models: firstly, the representation abstracted from the learnt model, where we propose to leverage both feature vectors and gradient ones (which are largely ignored in prior work) into designing the representation of a neural network. Secondly, we define the employed similarity index which gives desired invariance properties, and we facilitate the chosen ones with sketching techniques for comparing various datasets efficiently. Empirically, we show that the proposed approach provides a state-of-the-art method for computing similarity of neural networks that are trained independently on different datasets and the tasks defined by the datasets.

ORL: Reinforcement Learning Benchmarks for Online Stochastic Optimization Problems

Reinforcement Learning (RL) has achieved state-of-the-art results in domains such as robotics and games. We build on this previous work by applying RL algorithms to a selection of canonical online stochastic optimization problems with a range of practical applications: Bin Packing, Newsvendor, and Vehicle Routing. While there is a nascent literature that applies RL to these problems, there are no commonly accepted benchmarks which can be used to compare proposed approaches rigorously in terms of performance, scale, or generalizability. This paper aims to fill that gap. For each problem we apply both standard approaches as well as newer RL algorithms and analyze results. In each case, the performance of the trained RL policy is competitive with or superior to the corresponding baselines, while not requiring much in the way of domain knowledge. This highlights the potential of RL in real-world dynamic resource allocation problems.

Variational Information Distillation for Knowledge Transfer

Transferring knowledge from a teacher neural network pretrained on the same or a similar task to a student neural network can significantly improve the performance of the student neural network. Existing knowledge transfer approaches match the activations or the corresponding hand-crafted features of the teacher and the student networks. We propose an information-theoretic framework for knowledge transfer which formulates knowledge transfer as maximizing the mutual information between the teacher and the student networks. We compare our method with existing knowledge transfer methods on both knowledge distillation and transfer learning tasks and show that our method consistently outperforms existing methods. We further demonstrate the strength of our method on knowledge transfer across heterogeneous network architectures by transferring knowledge from a convolutional neural network (CNN) to a multi-layer perceptron (MLP) on CIFAR-10. The resulting MLP significantly outperforms the-state-of-the-art methods and it achieves similar performance to the CNN with a single convolutional layer.

Deep Gaussian Processes for Multi-fidelity Modeling

Multi-fidelity methods are prominently used when cheaply-obtained, but possibly biased and noisy, observations must be effectively combined with limited or expensive true data in order to construct reliable models. This arises in both fundamental machine learning procedures such as Bayesian optimization, as well as more practical science and engineering applications. In this paper we develop a novel multi-fidelity model which treats layers of a deep Gaussian process as fidelity levels, and uses a variational inference scheme to propagate uncertainty across them. This allows for capturing nonlinear correlations between fidelities with lower risk of overfitting than existing methods exploiting compositional structure, which are conversely burdened by structural assumptions and constraints. We show that the proposed approach makes substantial improvements in quantifying and propagating uncertainty in multi-fidelity set-ups, which in turn improves their effectiveness in decision making pipelines.

Transferring Knowledge across Learning Processes

In complex transfer learning scenarios new tasks might not be tightly linked to previous tasks. Approaches that transfer information contained only in the final parameters of a source model will therefore struggle. Instead, transfer learning at a higher level of abstraction is needed. We propose Leap, a framework that achieves this by transferring knowledge across learning processes. We associate each task with a manifold on which the training process travels from initialization to final parameters and construct a meta learning objective that minimizes the expected length of this path. Our framework leverages only information obtained during training and can be computed on the fly at negligible cost. We demonstrate that our framework outperforms competing methods, both in meta learning and transfer learning, on a set of computer vision tasks. Finally, we demonstrate that Leap can transfer knowledge across learning processes in demanding Reinforcement Learning environments (Atari) that involve millions of gradient steps.