arXiv subjects

Clare Lyle

Publications and source records attributed to Clare Lyle.

44 records · Page 3Linked to original sources

arXiv2021

Unpacking Information Bottlenecks: Unifying Information-Theoretic Objectives in Deep Learning

The Information Bottleneck principle offers both a mechanism to explain how deep neural networks train and generalize, as well as a regularized objective with which to train models. However, multiple competing objectives are proposed in the literature, and the information-theoretic quantities used in these objectives are difficult to compute for large deep neural networks, which in turn limits their use as a training objective. In this work, we review these quantities and compare and unify previously proposed objectives, which allows us to develop surrogate objectives more friendly to optimization without relying on cumbersome tools such as density estimation. We find that these surrogate objectives allow us to apply the information bottleneck to modern neural network architectures. We demonstrate our insights on MNIST, CIFAR-10 and Imagenette with modern DNN architectures (ResNets).

cs.LG↗

arXiv2020

A Bayesian Perspective on Training Speed and Model Selection

We take a Bayesian perspective to illustrate a connection between training speed and the marginal likelihood in linear models. This provides two major insights: first, that a measure of a model's training speed can be used to estimate its marginal likelihood. Second, that this measure, under certain conditions, predicts the relative weighting of models in linear model combinations trained to minimize a regression loss. We verify our results in model selection tasks for linear models and for the infinite-width limit of deep neural networks. We further provide encouraging empirical evidence that the intuition developed in these settings also holds for deep neural networks trained with stochastic gradient descent. Our results suggest a promising new direction towards explaining why neural networks trained with stochastic gradient descent are biased towards functions that generalize well.

cs.LG↗

arXiv2020

Invariant Causal Prediction for Block MDPs

Generalization across environments is critical to the successful application of reinforcement learning algorithms to real-world challenges. In this paper, we consider the problem of learning abstractions that generalize in block MDPs, families of environments with a shared latent state space and dynamics structure over that latent space, but varying observations. We leverage tools from causal inference to propose a method of invariant prediction to learn model-irrelevance state abstractions (MISA) that generalize to novel observations in the multi-environment setting. We prove that for certain classes of environments, this approach outputs with high probability a state abstraction corresponding to the causal feature set with respect to the return. We further provide more general bounds on model error and generalization error in the multi-environment setting, in the process showing a connection between causal variable selection and the state abstraction framework for MDPs. We give empirical evidence that our methods work in both linear and nonlinear settings, attaining improved generalization over single- and multi-task baselines.

cs.LG↗

arXiv2020

On the Benefits of Invariance in Neural Networks

Many real world data analysis problems exhibit invariant structure, and models that take advantage of this structure have shown impressive empirical performance, particularly in deep learning. While the literature contains a variety of methods to incorporate invariance into models, theoretical understanding is poor and there is no way to assess when one method should be preferred over another. In this work, we analyze the benefits and limitations of two widely used approaches in deep learning in the presence of invariance: data augmentation and feature averaging. We prove that training with data augmentation leads to better estimates of risk and gradients thereof, and we provide a PAC-Bayes generalization bound for models trained with data augmentation. We also show that compared to data augmentation, feature averaging reduces generalization error when used with convex losses, and tightens PAC-Bayes bounds. We provide empirical support of these theoretical results, including a demonstration of why generalization may not improve by training with data augmentation: the `learned invariance' fails outside of the training distribution.

cs.LG↗

arXiv2019

A Geometric Perspective on Optimal Representations for Reinforcement Learning

We propose a new perspective on representation learning in reinforcement learning based on geometric properties of the space of value functions. We leverage this perspective to provide formal evidence regarding the usefulness of value functions as auxiliary tasks. Our formulation considers adapting the representation to minimize the (linear) approximation of the value function of all stationary policies for a given environment. We show that this optimization reduces to making accurate predictions regarding a special class of value functions which we call adversarial value functions (AVFs). We demonstrate that using value functions as auxiliary tasks corresponds to an expected-error relaxation of our formulation, with AVFs a natural candidate, and identify a close relationship with proto-value functions (Mahadevan, 2005). We highlight characteristics of AVFs and their usefulness as auxiliary tasks in a series of experiments on the four-room domain.

cs.LG↗

arXiv2019

A Comparative Analysis of Expected and Distributional Reinforcement Learning

Since their introduction a year ago, distributional approaches to reinforcement learning (distributional RL) have produced strong results relative to the standard approach which models expected values (expected RL). However, aside from convergence guarantees, there have been few theoretical results investigating the reasons behind the improvements distributional RL provides. In this paper we begin the investigation into this fundamental question by analyzing the differences in the tabular, linear approximation, and non-linear approximation settings. We prove that in many realizations of the tabular and linear approximation settings, distributional RL behaves exactly the same as expected RL. In cases where the two methods behave differently, distributional RL can in fact hurt performance when it does not induce identical behaviour. We then continue with an empirical analysis comparing distributional and expected RL methods in control settings with non-linear approximators to tease apart where the improvements from distributional RL methods are coming from.

cs.LG↗

arXiv2018

GAN Q-learning

Distributional reinforcement learning (distributional RL) has seen empirical success in complex Markov Decision Processes (MDPs) in the setting of nonlinear function approximation. However, there are many different ways in which one can leverage the distributional approach to reinforcement learning. In this paper, we propose GAN Q-learning, a novel distributional RL method based on generative adversarial networks (GANs) and analyze its performance in simple tabular environments, as well as OpenAI Gym. We empirically show that our algorithm leverages the flexibility and blackbox approach of deep learning models while providing a viable alternative to traditional methods.

stat.ML↗

arXiv2016

Some Counterexamples for Compatible Triangulations

We consider the conjecture by Aichholzer, Aurenhammer, Hurtado, and Krasser that any two points sets with the same cardinality and the same size convex hull can be triangulated in the "same" way, more precisely via \emph{compatible triangulations}. We show counterexamples to various strengthened versions of this conjecture.

cs.CG↗