Kenji Kawaguchi

Discrete Compositional Representations as an Abstraction for Goal Conditioned Reinforcement Learning

Hongyu Zang

Xin Li

Romain Laroche

Remi Tachet des Combes

Goal-conditioned reinforcement learning (RL) is a promising direction for training agents that are capable of solving multiple tasks and rea… (see more)ch a diverse set of objectives. How to \textit{specify} and \textit{ground} these goals in such a way that we can both reliably reach goals during training as well as generalize to new goals during evaluation remains an open area of research. Defining goals in the space of noisy, high-dimensional sensory inputs is one possibility, yet this poses a challenge for training goal-conditioned agents, or even for generalization to novel goals. We propose to address this by learning compositional representations of goals and processing the resulting representation via a discretization bottleneck, for coarser specification of goals, through an approach we call DGRL. We show that discretizing outputs from goal encoders through a bottleneck can work well in goal-conditioned RL setups, by experimentally evaluating this method on tasks ranging from maze environments to complex robotic navigation and manipulation tasks. Additionally, we show a theoretical result which bounds the expected return for goals not observed during training, while still allowing for specifying goals with expressive combinatorial structure.

openreview.net

Discrete-Valued Neural Communication in Structured Architectures Enhances Generalization

Dianbo Liu

Alex Lamb

Anirudh Goyal

Chen Sun

Michael Curtis Mozer

In this appendix, as a complementary to Theorems 1–2, we provide additional theorems, Theorems 3–4, which further illustrate the two adv… (see more)antages of the discretization process by considering an abstract model with the discretization bottleneck. For the advantage on the sensitivity, the error due to potential noise and perturbation without discretization — the third term ξ(w, r′,M′, d) > 0 in Theorem 4 — is shown to be minimized to zero with discretization in Theorems 3. For the second advantage, the underlying dimensionality of N(M′,d′)(r,H) + ln(N(M,d)(r,Θ)/δ) without discretization (in the bound of Theorem 4) is proven to be reduced to the typically much smaller underlying dimensionality of L + ln(N(M,d)(r, E ×Θ) with discretization in Theorems 3. Here, for any metric space (M, d) and subset M ⊆ M, the r-converging number of M is defined by N(M,d)(r,M) = min { |C| : C ⊆ M,M ⊆ ∪c∈CB(M,d)[c, r]} where the (closed) ball of radius r at centered at c is denoted by B(M,d)[c, r] = {x ∈M : d(x, c) ≤ r}. See Appendix C.1 for a simple comparison between the bound of Theorem 3 and that of Theorem 4 when the metric spaces (M, d) and (M′, d′) are chosen to be Euclidean spaces.

Discrete-Valued Neural Communication

Dianbo Liu

Alex Lamb

Anirudh Goyal

Chen Sun

Michael Curtis Mozer

Deep learning has advanced from fully connected architectures to structured models organized into components, e.g., the transformer composed… (see more) of positional elements, modular architectures divided into slots, and graph neural nets made up of nodes. In structured models, an interesting question is how to conduct dynamic and possibly sparse communication among the separate components. Here, we explore the hypothesis that restricting the transmitted information among components to discrete representations is a beneficial bottleneck. The motivating intuition is human language in which communication occurs through discrete symbols. Even though individuals have different understandings of what a"cat"is based on their specific experiences, the shared discrete token makes it possible for communication among individuals to be unimpeded by individual differences in internal representation. To discretize the values of concepts dynamically communicated among specialist components, we extend the quantization mechanism from the Vector-Quantized Variational Autoencoder to multi-headed discretization with shared codebooks and use it for discrete-valued neural communication (DVNC). Our experiments show that DVNC substantially improves systematic generalization in a variety of architectures -- transformers, modular architectures, and graph neural networks. We also show that the DVNC is robust to the choice of hyperparameters, making the method very useful in practice. Moreover, we establish a theoretical justification of our discretization process, proving that it has the ability to increase noise robustness and reduce the underlying dimensionality of the model.

openreview.net

GraphMix: Improved Training of GNNs for Semi-Supervised Learning

Juho Kannala

We present GraphMix, a regularization method for Graph Neural Network based semi-supervised object classification, whereby we propose to tra… (see more)in a fully-connected network jointly with the graph neural network via parameter sharing and interpolation-based regularization. Further, we provide a theoretical analysis of how GraphMix improves the generalization bounds of the underlying graph neural network, without making any assumptions about the "aggregation" layer or the depth of the graph neural networks. We experimentally validate this analysis by applying GraphMix to various architectures such as Graph Convolutional Networks, Graph Attention Networks and Graph-U-Net. Despite its simplicity, we demonstrate that GraphMix can consistently improve or closely match state-of-the-art performance using even simpler architectures such as Graph Convolutional Networks, across three established graph benchmarks: Cora, Citeseer and Pubmed citation network datasets, as well as three newly proposed datasets: Cora-Full, Co-author-CS and Co-author-Physics.

2020-10-11

AAAI Conference on Artificial Intelligence (published)

Depth with Nonlinearity Creates No Bad Local Minima in ResNets

2019-10-01

Neural Networks (published)

Interpolation Consistency Training for Semi-Supervised Learning

Juho Kannala

David Lopez-Paz

Arno Solin

2019-08-10

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence (published)

Generalization in Machine Learning via Analytical Learning Theory

This paper introduces a novel measure-theoretic theory for machine learning that does not require statistical assumptions. Based on this the… (see more)ory, a new regularization method in deep learning is derived and shown to outperform previous methods in CIFAR-10, CIFAR-100, and SVHN. Moreover, the proposed theory provides a theoretical basis for a family of practically successful regularization methods in deep learning. We discuss several consequences of our results on one-shot learning, representation learning, deep learning, and curriculum learning. Unlike statistical learning theory, the proposed learning theory analyzes each problem instance individually via measure theory, rather than a set of problem instances via statistics. As a result, it provides different types of results and insights when compared to statistical learning theory.

2018-02-21

arXiv.org (preprint)

dblp.uni-trier.de

Towards Understanding Generalization via Analytical Learning Theory

This paper introduces a novel measure-theoretic theory for machine learning that does not require statistical assumptions. Based on this the… (see more)ory, a new regularization method in deep learning is derived and shown to outperform previous methods in CIFAR-10, CIFAR-100, and SVHN. Moreover, the proposed theory provides a theoretical basis for a family of practically successful regularization methods in deep learning. We discuss several consequences of our results on one-shot learning, representation learning, deep learning, and curriculum learning. Unlike statistical learning theory, the proposed learning theory analyzes each problem instance individually via measure theory, rather than a set of problem instances via statistics. As a result, it provides different types of results and insights when compared to statistical learning theory.

2018-02-21

ArXiv (preprint)