Pascal Vincent

Stochastic Hamiltonian Gradient Methods for Smooth Games

The success of adversarial formulations in machine learning has brought renewed motivation for smooth games. In this work, we focus on the c… (see more)lass of stochastic Hamiltonian methods and provide the first convergence guarantees for certain classes of stochastic smooth games. We propose a novel unbiased estimator for the stochastic Hamiltonian gradient descent (SHGD) and highlight its benefits. Using tools from the optimization literature we show that SHGD converges linearly to the neighbourhood of a stationary point. To guarantee convergence to the exact solution, we analyze SHGD with a decreasing step-size and we also present the first stochastic variance reduced Hamiltonian method. Our results provide the first global non-asymptotic last-iterate convergence guarantees for the class of stochastic unconstrained bilinear games and for the more general class of stochastic games that satisfy a "sufficiently bilinear" condition, notably including some non-convex non-concave problems. We supplement our analysis with experiments on stochastic bilinear and sufficiently bilinear games, where our theory is shown to be tight, and on simple adversarial machine learning formulations.

2020-11-20

Proceedings of the 37th International Conference on Machine Learning (published)

doi.org

proceedings.mlr.press

Randomized Value Functions via Multiplicative Normalizing Flows

Randomized value functions offer a promising approach towards the challenge of efficient exploration in complex environments with high dimen… (see more)sional state and action spaces. Unlike traditional point estimate methods, randomized value functions maintain a posterior distribution over action-space values. This prevents the agent's behavior policy from prematurely exploiting early estimates and falling into local optima. In this work, we leverage recent advances in variational Bayesian neural networks and combine these with traditional Deep Q-Networks (DQN) and Deep Deterministic Policy Gradient (DDPG) to achieve randomized value functions for high-dimensional domains. In particular, we augment DQN and DDPG with multiplicative normalizing flows in order to track a rich approximate posterior distribution over the parameters of the value function. This allows the agent to perform approximate Thompson sampling in a computationally efficient manner via stochastic gradient methods. We demonstrate the benefits of our approach through an empirical comparison in high dimensional environments.

2020-08-05

Conference on Uncertainty in Artificial Intelligence (published)

doi.org

proceedings.mlr.press

SVRG for Policy Evaluation with Fewer Gradient Evaluations

Stochastic variance-reduced gradient (SVRG) is an optimization method originally designed for tackling machine learning problems with a fini… (see more)te sum structure. SVRG was later shown to work for policy evaluation, a problem in reinforcement learning in which one aims to estimate the value function of a given policy. SVRG makes use of gradient estimates at two scales. At the slower scale, SVRG computes a full gradient over the whole dataset, which could lead to prohibitive computation costs. In this work, we show that two variants of SVRG for policy evaluation could significantly diminish the number of gradient calculations while preserving a linear convergence speed. More importantly, our theoretical result implies that one does not need to use the entire dataset in every epoch of SVRG when it is applied to policy evaluation with linear function approximation. Our experiments demonstrate large computational savings provided by the proposed methods.

2020-07-10

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

doi.org

arxiv.org

Stochastic Neural Network with Kronecker Flow

Chin-wei Huang

Ahmed Touati

Pascal Vincent

Gintare Karolina Dziugaite

Alexandre Lacoste

Aaron Courville

Recent advances in variational inference enable the modelling of highly structured joint distributions, but are limited in their capacity to… (see more) scale to the high-dimensional setting of stochastic neural networks. This limitation motivates a need for scalable parameterizations of the noise generation process, in a manner that adequately captures the dependencies among the various parameters. In this work, we address this need and present the Kronecker Flow, a generalization of the Kronecker product to invertible mappings designed for stochastic neural networks. We apply our method to variational Bayesian neural networks on predictive tasks, PAC-Bayes generalization bound estimation, and approximate Thompson sampling in contextual bandits. In all setups, our methods prove to be competitive with existing methods and better than the baselines.

2020-06-02

Artificial Intelligence and Statistics (published)

doi.org

proceedings.mlr.press

An Empirical Study of Batch Normalization and Group Normalization in Conditional Computation

Vincent Michalski

Vikram Voleti

Samira Ebrahimi Kahou

Anthony Ortiz

Pascal Vincent

Chris Pal

Doina Precup

Batch normalization has been widely used to improve optimization in deep neural networks. While the uncertainty in batch statistics can act … (see more)as a regularizer, using these dataset statistics specific to the training set impairs generalization in certain tasks. Recently, alternative methods for normalizing feature activations in neural networks have been proposed. Among them, group normalization has been shown to yield similar, in some domains even superior performance to batch normalization. All these methods utilize a learned affine transformation after the normalization operation to increase representational power. Methods used in conditional computation define the parameters of these transformations as learnable functions of conditioning information. In this work, we study whether and where the conditional formulation of group normalization can improve generalization compared to conditional batch normalization. We evaluate performances on the tasks of visual question answering, few-shot learning, and conditional image generation.

2018-12-31

arXiv (preprint)

doi.org

arxiv.org

Convergent Tree Backup and Retrace with Function Approximation

Off-policy learning is key to scaling up reinforcement learning as it allows to learn about a target policy from the experience generated by… (see more) a different behavior policy. Unfortunately, it has been challenging to combine off-policy learning with function approximation and multi-step bootstrapping in a way that leads to both stable and efficient algorithms. In this work, we show that the \textsc{Tree Backup} and \textsc{Retrace} algorithms are unstable with linear function approximation, both in theory and in practice with specific examples. Based on our analysis, we then derive stable and efficient gradient-based algorithms using a quadratic convex-concave saddle-point formulation. By exploiting the problem structure proper to these algorithms, we are able to provide convergence guarantees and finite-sample bounds. The applicability of our new analysis also goes beyond \textsc{Tree Backup} and \textsc{Retrace} and allows us to provide new convergence rates for the GTD and GTD2 algorithms without having recourse to projections or Polyak averaging.

2018-07-02

Proceedings of the 35th International Conference on Machine Learning (published)

doi.org

proceedings.mlr.press

Learning to Compute Word Embeddings on the Fly

Dzmitry Bahdanau

Tom Bosc

Stanisław Jastrzębski

Edward Grefenstette

Pascal Vincent

Yoshua Bengio

Words in natural language follow a Zipfian distribution whereby some words are frequent but most are rare. Learning representations for word… (see more)s in the "long tail" of this distribution requires enormous amounts of data. Representations of rare words trained directly on end tasks are usually poor, requiring us to pre-train embeddings on external data, or treat all rare words as out-of-vocabulary words with a unique representation. We provide a method for predicting embeddings of rare words on the fly from small amounts of auxiliary data with a network trained end-to-end for the downstream task. We show that this improves results against baselines where embeddings are trained on the end task for reading comprehension, recognizing textual entailment and language modeling.

2016-12-31

Computing Research Repository (published)

doi.org

openreview.net

Hierarchical Memory Networks

Gerald Tesauro

Memory networks are neural networks with an explicit memory component that can be both read and written to by the network. The memory is oft… (see more)en addressed in a soft way using a softmax function, making end-to-end training with backpropagation possible. However, this is not computationally scalable for applications which require the network to read from extremely large memories. On the other hand, it is well known that hard attention mechanisms based on reinforcement learning are challenging to train successfully. In this paper, we explore a form of hierarchical memory network, which can be considered as a hybrid between hard and soft attention memory networks. The memory is organized in a hierarchical structure such that reading from it is done with less computation than soft attention over a flat memory, while also being easier to train than hard attention over a flat memory. Specifically, we propose to incorporate Maximum Inner Product Search (MIPS) in the training and inference procedures for our hierarchical memory network. We explore the use of various state-of-the art approximate MIPS techniques and report results on SimpleQuestions, a challenging large scale factoid question answering task.

2015-12-31

CoRR (published)

doi.org

arxiv.org

Theano: A Python framework for fast computation of mathematical expressions

The Theano Development Team

Rami Al-Rfou

Guillaume Alain

Amjad Almahairi

Christof Angermueller

Dzmitry Bahdanau

Nicolas Ballas

Frédéric Bastien

Justin Bayer

Anatoly Belikov

Alexander Belopolsky

Josh Bleecher Snyder

Nicolas Boulanger-Lewandowski

Xavier Bouthillier

Alexandre De Brébisson … (see 93 more)

Pierre-Luc Carrier

Paul Christiano

Myriam Côté

Yann N. Dauphin

Julien Demouth

Sander Dieleman

Samira Ebrahimi Kahou

Ziye Fan

Matt Graham

Balázs Hidasi

Arjun Jain

Kai Jia

Mikhail Korobov

Vivek Kulkarni

Alex Lamb

Pascal Lamblin

Eric Larsen

César Laurent

Sean Lee

Simon Lefrancois

Simon Lemieux

Nicholas Léonard

Zhouhan Lin

Jesse A. Livezey

Cory Lorenz

Jeremiah Lowin

Qianli Ma

Pierre-Antoine Manzagol

Robert T. McGibbon

Mehdi Mirza

Alberto Orlandi

Christopher Pal

Razvan Pascanu

Mohammad Pezeshki

Colin Raffel

Daniel Renshaw

Matthew Rocklin

Adriana Romero

Markus Roth

Peter Sadowski

John Salvatier

François Savard

Jan Schlüter

John Schulman

Gabriel Schwartz

Iulian Vlad Serban

Dmitriy Serdyuk

Samira Shabanian

Etienne Simon

Sigurd Spieckermann

S. Ramana Subramanyam

Gijs van Tulder

Sebastian Urban

Dustin J. Webb

Matthew Willson

Lijun Xue

Theano is a Python library that allows to define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays efficie… (see more)ntly. Since its introduction, it has been one of the most used CPU and GPU mathematical compilers - especially in the machine learning community - and has shown steady performance improvements. Theano is being actively and continuously developed since 2008, multiple frameworks have been built on top of it and it has been used to produce many state-of-the-art machine learning models. The present article is structured as follows. Section I provides an overview of the Theano software and its community. Section II presents the principal features of Theano and how to use them, and compares them with other similar projects. Section III focuses on recently-introduced functionalities and improvements. Section IV compares the performance of Theano against Torch7 and TensorFlow on several machine learning models. Section V discusses current limitations of Theano and potential ways of improving it.

2015-12-31

Computing Research Repository (published)

doi.org

arxiv.org

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Pascal Vincent

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Pascal Vincent

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