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Max Jaderberg

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13 papers

2 author rows

NeurIPS Conference 2020 Conference Paper

Real World Games Look Like Spinning Tops

Wojciech M. Czarnecki
Gauthier Gidel
Brendan Tracey
Karl Tuyls
Shayegan Omidshafiei
David Balduzzi
Max Jaderberg

This paper investigates the geometrical properties of real world games (e. g. Tic-Tac-Toe, Go, StarCraft II). We hypothesise that their geometrical structure resembles a spinning top, with the upright axis representing transitive strength, and the radial axis representing the non-transitive dimension, which corresponds to the number of cycles that exist at a particular transitive strength. We prove the existence of this geometry for a wide class of real world games by exposing their temporal nature. Additionally, we show that this unique structure also has consequences for learning - it clarifies why populations of strategies are necessary for training of agents, and how population size relates to the structure of the game. Finally, we empirically validate these claims by using a selection of nine real world two-player zero-sum symmetric games, showing 1) the spinning top structure is revealed and can be easily reconstructed by using a new method of Nash clustering to measure the interaction between transitive and cyclical strategy behaviour, and 2) the effect that population size has on the convergence of learning in these games.

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ICML Conference 2020 Conference Paper

Stabilizing Transformers for Reinforcement Learning

Emilio Parisotto
H. Francis Song
Jack W. Rae
Razvan Pascanu
Çaglar Gülçehre
Siddhant M. Jayakumar
Max Jaderberg
Raphaël Lopez Kaufman

Owing to their ability to both effectively integrate information over long time horizons and scale to massive amounts of data, self-attention architectures have recently shown breakthrough success in natural language processing (NLP). Harnessing the transformer’s ability to process long time horizons of information could provide a similar performance boost in partially observable reinforcement learning (RL) domains, but the large-scale transformers used in NLP have yet to be successfully applied to the RL setting. In this work we demonstrate that the standard transformer architecture is difficult to optimize, which was previously observed in the supervised learning setting but becomes especially pronounced with RL objectives. We propose architectural modifications that substantially improve the stability and learning speed of the original Transformer and XL variant. The proposed architecture, the Gated Transformer-XL (GTrXL), surpasses LSTMs on challenging memory environments and achieves state-of-the-art results on the multi-task DMLab-30 benchmark suite, exceeding the performance of an external memory architecture. We show that the GTrXL has stability and performance that consistently matches or exceeds a competitive LSTM baseline, including on more reactive tasks where memory is less critical.

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ICML Conference 2019 Conference Paper

Open-ended learning in symmetric zero-sum games

David Balduzzi
Marta Garnelo
Yoram Bachrach
Wojciech Czarnecki 0001
Julien Pérolat
Max Jaderberg
Thore Graepel

Zero-sum games such as chess and poker are, abstractly, functions that evaluate pairs of agents, for example labeling them ‘winner’ and ‘loser’. If the game is approximately transitive, then self-play generates sequences of agents of increasing strength. However, nontransitive games, such as rock-paper-scissors, can exhibit strategic cycles, and there is no longer a clear objective – we want agents to increase in strength, but against whom is unclear. In this paper, we introduce a geometric framework for formulating agent objectives in zero-sum games, in order to construct adaptive sequences of objectives that yield open-ended learning. The framework allows us to reason about population performance in nontransitive games, and enables the development of a new algorithm (rectified Nash response, PSRO_rN) that uses game-theoretic niching to construct diverse populations of effective agents, producing a stronger set of agents than existing algorithms. We apply PSRO_rN to two highly nontransitive resource allocation games and find that PSRO_rN consistently outperforms the existing alternatives.

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ICML Conference 2018 Conference Paper

Mix & Match Agent Curricula for Reinforcement Learning

Wojciech Czarnecki 0001
Siddhant M. Jayakumar
Max Jaderberg
Leonard Hasenclever
Yee Whye Teh
Nicolas Heess
Simon Osindero
Razvan Pascanu

We introduce Mix and match (M&M) – a training framework designed to facilitate rapid and effective learning in RL agents that would be too slow or too challenging to train otherwise. The key innovation is a procedure that allows us to automatically form a curriculum over agents. Through such a curriculum we can progressively train more complex agents by, effectively, bootstrapping from solutions found by simpler agents. In contradistinction to typical curriculum learning approaches, we do not gradually modify the tasks or environments presented, but instead use a process to gradually alter how the policy is represented internally. We show the broad applicability of our method by demonstrating significant performance gains in three different experimental setups: (1) We train an agent able to control more than 700 actions in a challenging 3D first-person task; using our method to progress through an action-space curriculum we achieve both faster training and better final performance than one obtains using traditional methods. (2) We further show that M&M can be used successfully to progress through a curriculum of architectural variants defining an agents internal state. (3) Finally, we illustrate how a variant of our method can be used to improve agent performance in a multitask setting.

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AAMAS Conference 2018 Conference Paper

Value-Decomposition Networks For Cooperative Multi-Agent Learning Based On Team Reward

Peter Sunehag
Guy Lever
Audrunas Gruslys
Wojciech Marian Czarnecki
Vinicius Zambaldi
Max Jaderberg
Marc Lanctot
Nicolas Sonnerat

We study the problem of cooperative multi-agent reinforcement learning with a single joint reward signal. This class of learning problems is difficult because of the often large combined action and observation spaces. In the fully centralized and decentralized approaches, we find the problem of spurious rewards and a phenomenon we call the “lazy agent” problem, which arises due to partial observability. We address these problems by training individual agents with a novel value-decomposition network architecture, which learns to decompose the team value function into agent-wise value functions.

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ICML Conference 2017 Conference Paper

Decoupled Neural Interfaces using Synthetic Gradients

Max Jaderberg
Wojciech Czarnecki 0001
Simon Osindero
Oriol Vinyals
Alex Graves
David Silver 0001
Koray Kavukcuoglu

Training directed neural networks typically requires forward-propagating data through a computation graph, followed by backpropagating error signal, to produce weight updates. All layers, or more generally, modules, of the network are therefore locked, in the sense that they must wait for the remainder of the network to execute forwards and propagate error backwards before they can be updated. In this work we break this constraint by decoupling modules by introducing a model of the future computation of the network graph. These models predict what the result of the modelled subgraph will produce using only local information. In particular we focus on modelling error gradients: by using the modelled synthetic gradient in place of true backpropagated error gradients we decouple subgraphs, and can update them independently and asynchronously i. e. we realise decoupled neural interfaces. We show results for feed-forward models, where every layer is trained asynchronously, recurrent neural networks (RNNs) where predicting one’s future gradient extends the time over which the RNN can effectively model, and also a hierarchical RNN system with ticking at different timescales. Finally, we demonstrate that in addition to predicting gradients, the same framework can be used to predict inputs, resulting in models which are decoupled in both the forward and backwards pass – amounting to independent networks which co-learn such that they can be composed into a single functioning corporation.

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ICML Conference 2017 Conference Paper

FeUdal Networks for Hierarchical Reinforcement Learning

Alexander Sasha Vezhnevets
Simon Osindero
Tom Schaul
Nicolas Heess
Max Jaderberg
David Silver 0001
Koray Kavukcuoglu

We introduce FeUdal Networks (FuNs): a novel architecture for hierarchical reinforcement learning. Our approach is inspired by the feudal reinforcement learning proposal of Dayan and Hinton, and gains power and efficacy by decoupling end-to-end learning across multiple levels – allowing it to utilise different resolutions of time. Our framework employs a Manager module and a Worker module. The Manager operates at a slower time scale and sets abstract goals which are conveyed to and enacted by the Worker. The Worker generates primitive actions at every tick of the environment. The decoupled structure of FuN conveys several benefits – in addition to facilitating very long timescale credit assignment it also encourages the emergence of sub-policies associated with different goals set by the Manager. These properties allow FuN to dramatically outperform a strong baseline agent on tasks that involve long-term credit assignment or memorisation.

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ICLR Conference 2017 Conference Paper

Reinforcement Learning with Unsupervised Auxiliary Tasks

Max Jaderberg
Volodymyr Mnih
Wojciech Czarnecki 0001
Tom Schaul
Joel Z. Leibo
David Silver 0001
Koray Kavukcuoglu

Deep reinforcement learning agents have achieved state-of-the-art results by directly maximising cumulative reward. However, environments contain a much wider variety of possible training signals. In this paper, we introduce an agent that also maximises many other pseudo-reward functions simultaneously by reinforcement learning. All of these tasks share a common representation that, like unsupervised learning, continues to develop in the absence of extrinsic rewards. We also introduce a novel mechanism for focusing this representation upon extrinsic rewards, so that learning can rapidly adapt to the most relevant aspects of the actual task. Our agent significantly outperforms the previous state-of-the-art on Atari, averaging 880\% expert human performance, and a challenging suite of first-person, three-dimensional \emph{Labyrinth} tasks leading to a mean speedup in learning of 10$\times$ and averaging 87\% expert human performance on Labyrinth.

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NeurIPS Conference 2017 Conference Paper

Sobolev Training for Neural Networks

Wojciech Czarnecki
Simon Osindero
Max Jaderberg
Grzegorz Swirszcz
Razvan Pascanu

At the heart of deep learning we aim to use neural networks as function approximators - training them to produce outputs from inputs in emulation of a ground truth function or data creation process. In many cases we only have access to input-output pairs from the ground truth, however it is becoming more common to have access to derivatives of the target output with respect to the input -- for example when the ground truth function is itself a neural network such as in network compression or distillation. Generally these target derivatives are not computed, or are ignored. This paper introduces Sobolev Training for neural networks, which is a method for incorporating these target derivatives in addition the to target values while training. By optimising neural networks to not only approximate the function’s outputs but also the function’s derivatives we encode additional information about the target function within the parameters of the neural network. Thereby we can improve the quality of our predictors, as well as the data-efficiency and generalization capabilities of our learned function approximation. We provide theoretical justifications for such an approach as well as examples of empirical evidence on three distinct domains: regression on classical optimisation datasets, distilling policies of an agent playing Atari, and on large-scale applications of synthetic gradients. In all three domains the use of Sobolev Training, employing target derivatives in addition to target values, results in models with higher accuracy and stronger generalisation.

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ICML Conference 2017 Conference Paper

Understanding Synthetic Gradients and Decoupled Neural Interfaces

Wojciech Czarnecki 0001
Grzegorz Swirszcz
Max Jaderberg
Simon Osindero
Oriol Vinyals
Koray Kavukcuoglu

When training neural networks, the use of Synthetic Gradients (SG) allows layers or modules to be trained without update locking – without waiting for a true error gradient to be backpropagated – resulting in Decoupled Neural Interfaces (DNIs). This unlocked ability of being able to update parts of a neural network asynchronously and with only local information was demonstrated to work empirically in Jaderberg et al (2016). However, there has been very little demonstration of what changes DNIs and SGs impose from a functional, representational, and learning dynamics point of view. In this paper, we study DNIs through the use of synthetic gradients on feed-forward networks to better understand their behaviour and elucidate their effect on optimisation. We show that the incorporation of SGs does not affect the representational strength of the learning system for a neural network, and prove the convergence of the learning system for linear and deep linear models. On practical problems we investigate the mechanism by which synthetic gradient estimators approximate the true loss, and, surprisingly, how that leads to drastically different layer-wise representations. Finally, we also expose the relationship of using synthetic gradients to other error approximation techniques and find a unifying language for discussion and comparison.

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NeurIPS Conference 2016 Conference Paper

Unsupervised Learning of 3D Structure from Images

Danilo Jimenez Rezende
S. M. Ali Eslami
Shakir Mohamed
Peter Battaglia
Max Jaderberg
Nicolas Heess

A key goal of computer vision is to recover the underlying 3D structure that gives rise to 2D observations of the world. If endowed with 3D understanding, agents can abstract away from the complexity of the rendering process to form stable, disentangled representations of scene elements. In this paper we learn strong deep generative models of 3D structures, and recover these structures from 2D images via probabilistic inference. We demonstrate high-quality samples and report log-likelihoods on several datasets, including ShapeNet, and establish the first benchmarks in the literature. We also show how these models and their inference networks can be trained jointly, end-to-end, and directly from 2D images without any use of ground-truth 3D labels. This demonstrates for the first time the feasibility of learning to infer 3D representations of the world in a purely unsupervised manner.

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ICLR Conference 2015 Conference Paper

Deep Structured Output Learning for Unconstrained Text Recognition

Max Jaderberg
Karen Simonyan
Andrea Vedaldi
Andrew Zisserman

We develop a representation suitable for the unconstrained recognition of words in natural images: the general case of no fixed lexicon and unknown length. To this end we propose a convolutional neural network (CNN) based architecture which incorporates a Conditional Random Field (CRF) graphical model, taking the whole word image as a single input. The unaries of the CRF are provided by a CNN that predicts characters at each position of the output, while higher order terms are provided by another CNN that detects the presence of N-grams. We show that this entire model (CRF, character predictor, N-gram predictor) can be jointly optimised by back-propagating the structured output loss, essentially requiring the system to perform multi-task learning, and training uses purely synthetically generated data. The resulting model is a more accurate system on standard real-world text recognition benchmarks than character prediction alone, setting a benchmark for systems that have not been trained on a particular lexicon. In addition, our model achieves state-of-the-art accuracy in lexicon-constrained scenarios, without being specifically modelled for constrained recognition. To test the generalisation of our model, we also perform experiments with random alpha-numeric strings to evaluate the method when no visual language model is applicable.

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NeurIPS Conference 2015 Conference Paper

Spatial Transformer Networks

Max Jaderberg
Karen Simonyan
Andrew Zisserman
Koray Kavukcuoglu

Convolutional Neural Networks define an exceptionallypowerful class of model, but are still limited by the lack of abilityto be spatially invariant to the input data in a computationally and parameterefficient manner. In this work we introduce a new learnable module, theSpatial Transformer, which explicitly allows the spatial manipulation ofdata within the network. This differentiable module can be insertedinto existing convolutional architectures, giving neural networks the ability toactively spatially transform feature maps, conditional on the feature map itself, without any extra training supervision or modification to the optimisation process. We show that the useof spatial transformers results in models which learn invariance to translation, scale, rotation and more generic warping, resulting in state-of-the-artperformance on several benchmarks, and for a numberof classes of transformations.

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