arXiv subjects

Anirudh Goyal

Publications and source records attributed to Anirudh Goyal.

At least 109 records · Page 6Linked to original sources

arXiv2019

Learning the Arrow of Time

We humans seem to have an innate understanding of the asymmetric progression of time, which we use to efficiently and safely perceive and manipulate our environment. Drawing inspiration from that, we address the problem of learning an arrow of time in a Markov (Decision) Process. We illustrate how a learned arrow of time can capture meaningful information about the environment, which in turn can be used to measure reachability, detect side-effects and to obtain an intrinsic reward signal. We show empirical results on a selection of discrete and continuous environments, and demonstrate for a class of stochastic processes that the learned arrow of time agrees reasonably well with a known notion of an arrow of time given by the celebrated Jordan-Kinderlehrer-Otto result.

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arXiv2019

Reinforcement Learning with Competitive Ensembles of Information-Constrained Primitives

Reinforcement learning agents that operate in diverse and complex environments can benefit from the structured decomposition of their behavior. Often, this is addressed in the context of hierarchical reinforcement learning, where the aim is to decompose a policy into lower-level primitives or options, and a higher-level meta-policy that triggers the appropriate behaviors for a given situation. However, the meta-policy must still produce appropriate decisions in all states. In this work, we propose a policy design that decomposes into primitives, similarly to hierarchical reinforcement learning, but without a high-level meta-policy. Instead, each primitive can decide for themselves whether they wish to act in the current state. We use an information-theoretic mechanism for enabling this decentralized decision: each primitive chooses how much information it needs about the current state to make a decision and the primitive that requests the most information about the current state acts in the world. The primitives are regularized to use as little information as possible, which leads to natural competition and specialization. We experimentally demonstrate that this policy architecture improves over both flat and hierarchical policies in terms of generalization.

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arXiv2019

Learning Powerful Policies by Using Consistent Dynamics Model

Model-based Reinforcement Learning approaches have the promise of being sample efficient. Much of the progress in learning dynamics models in RL has been made by learning models via supervised learning. But traditional model-based approaches lead to `compounding errors' when the model is unrolled step by step. Essentially, the state transitions that the learner predicts (by unrolling the model for multiple steps) and the state transitions that the learner experiences (by acting in the environment) may not be consistent. There is enough evidence that humans build a model of the environment, not only by observing the environment but also by interacting with the environment. Interaction with the environment allows humans to carry out experiments: taking actions that help uncover true causal relationships which can be used for building better dynamics models. Analogously, we would expect such interactions to be helpful for a learning agent while learning to model the environment dynamics. In this paper, we build upon this intuition by using an auxiliary cost function to ensure consistency between what the agent observes (by acting in the real world) and what it imagines (by acting in the `learned' world). We consider several tasks - Mujoco based control tasks and Atari games - and show that the proposed approach helps to train powerful policies and better dynamics models.

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arXiv2019

Maximum Entropy Generators for Energy-Based Models

Maximum likelihood estimation of energy-based models is a challenging problem due to the intractability of the log-likelihood gradient. In this work, we propose learning both the energy function and an amortized approximate sampling mechanism using a neural generator network, which provides an efficient approximation of the log-likelihood gradient. The resulting objective requires maximizing entropy of the generated samples, which we perform using recently proposed nonparametric mutual information estimators. Finally, to stabilize the resulting adversarial game, we use a zero-centered gradient penalty derived as a necessary condition from the score matching literature. The proposed technique can generate sharp images with Inception and FID scores competitive with recent GAN techniques, does not suffer from mode collapse, and is competitive with state-of-the-art anomaly detection techniques.

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arXiv2019

State-Reification Networks: Improving Generalization by Modeling the Distribution of Hidden Representations

Machine learning promises methods that generalize well from finite labeled data. However, the brittleness of existing neural net approaches is revealed by notable failures, such as the existence of adversarial examples that are misclassified despite being nearly identical to a training example, or the inability of recurrent sequence-processing nets to stay on track without teacher forcing. We introduce a method, which we refer to as \emph{state reification}, that involves modeling the distribution of hidden states over the training data and then projecting hidden states observed during testing toward this distribution. Our intuition is that if the network can remain in a familiar manifold of hidden space, subsequent layers of the net should be well trained to respond appropriately. We show that this state-reification method helps neural nets to generalize better, especially when labeled data are sparse, and also helps overcome the challenge of achieving robust generalization with adversarial training.

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arXiv2019

Learning Dynamics Model in Reinforcement Learning by Incorporating the Long Term Future

In model-based reinforcement learning, the agent interleaves between model learning and planning. These two components are inextricably intertwined. If the model is not able to provide sensible long-term prediction, the executed planner would exploit model flaws, which can yield catastrophic failures. This paper focuses on building a model that reasons about the long-term future and demonstrates how to use this for efficient planning and exploration. To this end, we build a latent-variable autoregressive model by leveraging recent ideas in variational inference. We argue that forcing latent variables to carry future information through an auxiliary task substantially improves long-term predictions. Moreover, by planning in the latent space, the planner's solution is ensured to be within regions where the model is valid. An exploration strategy can be devised by searching for unlikely trajectories under the model. Our method achieves higher reward faster compared to baselines on a variety of tasks and environments in both the imitation learning and model-based reinforcement learning settings.

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arXiv2019

A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms

We propose to meta-learn causal structures based on how fast a learner adapts to new distributions arising from sparse distributional changes, e.g. due to interventions, actions of agents and other sources of non-stationarities. We show that under this assumption, the correct causal structural choices lead to faster adaptation to modified distributions because the changes are concentrated in one or just a few mechanisms when the learned knowledge is modularized appropriately. This leads to sparse expected gradients and a lower effective number of degrees of freedom needing to be relearned while adapting to the change. It motivates using the speed of adaptation to a modified distribution as a meta-learning objective. We demonstrate how this can be used to determine the cause-effect relationship between two observed variables. The distributional changes do not need to correspond to standard interventions (clamping a variable), and the learner has no direct knowledge of these interventions. We show that causal structures can be parameterized via continuous variables and learned end-to-end. We then explore how these ideas could be used to also learn an encoder that would map low-level observed variables to unobserved causal variables leading to faster adaptation out-of-distribution, learning a representation space where one can satisfy the assumptions of independent mechanisms and of small and sparse changes in these mechanisms due to actions and non-stationarities.

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arXiv2019

Recall Traces: Backtracking Models for Efficient Reinforcement Learning

In many environments only a tiny subset of all states yield high reward. In these cases, few of the interactions with the environment provide a relevant learning signal. Hence, we may want to preferentially train on those high-reward states and the probable trajectories leading to them. To this end, we advocate for the use of a backtracking model that predicts the preceding states that terminate at a given high-reward state. We can train a model which, starting from a high value state (or one that is estimated to have high value), predicts and sample for which the (state, action)-tuples may have led to that high value state. These traces of (state, action) pairs, which we refer to as Recall Traces, sampled from this backtracking model starting from a high value state, are informative as they terminate in good states, and hence we can use these traces to improve a policy. We provide a variational interpretation for this idea and a practical algorithm in which the backtracking model samples from an approximate posterior distribution over trajectories which lead to large rewards. Our method improves the sample efficiency of both on- and off-policy RL algorithms across several environments and tasks.

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arXiv2018

Sparse Attentive Backtracking: Temporal CreditAssignment Through Reminding

Learning long-term dependencies in extended temporal sequences requires credit assignment to events far back in the past. The most common method for training recurrent neural networks, back-propagation through time (BPTT), requires credit information to be propagated backwards through every single step of the forward computation, potentially over thousands or millions of time steps. This becomes computationally expensive or even infeasible when used with long sequences. Importantly, biological brains are unlikely to perform such detailed reverse replay over very long sequences of internal states (consider days, months, or years.) However, humans are often reminded of past memories or mental states which are associated with the current mental state. We consider the hypothesis that such memory associations between past and present could be used for credit assignment through arbitrarily long sequences, propagating the credit assigned to the current state to the associated past state. Based on this principle, we study a novel algorithm which only back-propagates through a few of these temporal skip connections, realized by a learned attention mechanism that associates current states with relevant past states. We demonstrate in experiments that our method matches or outperforms regular BPTT and truncated BPTT in tasks involving particularly long-term dependencies, but without requiring the biologically implausible backward replay through the whole history of states. Additionally, we demonstrate that the proposed method transfers to longer sequences significantly better than LSTMs trained with BPTT and LSTMs trained with full self-attention.

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arXiv2018

Generalization of Equilibrium Propagation to Vector Field Dynamics

The biological plausibility of the backpropagation algorithm has long been doubted by neuroscientists. Two major reasons are that neurons would need to send two different types of signal in the forward and backward phases, and that pairs of neurons would need to communicate through symmetric bidirectional connections. We present a simple two-phase learning procedure for fixed point recurrent networks that addresses both these issues. In our model, neurons perform leaky integration and synaptic weights are updated through a local mechanism. Our learning method generalizes Equilibrium Propagation to vector field dynamics, relaxing the requirement of an energy function. As a consequence of this generalization, the algorithm does not compute the true gradient of the objective function, but rather approximates it at a precision which is proven to be directly related to the degree of symmetry of the feedforward and feedback weights. We show experimentally that our algorithm optimizes the objective function.

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arXiv2018

Fortified Networks: Improving the Robustness of Deep Networks by Modeling the Manifold of Hidden Representations

Deep networks have achieved impressive results across a variety of important tasks. However a known weakness is a failure to perform well when evaluated on data which differ from the training distribution, even if these differences are very small, as is the case with adversarial examples. We propose Fortified Networks, a simple transformation of existing networks, which fortifies the hidden layers in a deep network by identifying when the hidden states are off of the data manifold, and maps these hidden states back to parts of the data manifold where the network performs well. Our principal contribution is to show that fortifying these hidden states improves the robustness of deep networks and our experiments (i) demonstrate improved robustness to standard adversarial attacks in both black-box and white-box threat models; (ii) suggest that our improvements are not primarily due to the gradient masking problem and (iii) show the advantage of doing this fortification in the hidden layers instead of the input space.

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arXiv2017

Z-Forcing: Training Stochastic Recurrent Networks

Many efforts have been devoted to training generative latent variable models with autoregressive decoders, such as recurrent neural networks (RNN). Stochastic recurrent models have been successful in capturing the variability observed in natural sequential data such as speech. We unify successful ideas from recently proposed architectures into a stochastic recurrent model: each step in the sequence is associated with a latent variable that is used to condition the recurrent dynamics for future steps. Training is performed with amortized variational inference where the approximate posterior is augmented with a RNN that runs backward through the sequence. In addition to maximizing the variational lower bound, we ease training of the latent variables by adding an auxiliary cost which forces them to reconstruct the state of the backward recurrent network. This provides the latent variables with a task-independent objective that enhances the performance of the overall model. We found this strategy to perform better than alternative approaches such as KL annealing. Although being conceptually simple, our model achieves state-of-the-art results on standard speech benchmarks such as TIMIT and Blizzard and competitive performance on sequential MNIST. Finally, we apply our model to language modeling on the IMDB dataset where the auxiliary cost helps in learning interpretable latent variables. Source Code: \url{https://github.com/anirudh9119/zforcing_nips17}

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arXiv2017

ACtuAL: Actor-Critic Under Adversarial Learning

Generative Adversarial Networks (GANs) are a powerful framework for deep generative modeling. Posed as a two-player minimax problem, GANs are typically trained end-to-end on real-valued data and can be used to train a generator of high-dimensional and realistic images. However, a major limitation of GANs is that training relies on passing gradients from the discriminator through the generator via back-propagation. This makes it fundamentally difficult to train GANs with discrete data, as generation in this case typically involves a non-differentiable function. These difficulties extend to the reinforcement learning setting when the action space is composed of discrete decisions. We address these issues by reframing the GAN framework so that the generator is no longer trained using gradients through the discriminator, but is instead trained using a learned critic in the actor-critic framework with a Temporal Difference (TD) objective. This is a natural fit for sequence modeling and we use it to achieve improvements on language modeling tasks over the standard Teacher-Forcing methods.

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arXiv2017

Variational Walkback: Learning a Transition Operator as a Stochastic Recurrent Net

We propose a novel method to directly learn a stochastic transition operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model whose stationary distribution obeys detailed balance with respect to a parameterized energy function. The energy function is then modified so the model and data distributions match, with no guarantee on the number of steps required for the Markov chain to converge. Moreover, the detailed balance condition is highly restrictive: energy based models corresponding to neural networks must have symmetric weights, unlike biological neural circuits. In contrast, we develop a method for directly learning arbitrarily parameterized transition operators capable of expressing non-equilibrium stationary distributions that violate detailed balance, thereby enabling us to learn more biologically plausible asymmetric neural networks and more general non-energy based dynamical systems. The proposed training objective, which we derive via principled variational methods, encourages the transition operator to "walk back" in multi-step trajectories that start at data-points, as quickly as possible back to the original data points. We present a series of experimental results illustrating the soundness of the proposed approach, Variational Walkback (VW), on the MNIST, CIFAR-10, SVHN and CelebA datasets, demonstrating superior samples compared to earlier attempts to learn a transition operator. We also show that although each rapid training trajectory is limited to a finite but variable number of steps, our transition operator continues to generate good samples well past the length of such trajectories, thereby demonstrating the match of its non-equilibrium stationary distribution to the data distribution. Source Code: http://github.com/anirudh9119/walkback_nips17

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arXiv2017

Sparse Attentive Backtracking: Long-Range Credit Assignment in Recurrent Networks

A major drawback of backpropagation through time (BPTT) is the difficulty of learning long-term dependencies, coming from having to propagate credit information backwards through every single step of the forward computation. This makes BPTT both computationally impractical and biologically implausible. For this reason, full backpropagation through time is rarely used on long sequences, and truncated backpropagation through time is used as a heuristic. However, this usually leads to biased estimates of the gradient in which longer term dependencies are ignored. Addressing this issue, we propose an alternative algorithm, Sparse Attentive Backtracking, which might also be related to principles used by brains to learn long-term dependencies. Sparse Attentive Backtracking learns an attention mechanism over the hidden states of the past and selectively backpropagates through paths with high attention weights. This allows the model to learn long term dependencies while only backtracking for a small number of time steps, not just from the recent past but also from attended relevant past states.

cs.AI↗

arXiv2017

Zoneout: Regularizing RNNs by Randomly Preserving Hidden Activations

We propose zoneout, a novel method for regularizing RNNs. At each timestep, zoneout stochastically forces some hidden units to maintain their previous values. Like dropout, zoneout uses random noise to train a pseudo-ensemble, improving generalization. But by preserving instead of dropping hidden units, gradient information and state information are more readily propagated through time, as in feedforward stochastic depth networks. We perform an empirical investigation of various RNN regularizers, and find that zoneout gives significant performance improvements across tasks. We achieve competitive results with relatively simple models in character- and word-level language modelling on the Penn Treebank and Text8 datasets, and combining with recurrent batch normalization yields state-of-the-art results on permuted sequential MNIST.

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arXiv2017

An Actor-Critic Algorithm for Sequence Prediction

We present an approach to training neural networks to generate sequences using actor-critic methods from reinforcement learning (RL). Current log-likelihood training methods are limited by the discrepancy between their training and testing modes, as models must generate tokens conditioned on their previous guesses rather than the ground-truth tokens. We address this problem by introducing a \textit{critic} network that is trained to predict the value of an output token, given the policy of an \textit{actor} network. This results in a training procedure that is much closer to the test phase, and allows us to directly optimize for a task-specific score such as BLEU. Crucially, since we leverage these techniques in the supervised learning setting rather than the traditional RL setting, we condition the critic network on the ground-truth output. We show that our method leads to improved performance on both a synthetic task, and for German-English machine translation. Our analysis paves the way for such methods to be applied in natural language generation tasks, such as machine translation, caption generation, and dialogue modelling.

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arXiv2016

Professor Forcing: A New Algorithm for Training Recurrent Networks

The Teacher Forcing algorithm trains recurrent networks by supplying observed sequence values as inputs during training and using the network's own one-step-ahead predictions to do multi-step sampling. We introduce the Professor Forcing algorithm, which uses adversarial domain adaptation to encourage the dynamics of the recurrent network to be the same when training the network and when sampling from the network over multiple time steps. We apply Professor Forcing to language modeling, vocal synthesis on raw waveforms, handwriting generation, and image generation. Empirically we find that Professor Forcing acts as a regularizer, improving test likelihood on character level Penn Treebank and sequential MNIST. We also find that the model qualitatively improves samples, especially when sampling for a large number of time steps. This is supported by human evaluation of sample quality. Trade-offs between Professor Forcing and Scheduled Sampling are discussed. We produce T-SNEs showing that Professor Forcing successfully makes the dynamics of the network during training and sampling more similar.

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