Policy gradient methods are a widely used class of model-free reinforcement learning algorithms where a state-dependent baseline is used to reduce gradient estimator variance. Several recent papers extend the baseline to depend on both the state and action and suggest that this significantly reduces variance and improves sample efficiency without introducing bias into the gradient estimates. To better understand this development, we decompose the variance of the policy gradient estimator and numerically show that learned state-action-dependent baselines do not in fact reduce variance over a state-dependent baseline in commonly tested benchmark domains. We confirm this unexpected result by reviewing the open-source code accompanying these prior papers, and show that subtle implementation decisions cause deviations from the methods presented in the papers and explain the source of the previously observed empirical gains. Furthermore, the variance decomposition highlights areas for improvement, which we demonstrate by illustrating a simple change to the typical value function parameterization that can significantly improve performance.
Recent advances in deep reinforcement learning have made significant strides in performance on applications such as Go and Atari games. However, developing practical methods to balance exploration and exploitation in complex domains remains largely unsolved. Thompson Sampling and its extension to reinforcement learning provide an elegant approach to exploration that only requires access to posterior samples of the model. At the same time, advances in approximate Bayesian methods have made posterior approximation for flexible neural network models practical. Thus, it is attractive to consider approximate Bayesian neural networks in a Thompson Sampling framework. To understand the impact of using an approximate posterior on Thompson Sampling, we benchmark well-established and recently developed methods for approximate posterior sampling combined with Thompson Sampling over a series of contextual bandit problems. We found that many approaches that have been successful in the supervised learning setting underperformed in the sequential decision-making scenario. In particular, we highlight the challenge of adapting slowly converging uncertainty estimates to the online setting.
When used as a surrogate objective for maximum likelihood estimation in latent variable models, the evidence lower bound (ELBO) produces state-of-the-art results. Inspired by this, we consider the extension of the ELBO to a family of lower bounds defined by a particle filter's estimator of the marginal likelihood, the filtering variational objectives (FIVOs). FIVOs take the same arguments as the ELBO, but can exploit a model's sequential structure to form tighter bounds. We present results that relate the tightness of FIVO's bound to the variance of the particle filter's estimator by considering the generic case of bounds defined as log-transformed likelihood estimators. Experimentally, we show that training with FIVO results in substantial improvements over training the same model architecture with the ELBO on sequential data.
Learning in models with discrete latent variables is challenging due to high variance gradient estimators. Generally, approaches have relied on control variates to reduce the variance of the REINFORCE estimator. Recent work (Jang et al. 2016, Maddison et al. 2016) has taken a different approach, introducing a continuous relaxation of discrete variables to produce low-variance, but biased, gradient estimates. In this work, we combine the two approaches through a novel control variate that produces low-variance, \emph{unbiased} gradient estimates. Then, we introduce a modification to the continuous relaxation and show that the tightness of the relaxation can be adapted online, removing it as a hyperparameter. We show state-of-the-art variance reduction on several benchmark generative modeling tasks, generally leading to faster convergence to a better final log-likelihood.
There has recently been significant interest in hard attention models for tasks such as object recognition, visual captioning and speech recognition. Hard attention can offer benefits over soft attention such as decreased computational cost, but training hard attention models can be difficult because of the discrete latent variables they introduce. Previous work used REINFORCE and Q-learning to approach these issues, but those methods can provide high-variance gradient estimates and be slow to train. In this paper, we tackle the problem of learning hard attention for a sequential task using variational inference methods, specifically the recently introduced VIMCO and NVIL. Furthermore, we propose a novel baseline that adapts VIMCO to this setting. We demonstrate our method on a phoneme recognition task in clean and noisy environments and show that our method outperforms REINFORCE, with the difference being greater for a more complicated task.
Generative models have long been the dominant approach for speech recognition. The success of these models however relies on the use of sophisticated recipes and complicated machinery that is not easily accessible to non-practitioners. Recent innovations in Deep Learning have given rise to an alternative - discriminative models called Sequence-to-Sequence models, that can almost match the accuracy of state of the art generative models. While these models are easy to train as they can be trained end-to-end in a single step, they have a practical limitation that they can only be used for offline recognition. This is because the models require that the entirety of the input sequence be available at the beginning of inference, an assumption that is not valid for instantaneous speech recognition. To address this problem, online sequence-to-sequence models were recently introduced. These models are able to start producing outputs as data arrives, and the model feels confident enough to output partial transcripts. These models, like sequence-to-sequence are causal - the output produced by the model until any time, $t$, affects the features that are computed subsequently. This makes the model inherently more powerful than generative models that are unable to change features that are computed from the data. This paper highlights two main contributions - an improvement to online sequence-to-sequence model training, and its application to noisy settings with mixed speech from two speakers.
We introduce dropout compaction, a novel method for training feed-forward neural networks which realizes the performance gains of training a large model with dropout regularization, yet extracts a compact neural network for run-time efficiency. In the proposed method, we introduce a sparsity-inducing prior on the per unit dropout retention probability so that the optimizer can effectively prune hidden units during training. By changing the prior hyperparameters, we can control the size of the resulting network. We performed a systematic comparison of dropout compaction and competing methods on several real-world speech recognition tasks and found that dropout compaction achieved comparable accuracy with fewer than 50% of the hidden units, translating to a 2.5x speedup in run-time.
We propose a max-pooling based loss function for training Long Short-Term Memory (LSTM) networks for small-footprint keyword spotting (KWS), with low CPU, memory, and latency requirements. The max-pooling loss training can be further guided by initializing with a cross-entropy loss trained network. A posterior smoothing based evaluation approach is employed to measure keyword spotting performance. Our experimental results show that LSTM models trained using cross-entropy loss or max-pooling loss outperform a cross-entropy loss trained baseline feed-forward Deep Neural Network (DNN). In addition, max-pooling loss trained LSTM with randomly initialized network performs better compared to cross-entropy loss trained LSTM. Finally, the max-pooling loss trained LSTM initialized with a cross-entropy pre-trained network shows the best performance, which yields $67.6\%$ relative reduction compared to baseline feed-forward DNN in Area Under the Curve (AUC) measure.
The policy gradients of the expected return objective can react slowly to rare rewards. Yet, in some cases agents may wish to emphasize the low or high returns regardless of their probability. Borrowing from the economics and control literature, we review the risk-sensitive value function that arises from an exponential utility and illustrate its effects on an example. This risk-sensitive value function is not always applicable to reinforcement learning problems, so we introduce the particle value function defined by a particle filter over the distributions of an agent's experience, which bounds the risk-sensitive one. We illustrate the benefit of the policy gradients of this objective in Cliffworld.
We systematically explore regularizing neural networks by penalizing low entropy output distributions. We show that penalizing low entropy output distributions, which has been shown to improve exploration in reinforcement learning, acts as a strong regularizer in supervised learning. Furthermore, we connect a maximum entropy based confidence penalty to label smoothing through the direction of the KL divergence. We exhaustively evaluate the proposed confidence penalty and label smoothing on 6 common benchmarks: image classification (MNIST and Cifar-10), language modeling (Penn Treebank), machine translation (WMT'14 English-to-German), and speech recognition (TIMIT and WSJ). We find that both label smoothing and the confidence penalty improve state-of-the-art models across benchmarks without modifying existing hyperparameters, suggesting the wide applicability of these regularizers.