This paper demonstrates a novel method for separately estimating aleatoric risk and epistemic uncertainty in deep reinforcement learning. Aleatoric risk, which arises from inherently stochastic environments or agents, must be accounted for in the design of risk-sensitive algorithms. Epistemic uncertainty, which stems from limited data, is important both for risk-sensitivity and to efficiently explore an environment. We first present a Bayesian framework for learning the return distribution in reinforcement learning, which provides theoretical foundations for quantifying both types of uncertainty. Based on this framework, we show that the disagreement between only two neural networks is sufficient to produce a low-variance estimate of the epistemic uncertainty on the return distribution, thus providing a simple and computationally cheap uncertainty metric. We demonstrate experiments that illustrate our method and some applications.
There has been increasing interest in developing practical methods for uncertainty estimation in reinforcement learning, with prior work mostly focusing either on aleatoric risk or epistemic uncertainty. For the estimation of epistemic uncertainty in complex environments, several methods have been proposed. Pseudo-counts @cite_38 @cite_13 that approximate the number of visits of states or state-action pairs by an agent can be interpreted as an uncertainty measure. Bayesian inference techniques over the parameters that define the value function have been demonstrated @cite_23 @cite_5 @cite_36 . The disagreement between the predictions of an ensemble of neural networks has also been proposed as a way of estimating uncertainty @cite_15 @cite_27 @cite_9 @cite_28 @cite_31 @cite_17 @cite_40 . Dropout in neural networks has also been used @cite_43 @cite_30 . Our work builds on epistemic uncertainty estimation using dropout @cite_43 and anchored neural networks @cite_28 and proposes an expansion to the distributional setting, thus allowing us to consider both aleatoric and epistemic uncertainty in a single framework.
@cite_30 @cite_38 @cite_31 @cite_36 @cite_28 @cite_9 @cite_43 @cite_27 @cite_40 @cite_23 @cite_5 @cite_15 @cite_13 @cite_17
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We provide frequentist estimates of aleatoric and epistemic uncertainty for deep neural networks. To estimate aleatoric uncertainty we propose simultaneous quantile regression, a loss function to learn all the conditional quantiles of a given target variable. These quantiles lead to well-calibrated prediction intervals. To estimate epistemic uncertainty we propose training certificates, a collection of diverse non-trivial functions that map all training samples to zero. These certificates map out-of-distribution examples to non-zero values, signaling high epistemic uncertainty. We compare our proposals to prior art in various experiments. This paper studies directed exploration for reinforcement learning agents by tracking uncertainty about the value of each available action. We identify two sources of uncertainty that are relevant for exploration. The first originates from limited data (parametric uncertainty), while the second originates from the distribution of the returns (return uncertainty). We identify methods to learn these distributions with deep neural networks, where we estimate parametric uncertainty with Bayesian drop-out, while return uncertainty is propagated through the Bellman equation as a Gaussian distribution. Then, we identify that both can be jointly estimated in one network, which we call the Double Uncertain Value Network. The policy is directly derived from the learned distributions based on Thompson sampling. Experimental results show that both types of uncertainty may vastly improve learning in domains with a strong exploration challenge. As deep neural networks (DNNs) are applied to increasingly challenging problems, they will need to be able to represent their own uncertainty. Modeling uncertainty is one of the key features of Bayesian methods. Using Bernoulli dropout with sampling at prediction time has recently been proposed as an efficient and well performing variational inference method for DNNs. However, sampling from other multiplicative noise based variational distributions has not been investigated in depth. We evaluated Bayesian DNNs trained with Bernoulli or Gaussian multiplicative masking of either the units (dropout) or the weights (dropconnect). We tested the calibration of the probabilistic predictions of Bayesian convolutional neural networks (CNNs) on MNIST and CIFAR-10. Sampling at prediction time increased the calibration of the DNNs' probabalistic predictions. Sampling weights, whether Gaussian or Bernoulli, led to more robust representation of uncertainty compared to sampling of units. However, using either Gaussian or Bernoulli dropout led to increased test set classification accuracy. Based on these findings we used both Bernoulli dropout and Gaussian dropconnect concurrently, which we show approximates the use of a spike-and-slab variational distribution without increasing the number of learned parameters. We found that spike-and-slab sampling had higher test set performance than Gaussian dropconnect and more robustly represented its uncertainty compared to Bernoulli dropout. There are two major types of uncertainty one can model. Aleatoric uncertainty captures noise inherent in the observations. On the other hand, epistemic uncertainty accounts for uncertainty in the model - uncertainty which can be explained away given enough data. Traditionally it has been difficult to model epistemic uncertainty in computer vision, but with new Bayesian deep learning tools this is now possible. We study the benefits of modeling epistemic vs. aleatoric uncertainty in Bayesian deep learning models for vision tasks. For this we present a Bayesian deep learning framework combining input-dependent aleatoric uncertainty together with epistemic uncertainty. We study models under the framework with per-pixel semantic segmentation and depth regression tasks. Further, our explicit uncertainty formulation leads to new loss functions for these tasks, which can be interpreted as learned attenuation. This makes the loss more robust to noisy data, also giving new state-of-the-art results on segmentation and depth regression benchmarks.