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f-GAIL: Learning f-Divergence for Generative Adversarial Imitation Learning
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null (Ed.)Imitation learning (IL) aims to learn a policy from expert demonstrations that minimizes the discrepancy between the learner and expert behaviors. Various imitation learning algorithms have been proposed with different pre-determined divergences to quantify the discrepancy. This naturally gives rise to the following question: Given a set of expert demonstrations, which divergence can recover the expert policy more accurately with higher data efficiency? In this work, we propose f-GAIL – a new generative adversarial imitation learning model – that automatically learns a discrepancy measure from the f-divergence family as well as a policy capable of producing expert-like behaviors. Compared with IL baselines with various predefined divergence measures, f-GAIL learns better policies with higher data efficiency in six physics-based control tasks.more » « less
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Abstract Spread‐F (SF) is a feature that can be visually observed on ionograms when the ionosonde signals are significantly impacted by plasma irregularities in the ionosphere. Depending on the scale of the plasma irregularities, radio waves of different frequencies are impacted differently when the signals pass through the ionosphere. An automated method for detecting SF in ionograms is presented in this study. Through detecting the existence of SF in ionograms, we can help identify instances of plasma irregularities that are potentially affecting the high‐frequency radio‐wave systems. The ionogram images from Jicamarca observatory in Peru, during the years 2008–2019, are used in this study. Three machine learning approaches have been carried out: supervised learning using Support Vector Machines, and two neural network‐based learning methods: autoencoder and transfer learning. Of these three methods, the transfer learning approach, which uses convolutional neural network architectures, demonstrates the best performance. The best existing architecture that is suitable for this problem appears to be the ResNet50. With respect to the training epoch number, the ResNet50 showed the greatest change in the metric values for the key metrics that we were tracking. Furthermore, on a test set of 2050 ionograms, the model based on the ResNet50 architecture provides an accuracy of 89%, recall of 87%, precision of 95%, as well as Area Under the Curve of 96%. The work also provides a labeled data set of around 28,000 ionograms, which is extremely useful for the community for future machine learning studies.more » « less
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null (Ed.)Abstract We consider the inequality $$f \geqslant f\star f$$ for real functions in $$L^1({\mathbb{R}}^d)$$ where $$f\star f$$ denotes the convolution of $$f$$ with itself. We show that all such functions $$f$$ are nonnegative, which is not the case for the same inequality in $L^p$ for any $$1 < p \leqslant 2$$, for which the convolution is defined. We also show that all solutions in $$L^1({\mathbb{R}}^d)$$ satisfy $$\int _{{\mathbb{R}}^{\textrm{d}}}f(x)\ \textrm{d}x \leqslant \tfrac 12$$. Moreover, if $$\int _{{\mathbb{R}}^{\textrm{d}}}f(x)\ \textrm{d}x = \tfrac 12$$, then $$f$$ must decay fairly slowly: $$\int _{{\mathbb{R}}^{\textrm{d}}}|x| f(x)\ \textrm{d}x = \infty $$, and this is sharp since for all $r< 1$, there are solutions with $$\int _{{\mathbb{R}}^{\textrm{d}}}f(x)\ \textrm{d}x = \tfrac 12$$ and $$\int _{{\mathbb{R}}^{\textrm{d}}}|x|^r f(x)\ \textrm{d}x <\infty $$. However, if $$\int _{{\mathbb{R}}^{\textrm{d}}}f(x)\ \textrm{d}x =: a < \tfrac 12$$, the decay at infinity can be much more rapid: we show that for all $$a<\tfrac 12$$, there are solutions such that for some $$\varepsilon>0$$, $$\int _{{\mathbb{R}}^{\textrm{d}}}e^{\varepsilon |x|}f(x)\ \textrm{d}x < \infty $$.more » « less
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