**Risk-Sensitive GAIL (RS-GAIL)**

We study risk-sensitive imitation learning where the agent’s goal is to perform at least as well as the expert in terms of a risk profile. We first formulate our risk-sensitive imitation learning setting. We consider the generative adversarial approach to imitation learning (GAIL) and derive an optimization problem for our formulation, which we call risk-sensitive GAIL (RS-GAIL). We then derive two different versions of our RS-GAIL optimization problem that aim at matching the risk profiles of the agent and the expert w.r.t. Jensen-Shannon (JS) divergence and Wasserstein distance, and develop risk-sensitive generative adversarial imitation learning algorithms based on these optimization problems. We evaluate the performance of our JS-based algorithm and compare it with GAIL and the risk-averse imitation learning (RAIL) algorithm in two MuJoCo tasks. … **Metric Gaussian Variational Inference (MGVI)**

A variational Gaussian approximation of the posterior distribution can be an excellent way to infer posterior quantities. However, to capture all posterior correlations the parametrization of the full covariance is required, which scales quadratic with the problem size. This scaling prohibits full-covariance approximations for large-scale problems. As a solution to this limitation we propose Metric Gaussian Variational Inference (MGVI). This procedure approximates the variational covariance such that it requires no parameters on its own and still provides reliable posterior correlations and uncertainties for all model parameters. We approximate the variational covariance with the inverse Fisher metric, a local estimate of the true posterior uncertainty. This covariance is only stored implicitly and all necessary quantities can be extracted from it by independent samples drawn from the approximating Gaussian. MGVI requires the minimization of a stochastic estimate of the Kullback-Leibler divergence only with respect to the mean of the variational Gaussian, a quantity that only scales linearly with the problem size. We motivate the choice of this covariance from an information geometric perspective. The method is validated against established approaches in a small example and the scaling is demonstrated in a problem with over a million parameters. … **Transition-Entropy**

Recent years have seen rising needs for location-based services in our everyday life. Aside from the many advantages provided by these services, they have caused serious concerns regarding the location privacy of users. An adversary such as an untrusted location-based server can monitor the queried locations by a user to infer critical information such as the user’s home address, health conditions, shopping habits, etc. To address this issue, dummy-based algorithms have been developed to increase the anonymity of users, and thus, protecting their privacy. Unfortunately, the existing algorithms only consider a limited amount of side information known by an adversary which may face more serious challenges in practice. In this paper, we incorporate a new type of side information based on consecutive location changes of users and propose a new metric called transition-entropy to investigate the location privacy preservation, followed by two algorithms to improve the transition-entropy for a given dummy generation algorithm. Then, we develop an attack model based on the Viterbi algorithm which can significantly threaten the location privacy of the users. Next, in order to protect the users from Viterbi attack, we propose an algorithm called robust dummy generation (RDG) which can resist against the Viterbi attack while maintaining a high performance in terms of the privacy metrics introduced in the paper. All the algorithms are applied and analyzed on a real-life dataset. … **Gauss–Newton Algorithm (GNA)**

The Gauss-Newton algorithm is a method used to solve non-linear least squares problems. It is a modification of Newton’s method for finding a minimum of a function. Unlike Newton’s method, the Gauss-Newton algorithm can only be used to minimize a sum of squared function values, but it has the advantage that second derivatives, which can be challenging to compute, are not required. Non-linear least squares problems arise for instance in non-linear regression, where parameters in a model are sought such that the model is in good agreement with available observations. …

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