Kernel methods and Model predictive approaches for Learning and Control

Data-driven modeling and feedback control play a vital role in several application areas ranging from robotics, control theory, manufacturing to management of assets, financial portfolios and supply chains. Many such problems in one way or another are related to variational problems in optimal control and machine learning.

The following work first presents, a generalized representer theorem approach to solving such variational problems when closed, densely defined operators, like the differential operators, are involved. Furthermore, loss functionals on infinite dimensional Hilbert spaces are considered to allow for greater freedom in problem formulations. The statement of the theorem presents a necessary and sufficient condition for the existence of linear representer for optimal solutions of such problems. Finally, examples, applying the theorem to neural networks, stochastic regression, and sparsity-inducing regularization problems are presented.

The second part of the thesis deals with applications of variational optimization in control problems. Examples from optimal control and model predictive control are presented for applications in the domain of autonomous vehicles and airborne wind energy systems. First, a combination of manifold learning and model predictive control is presented for obstacle avoidance in autonomous driving. Manifold learning is presented as a means to describe boundaries of star-shaped sets for which a single inequality constraint is sufficient to check containment of a point in the set's interior. The approach presented, learns the largest star-shaped set within a circular range such that all obstacle points remain outside the set. The inequality condition for checking containment in such sets is incorporated into a multi-phase, free-end-time optimal control problem to plan trajectories and control inputs moving the vehicle from one point to another while remaining within a given collection of star-shaped sets. The multi-phase, free-end-time problem is adapted to a moving horizon form to give a model predictive path following controller that avoids obstacles by virtue of the manifold learning scheme. A real-time, dynamically updated manifold is learned using point cloud data from a lidar-like sensor on the vehicle to avoid any apriori unknown or moving obstacles. Convergence and recursive feasibility guarantees for the MPC scheme are provided under mild assumptions on the behavior of the obstacles and dynamics of the vehicle. An automated parking scenario in the presence of static and dynamic obstacles is demonstrated in simulation for the complete process of optimal trajectory planning and path following.

Next, a continuous time, path following model predictive control scheme is shown for an Airborne Wind Energy (AWE) system. Here stability and convergence guarantees are provided by combining the model predictive controller with terminal constraints inspired from a convergent vector field design problem. A formal stability proof relying on Lyapunov stability arguments is presented to show that for such a design of vector field terminal constraints the path following controller converges to a zero tracking error on the desired path.

The last part of the thesis deals with uncertainty in AWE systems due to wind conditions and unknown aerodynamic characteristics. A Gaussian process data-driven optimisation technique and a direct adaptive nonlinear controller design are presented for the same.

Machine learning for information retrieval

David Grangier

In this thesis, we explore the use of machine learning techniques for information retrieval. More specifically, we focus on ad-hoc retrieval, which is concerned with searching large corpora to identify the documents relevant to user queries. This identification is performed through a ranking task. Given a user query, an ad-hoc retrieval system ranks the corpus documents, so that the documents relevant to the query ideally appear above the others. In a machine learning framework, we are interested in proposing learning algorithms that can benefit from limited training data in order to identify a ranker likely to achieve high retrieval performance over unseen documents and queries. This problem presents novel challenges compared to traditional learning tasks, such as regression or classification. First, our task is a ranking problem, which means that the loss for a given query cannot be measured as a sum of an individual loss suffered for each corpus document. Second, most retrieval queries present a highly unbalanced setup, with a set of relevant documents accounting only for a very small fraction of the corpus. Third, ad-hoc retrieval corresponds to a kind of "double" generalization problem, since the learned model should not only generalize to new documents but also to new queries. Finally, our task also presents challenging efficiency constraints, since ad-hoc retrieval is typically applied to large corpora. The main objective of this thesis is to investigate the discriminative learning of ad-hoc retrieval models. For that purpose, we propose different models based on kernel machines or neural networks adapted to different retrieval contexts. The proposed approaches rely on different online learning algorithms that allow efficient learning over large corpora. The first part of the thesis focuses on text retrieval. In this case, we adopt a classical approach to the retrieval ranking problem, and order the text documents according to their estimated similarity to the text query. The assessment of semantic similarity between text items plays a key role in that setup and we propose a learning approach to identify an effective measure of text similarity. This identification is not performed relying on a set of queries with their corresponding relevant document sets, since such data are especially expensive to label and hence rare. Instead, we propose to rely on hyperlink data, since hyperlinks convey semantic proximity information that is relevant to similarity learning. This setup is hence a transfer learning setup, where we benefit from the proximity information encoded by hyperlinks to improve the performance over the ad-hoc retrieval task. We then investigate another retrieval problem, i.e. the retrieval of images from text queries. Our approach introduces a learning procedure optimizing a criterion related to the ranking performance. This criterion adapts our previous learning objective for learning textual similarity to the image retrieval problem. This yields an image ranking model that addresses the retrieval problem directly. This approach contrasts with previous research that relies on an intermediate image annotation task. Moreover, our learning procedure builds upon recent work on the online learning of kernel-based classifiers. This yields an efficient, scalable algorithm, which can benefit from recent kernels developed for image comparison. In the last part of the thesis, we show that the objective function used in the previous retrieval problems can be applied to the task of keyword spotting, i.e. the detection of given keywords in speech utterances. For that purpose, we formalize this problem as a ranking task: given a keyword, the keyword spotter should order the utterances so that the utterances containing the keyword appear above the others. Interestingly, this formulation yields an objective directly maximizing the area under the receiver operating curve, the most common keyword spotter evaluation measure. This objective is then used to train a model adapted to this intrinsically sequential problem. This model is then learned with a procedure derived from the algorithm previously introduced for the image retrieval task. To conclude, this thesis introduces machine learning approaches for ad-hoc retrieval. We propose learning models for various multi-modal retrieval setups, i.e. the retrieval of text documents from text queries, the retrieval of images from text queries and the retrieval of speech recordings from written keywords. Our approaches rely on discriminative learning and enjoy efficient training procedures, which yields effective and scalable models. In all cases, links with prior approaches were investigated and experimental comparisons were conducted.

EPFL2008

Neuroevolution: from architectures to learning

Peter Dürr, Dario Floreano, Claudio Mattiussi

Artificial neural networks are applied to many real-world problems, ranging from pattern classification to robot control. In order to design a neural network for a particular task, the choice of an architecture (including the choice of a neuron model), and the choice of a learning algorithm have to be addressed. Evolutionary search methods can provide an automatic solution to these problems. New insights in both neuroscience and evolutionary biology have led to the development of increasingly powerful neuroevolution techniques over the last decade. This paper gives an overview of the most prominent methods for evolving artificial neural networks with a special focus on recent advances in the synthesis of learning architectures.

2008

Robustness and invariance properties of image classifiers

Apostolos Modas

Deep neural networks have achieved impressive results in many image classification tasks. However, since their performance is usually measured in controlled settings, it is important to ensure that their decisions remain correct when deployed in noisy environments. In fact, deep networks are not robust to a large variety of semantic-preserving image modifications, even to imperceptible image changes -- known as adversarial perturbations -- that can arbitrarily flip the prediction of a classifier. The poor robustness of image classifiers to small data distribution shifts raises serious concerns regarding their trustworthiness. To build reliable machine learning models, we must design principled methods to analyze and understand the mechanisms that shape robustness and invariance. This is exactly the focus of this thesis.First, we study the problem of computing sparse adversarial perturbations, and exploit the geometry of the decision boundaries of image classifiers for computing sparse perturbations very fast. We evaluate the robustness of deep networks to sparse adversarial perturbations in high-dimensional datasets, and reveal a qualitative correlation between the location of the perturbed pixels and the semantic features of the images. Such correlation suggests a deep connection between adversarial examples and the data features that image classifiers learn.To better understand this connection, we provide a geometric framework that connects the distance of data samples to the decision boundary, with the features existing in the data. We show that deep classifiers have a strong inductive bias towards invariance to non-discriminative features, and that adversarial training exploits this property to confer robustness. We demonstrate that the invariances of robust classifiers are useful in data-scarce domains, while the improved understanding of the data influence on the inductive bias of deep networks can be exploited to design more robust classifiers. Finally, we focus on the challenging problem of generalization to unforeseen corruptions of the data, and we propose a novel data augmentation scheme that relies on simple families of max-entropy image transformations to confer robustness to common corruptions. We analyze our method and demonstrate the importance of the mixing strategy on synthesizing corrupted images, and we reveal the robustness-accuracy trade-offs arising in the context of common corruptions. The controllable nature of our method permits to easily adapt it to other tasks and achieve robustness to distribution shifts in data-scarce applications.Overall, our results contribute to the understanding of the fundamental mechanisms of deep image classifiers, and pave the way for building more reliable machine learning systems that can be deployed in real-world environments.