The design of sparse neural networks, i.e., of networks with a reduced number of parameters, has been attracting increasing research attention in the last few years. The use of sparse models may significantly reduce the computational and storage footprint in the inference phase. In this context, the lottery ticket hypothesis (LTH) constitutes a breakthrough result, that addresses not only the performance of the inference phase, but also of the training phase. It states that it is possible to extract effective sparse subnetworks, called winning tickets, that can be trained in isolation. The development of effective methods to play the lottery, i.e., to find winning tickets, is still an open problem. In this article, we propose a novel class of methods to play the lottery. The key point is the use of concave regularization to promote the sparsity of a relaxed binary mask, which represents the network topology. We theoretically analyze the effectiveness of the proposed method in the convex framework. Then, we propose extended numerical tests on various datasets and architectures, that show that the proposed method can improve the performance of state-of-the-art algorithms.

Heterogeneous networks have emerged as a popular solution for accommodating the growing number of connected devices and increasing traffic demands in cellular networks. While offering broader coverage, higher capacity, and lower latency, the escalating energy consumption poses sustainability challenges. In this paper a novel optimization approach for orthogonal heterogeneous networks is proposed to minimize transmission power while respecting individual users’ throughput constraints. The problem is formulated as a mixed integer geometric program, and optimizes at once multiple system variables such as user association, working bandwidth, and base stations transmission powers. Crucially, the proposed approach becomes a convex optimization problem when user-base station associations are provided. Evaluations in multiple realistic scenarios from the production mobile network of a major European operator and based on precise channel gains and throughput requirements from measured data validate the effectiveness of the proposed approach. Overall, our original solution paves the road for greener connectivity by reducing the energy footprint of heterogeneous mobile networks, hence fostering more sustainable communication systems.

In this article, we propose an efficient multiclass classification scheme based on sparse centroids classifiers. The proposed strategy exhibits linear complexity with respect to both the number of classes and the cardinality of the feature space. The classifier we introduce is based on binary space partitioning, performed by a decision tree where the assignation law at each node is defined via a sparse centroid classifier. We apply the presented strategy to the time series classification problem, showing by experimental evidence that it achieves performance comparable to that of state-of-the-art methods, but with a significantly lower classification time. The proposed technique can be an effective option in resource-constrained environments where the classification time and the computational cost are critical or, in scenarios, where real-time classification is necessary.

distance criteria, respectively, and perform simultaneous feature selection and classification, by detecting the features that are most relevant for the classification purpose. We formally prove that the training of the proposed sparse models, with both distance criteria, can be performed exactly (i.e., the globally optimal set of features is selected) at a linear computational cost. Especially, the proposed sparse classifiers are trained in O(mn)+O(mlogk) operations, where n is the number of samples, m is the total number of features, and k ≤ m is the number of features to be retained in the classifier. Furthermore, the complexity of testing and classifying a new sample is simply O(k) for both methods. The proposed models can be employed either as stand-alone sparse classifiers or fast feature-selection techniques for prefiltering the features to be later fed to other types of classifiers (e.g., SVMs). The experimental results show that the proposed methods are competitive in accuracy with state-of-the-art feature selection and classification techniques while having a substantially lower computational cost.

Autonomous driving is disrupting the automotive industry as we know it today. For this, fail-operational behavior is essential in the sense, plan, and act stages of the automation chain in order to handle safety-critical situations on its own, which currently is not reached with state-of-the-art approaches.The European ECSEL research project PRYSTINE realizes Fail-operational Urban Surround perceptION (FUSION) based on robust Radar and LiDAR sensor fusion and control functions in order to enable safe automated driving in urban and rural environments. This paper showcases some of the key exploitable results (e.g., novel Radar sensors, innovative embedded control and E/E architectures, pioneering sensor fusion approaches, AI-controlled vehicle demonstrators) achieved until its final year 3.

An algorithm is proposed to determine output feedback policies that solve finite-horizon linear-quadratic (LQ) optimal control problems without requiring knowledge of the system dynamical matrices. To reach this goal, the Q -factors arising from finite-horizon LQ problems are first characterized in the state feedback case. It is then shown how they can be parameterized as functions of the input-output vectors. A procedure is then proposed for estimating these functions from input/output data and using these estimates for computing the optimal control via the measured inputs and outputs.

In this paper, we show that a one-layer feedforward neural network with exponential activation functions in the inner layer and logarithmic activation in the output neuron is a universal approximator of convex functions. Such a network represents a family of scaled log-sum exponential functions, here named log-sum-exp (LSET). Under a suitable exponential transformation, the class of LSETfunctions maps to a family of generalized posynomials GPOST, which we similarly show to be universal approximators for log-log-convex functions. A key feature of an LSETnetwork is that, once it is trained on data, the resulting model is convex in the variables, which makes it readily amenable to efficient design based on convex optimization. Similarly, once a GPOSTmodel is trained on data, it yields a posynomial model that can be efficiently optimized with respect to its variables by using geometric programming (GP). The proposed methodology is illustrated by two numerical examples, in which, first, models are constructed from simulation data of the two physical processes (namely, the level of vibration in a vehicle suspension system, and the peak power generated by the combustion of propane), and then optimization-based design is performed on these models.

We show that a neural network whose output is obtained as the difference of the outputs of two feedforward networks with exponential activation function in the hidden layer and logarithmic activation function in the output node, referred to as log-sum-exp (LSE) network, is a smooth universal approximator of continuous functions over convex, compact sets. By using a logarithmic transform, this class of network maps to a family of subtraction-free ratios of generalized posynomials (GPOS), which we also show to be universal approximators of positive functions over log-convex, compact subsets of the positive orthant. The main advantage of difference-LSE networks with respect to classical feedforward neural networks is that, after a standard training phase, they provide surrogate models for a design that possesses a specific difference-of-convex-functions form, which makes them optimizable via relatively efficient numerical methods. In particular, by adapting an existing difference-of-convex algorithm to these models, we obtain an algorithm for performing an effective optimization-based design. We illustrate the proposed approach by applying it to the data-driven design of a diet for a patient with type-2 diabetes and to a nonconvex optimization problem.

Pose graph optimization (PGO) is the problem of estimating a set of poses from pairwise relative measurements. PGO is a nonconvex problem and, currently, no known technique can guarantee the computation of a global optimal solution. In this paper, we show that Lagrangian duality allows computing a globally optimal solution under conditions that are satisfied in most robotics applications and enables to certify optimality of a given estimate. Our first contribution is to frame planar PGO in the complex domain. This makes analysis easier and allows drawing connections with existing literature on unit gain graphs. The second contribution is to formulate and analyze the properties of the Lagrangian dual problem in the complex domain. Our analysis shows that the duality gap is connected to the number of zero eigenvalues of the penalized pose graph matrix. We prove that if this matrix has a single zero eigenvalue, then 1) the duality gap is zero, 2) the primal PGO problem has a unique solution (up to an arbitrary roto-translation), and 3) the primal solution can be computed by scaling an eigenvector of the penalized pose graph matrix. The third contribution is algorithmic: We leverage duality to devise and algorithm that computes the optimal solution when the penalized matrix has a single zero eigenvalue. We also propose a suboptimal variant when the zero eigenvalues are multiple. Finally, we show that duality provides computational tools to verify if a given estimate (e.g., computed using iterative solvers) is globally optimal. We conclude the paper with an extensive numerical analysis. Empirical evidence shows that, in the vast majority of cases (100% of the tests under noise regimes of practical robotics applications), the penalized pose graph matrix has a single zero eigenvalue; hence, our approach allows computing (or verifying) the optimal solution.

State-of-the-art techniques for simultaneous localization and mapping (SLAM) employ iterative nonlinear optimization methods to compute an estimate for robot poses. While these techniques often work well in practice, they do not provide guarantees on the quality of the estimate. This paper shows that Lagrangian duality is a powerful tool to assess the quality of a given candidate solution. Our contribution is threefold. First, we discuss a revised formulation of the SLAM inference problem. We show that this formulation is probabilistically grounded and has the advantage of leading to an optimization problem with quadratic objective. The second contribution is the derivation of the corresponding Lagrangian dual problem. The SLAM dual problem is a (convex) semidefinite program, which can be solved reliably and globally by off-the-shelf solvers. The third contribution is to discuss the relation between the original SLAM problem and its dual. We show that from the dual problem, one can evaluate the quality (i.e., the suboptimality gap) of a candidate SLAM solution, and ultimately provide a certificate of optimality. Moreover, when the duality gap is zero, one can compute a guaranteed optimal SLAM solution from the dual problem, circumventing non-convex optimization. We present extensive (real and simulated) experiments supporting our claims and discuss practical relevance and open problems.

This paper discusses a computational methodology for solving multi-period dynamic asset allocation problems using empirical asymmetric measures of risk. Three features distinguish the proposed approach from the mainstream ones. First, our approach is nonparametric, in the sense that it does not require explicit estimation of a statistical model for the returns distribution. Second, it employs affine decision policies, which make the multi-period formulation of the problem amenable to efficient convex optimization format. Third, it uses asymmetric, unilateral, measures of risk which, unlike standard symmetric measures such as variance, capture the fact that investors are usually not averse to return deviations from the expected target, if these deviations actually exceed the target.

This paper describes a novel approach for passivity enforcement of compact dynamical models of electrical interconnects. The proposed approach is based on a parameterization of general state-space scattering models with fixed poles. We formulate the passivity constraints as a unitary boundedness condition on the H∞norm of the system transfer function. When this condition is not verified, we use it as an explicit constraint within an iterative perturbation loop of the system state-space matrices. Since the resulting optimization framework is convex but nonsmooth, we solve it via localization based algorithms, such as the ellipsoid and the cutting plane methods. The proposed technique solves two critical bottleneck issues of the existing approaches for passivity enforcement of linear macromodels. Compared to quasi-optimal schemes based on singular value or Hamiltonian eigenvalue perturbation, we are able to guarantee convergence to the optimal solution. Compared to convex formulations based on direct Bounded Real Lemma constraints, we are able to reduce both memory and time requirements by orders of magnitude. We demonstrate the effectiveness of our approach on a number of cases for which existing algorithms either fail or exhibit very slow convergence.

Autonomous agents deployed or moving on land for the purpose of carrying out coordinated tasks need to have good knowledge of their absolute or relative position. For large formations, it is often impractical to equip each agent with an absolute sensor such as GPS, whereas relative range sensors measuring interagent distances are cheap and commonly available. In this setting, this paper considers the problem of autonomous distributed estimation of the position of each agent in a networked formation using noisy measurements of interagent distances. The underlying geometrical problem has been studied quite extensively in various fields, ranging from molecular biology to robotics, and it is known to lead to a hard nonconvex optimization problem. Centralized algorithms do exist that work reasonably well in finding local or global minimizers for this problem (e.g., semidefinite programming relaxations). Here, we explore a fully decentralized approach for localization from range measurements, and we propose a computational scheme based on a distributed gradient algorithm with Barzilai-Borwein stepsizes. The advantage of this distributed approach is that each agent may autonomously compute its position estimate, exchanging information only with its neighbors, without need of communicating with a central station and without needing complete knowledge of the network structure.

In this paper we address the problem of estimating the poses of a team of agents when they do not share any common reference frame. Each agent is capable of measuring the relative position and orientation of its neighboring agents, however these measurements are not exact but they are corrupted with noises. The goal is to compute the pose of each agent relative to an anchor node. We present a strategy where, first of all, the agents compute their orientations relative to the anchor. After that, they update the relative position measurements according to these orientations, to finally compute their positions. As contribution we discuss the proposed strategy, that has the interesting property that can be executed in a distributed fashion. The distributed implementation allows each agent to recover its pose using exclusively local information and local interactions with its neighbors. This algorithm has a low memory load, since it only requires each node to maintain an estimate of its own orientation and position.

This paper deals with the problem of optimally matching two ordered sets of 3-D points by means of a rigid displacement. Contrary to the standard approach, where a sum-of-squared-errors criterion is minimized in order to obtain the optimal displacement, we here analyze the use of [maximum absolute error (MAE)] and [sum of absolute errors (SAE)] cost criteria for determining the optimal matching. Two numerically efficient (polynomial time) algorithms are developed in this paper to compute an approximately optimal solution for the MAE and SAE matching problems.

We propose a novel methodology for reliable localization of an autonomous mobile robot navigating in an unstructured environment using noisy absolute measurements from its exteroceptive sensors. A new deterministic filtering technique is introduced, which is based on the recursive computation of a bounding set that is guaranteed to contain the true state of the system, despite process and observation noise, and taking into explicit consideration uncertainties due to the linearization error. The proposed set-valued nonlinear filter relies on a two-step prediction-correction structure, with each step requiring the solution of a particular convex optimization problem. The method is illustrated by simulation on a localization problem for a nonholonomic rover, and it is compared with the standard extended Kalman filter approach.

This paper discusses the problem of approximating data points in n-dimensional Euclidean space using spherical and ellipsoidal surfaces. A closed form solution is provided for spherical approximation, while an efficient, globally optimal solution for the ellipsoidal problem is proposed in terms of semidefinite programming. In addition, the paper presents a result for robust fitting in presence of outliers, and illustrates the theory with several numerical examples. A brief survey is also presented on the solutions to other relevant geometric approximation problems, such as ellipsoidal covering of convex hulls and pattern separation.

This paper discusses the problem of approximating data points in n-dimensional Euclidean space, using spherical and ellipsoidal surfaces. For the specific cases of n = 2 and n = 3, the problem is of fundamental importance id computer vision and robotics. A closed form solution is provided for spherical approximation, while an efficient, globally optimal solution for the ellipsoidal problem is proposed in terms of semidefinite programming (SDP). The paper also presents a result for robust fitting in the presence of outliers, and illustrates the theory with several numerical examples.

Deals with the problem of multivariate affine regression in the presence of outliers in the data. The method discussed is based on weighted orthogonal least squares. The weights associated with the data satisfy a suitable optimality criterion and are computed by a two-step algorithm requiring a RANSAC step and a gradient-based optimization step. Issues related to the breakdown point of the method are discussed, and examples of application on various real multidimensional data sets are reported in the paper.

Common robot calibration procedures use least-squares (LS) techniques to obtain estimates of the identifiable parameters. The "quality" of the resulting estimates depends significantly upon the used excitation input. The search for the best excitation trajectory is usually posed as a nonlinear path optimization problem aimed at optimizing suitable measures of the LS normal equations matrix. In this paper a parametrization of the class of reference joints trajectories is introduced and a solution framework based on genetic evolution is proposed. The efficiency of the method is illustrated by experimental tests on a SCARA two-link manipulator. Issues related to data acquisition and signals reconstruction and filtering are also discussed.

This paper addresses the problem of finding whether a given set of three-dimensional (3D) vectors (the object) can be brought to match a second set of vectors (the template) by means of an affine motion, minimizing a measure of the mismatch error and satisfying an assigned set of geometrical constraints. This problem is encountered in many applications of computer vision, robotics, and manufacturing processes, and has been tackled by several authors in the unconstrained case. Spherical, ellipsoidal and polyhedral constraints are here introduced in the problem, and a solution scheme based on an efficient convex optimization algorithm is proposed. An example of application of the proposed methodology to a manufacturing tolerancing problem is also provided.