Published in "IEEE Robotics and Automation Magazine", DOI: 10.1109/MRA.2020.3044911 Matin Macktoobian, Denis Gillet, and Jean-Paul Kneib The authors are with the School of Engineering, Swiss Federal Institute of Technology in Lausanne (EPFL), Lausanne, Switzerland (e-mail: matin.macktoobian@epfl.ch; Abstract This paper introduces the emerging field of astrobotics, that is, a recently-established branch of robotics to be of service to astrophysics and observational astronomy. We first describe a modern requirement of dark matter studies, i.e., the generation of the map of the observable universe, using astrobots. Astrobots differ from conventional two-degree-of-freedom robotic manipulators in two respects. First, the dense formation of astrobots give rise to the extremely overlapping dynamics of neighboring astrobots which make them severely subject to collisions. Second, the structure of astrobots and their mechanical specifications are specialized due to the embedded optical fibers passed through them. We focus on the coordination problem of astrobots whose solutions shall be collision-free, fast execution, and complete in terms of the astrobots' convergence rates. We also illustrate the significant impact of astrobots assignments to observational targets on the quality of coordination solutions To present the current state of the field, we elaborate the open problems including next-generation astrophysical projects including 20,000 astrobots, and other fields, such as space debris tracking, in which astrobots may be potentially used. Astrobotics is an emerging field of swarm robotics aiming to the development and control of astrobots [1, 2] to be of service to astrophysical studies and cosmological spectroscopic observations. In particular, astrobotics addresses a wide range of swarm-robotic-related topics (see, Figure 1) which exhibit challenging problems in design, interaction, coordination, and mission planning corresponding to astrobots. There have been many astrophysical projects, such as the SDSS family [3] which seek the generation of the map of the observable universe.

Mathematical optimization is the workhorse behind several aspects of modern robotics and control. In these applications, the focus is on constrained optimization, and the ability to work on manifolds (such as the classical matrix Lie groups), along with a specific requirement for robustness and speed. In recent years, augmented Lagrangian methods have seen a resurgence due to their robustness and flexibility, their connections to (inexact) proximal-point methods, and their interoperability with Newton or semismooth Newton methods. In the sequel, we present primal-dual augmented Lagrangian method for inequality-constrained problems on manifolds, which we introduced in our recent work, as well as an efficient C++ implementation suitable for use in robotics applications and beyond.

We describe several features of parallel or distributed asynchronous iterative algorithms such as unbounded delays, possible out of order messages or flexible communication. We concentrate on the concept of macroiteration sequence which was introduced in order to study the convergence or termination of asynchronous iterations. A survey of asynchronous iterations for convex optimization problems is also presented. Finally, a new result of convergence for parallel or distributed asynchronous iterative algorithms with flexible communication for convex optimization problems and machine learning is proposed.

Peak detection is a problem in sequential data analysis that involves differentiating regions with higher counts (peaks) from regions with lower counts (background noise). It is crucial to correctly predict areas that deviate from the background noise, in both the train and test sets of labels. Dynamic programming changepoint algorithms have been proposed to solve the peak detection problem by constraining the mean to alternatively increase and then decrease. The current constrained changepoint algorithms only create predictions on the test set, while completely ignoring the train set. Changepoint algorithms that are both accurate when fitting the train set, and make predictions on the test set, have been proposed but not in the context of peak detection models. We propose to resolve these issues by creating a new dynamic programming algorithm, FLOPART, that has zero train label errors, and is able to provide highly accurate predictions on the test set. We provide an empirical analysis that shows FLOPART has a similar time complexity while being more accurate than the existing algorithms in terms of train and test label errors.

In this paper, we consider privacy aspects of wireless federated learning (FL) with Over-the-Air (OtA) transmission of gradient updates from multiple users/agents to an edge server. By exploiting the waveform superposition property of multiple access channels, OtA FL enables the users to transmit their updates simultaneously with linear processing techniques, which improves resource efficiency. However, this setting is vulnerable to privacy leakage since an adversary node can hear directly the uncoded message. Traditional perturbation-based methods provide privacy protection while sacrificing the training accuracy due to the reduced signal-to-noise ratio. In this work, we aim at minimizing privacy leakage to the adversary and the degradation of model accuracy at the edge server at the same time. More explicitly, spatially correlated perturbations are added to the gradient vectors at the users before transmission. Using the zero-sum property of the correlated perturbations, the side effect of the added perturbation on the aggregated gradients at the edge server can be minimized. In the meanwhile, the added perturbation will not be canceled out at the adversary, which prevents privacy leakage. Theoretical analysis of the perturbation covariance matrix, differential privacy, and model convergence is provided, based on which an optimization problem is formulated to jointly design the covariance matrix and the power scaling factor to balance between privacy protection and convergence performance. Simulation results validate the correlated perturbation approach can provide strong defense ability while guaranteeing high learning accuracy.

We propose topology-aware feature partitioning into $k$ disjoint partitions for given scene features as a method for object-centric representation learning. To this end, we propose to use minimum $s$-$t$ graph cuts as a partitioning method which is represented as a linear program. The method is topologically aware since it explicitly encodes neighborhood relationships in the image graph. To solve the graph cuts our solution relies on an efficient, scalable, and differentiable quadratic programming approximation. Optimizations specific to cut problems allow us to solve the quadratic programs and compute their gradients significantly more efficiently compared with the general quadratic programming approach. Our results show that our approach is scalable and outperforms existing methods on object discovery tasks with textured scenes and objects.

In recent years, decentralized bilevel optimization problems have received In recent years, fueled by the rise of machine learning and artificial increasing attention in the networking and machine learning intelligence in edge networks, decentralized bilevel optimization communities thanks to their versatility in modeling decentralized problems have received increasing attention in the networking and learning problems over peer-to-peer networks (e.g., multi-agent machine learning communities. This is due to the versatility of meta-learning, multi-agent reinforcement learning, personalized decentralized bilevel optimization in supporting many decentralized training, and Byzantine-resilient learning). However, for decentralized learning paradigms over peer-to-peer networks, such as the bilevel optimization over peer-to-peer networks with limited multi-agent versions of meta learning [22, 33, 33], hyperparameter computation and communication capabilities, how to achieve low optimization problem[24, 29], area under curve (AUC) problems sample and communication complexities are two fundamental challenges [19, 32], and reinforcement learning[9, 40]. To date, however, that remain under-explored so far. In this paper, we make there remain many challenges and open problems in decentralized the first attempt to investigate the class of decentralized bilevel bilevel learning over peer-to-peer networks. Two of the most optimization problems with nonconvex and strongly-convex structure fundamental challenges in decentralized bilevel optimization are corresponding to the outer and inner subproblems, respectively.

We consider the problem of learning discriminative representations for data in a high-dimensional space with distribution supported on or around multiple low-dimensional linear subspaces. That is, we wish to compute a linear injective map of the data such that the features lie on multiple orthogonal subspaces. Instead of treating this learning problem using multiple PCAs, we cast it as a sequential game using the closed-loop transcription (CTRL) framework recently proposed for learning discriminative and generative representations for general low-dimensional submanifolds. We prove that the equilibrium solutions to the game indeed give correct representations. Our approach unifies classical methods of learning subspaces with modern deep learning practice, by showing that subspace learning problems may be provably solved using the modern toolkit of representation learning. In addition, our work provides the first theoretical justification for the CTRL framework, in the important case of linear subspaces. We support our theoretical findings with compelling empirical evidence. We also generalize the sequential game formulation to more general representation learning problems. Our code, including methods for easy reproduction of experimental results, is publically available on GitHub.

Federated learning is a newly emerging paradigm for machine learning where multiple data holders (clients) collaborate to train a model on their combined dataset. Clients only share partially trained models and other statistics computed from their dataset, keeping their raw data local and private [McMahan et al., 2017, Kairouz et al., 2021]. By obviating the need for a third party to collect and store clients' data, federated learning has several advantages over the classical, centralized paradigm [Dean et al., 2012, Iandola et al., 2016, Goyal et al., 2017]: it ensures clients' consent is tied to the specific task at hand by requiring active participation of the clients in training, confers some basic level of privacy, and has the potential to make machine learning more participatory in general [Kulynych et al., 2020, Jones and Tonetti, 2020]. Further, widespread legislation of data portability and privacy requirements (such as GDPR and CCPA) might even make federated learning a necessity [Pentland et al., 2021]. Collaboration among clients is most attractive when clients have very different subsets of the combined dataset (data heterogeneity).

The robotics community has seen an exponential growth in the level of complexity of the theoretical tools presented for the modeling of soft robotics devices. Different solutions have been presented to overcome the difficulties related to the modeling of soft robots, often leveraging on other scientific disciplines, such as continuum mechanics, computational mechanics and computer graphics. These theoretical and computational foundations are often taken for granted and this leads to an intricate literature that, consequently, has rarely been the subject of a complete review. For the first time, we present here a structured overview of all the approaches proposed so far to model soft robots. The chosen classification, which is based on their theoretical and numerical grounds, allows us to provide a critical analysis about their uses and applicability. This will enable robotics researchers to learn the basics of these modeling techniques and their associated numerical methods, but also to have a critical perspective on their uses.