Optimal Statistical Rates for Decentralised Non-Parametric Regression with Linear Speed-Up

We analyse the learning performance of Distributed Gradient Descent in the context of multi-agent decentralised non-parametric regression with the square loss function when i.i.d. samples are assigned to agents. We show that if agents hold sufficiently many samples with respect to the network size, then Distributed Gradient Descent achieves optimal statistical rates with a number of iterations that scales, up to a threshold, with the inverse of the spectral gap of the gossip matrix divided by the number of samples owned by each agent raised to a problem-dependent power. The presence of the threshold comes from statistics. It encodes the existence of a "big data" regime where the number of required iterations does not depend on the network topology. In this regime, Distributed Gradient Descent achieves optimal statistical rates with the same order of iterations as gradient descent run with all the samples in the network. Provided the communication delay is sufficiently small, the distributed protocol yields a linear speed-up in runtime compared to the single-machine protocol. This is in contrast to decentralised optimisation algorithms that do not exploit statistics and only yield a linear speed-up in graphs where the spectral gap is bounded away from zero. Our results exploit the statistical concentration of quantities held by agents and shed new light on the interplay between statistics and communication in decentralised methods. Bounds are given in the standard non-parametric setting with source/capacity assumptions

A randomised primal-dual algorithm for distributed radio-interferometric imaging

Next generation radio telescopes, like the Square Kilometre Array, will acquire an unprecedented amount of data for radio astronomy. The development of fast, parallelisable or distributed algorithms for handling such large-scale data sets is of prime importance. Motivated by this, we investigate herein a convex optimisation algorithmic structure, based on primal-dual forward-backward iterations, for solving the radio interferometric imaging problem. It can encompass any convex prior of interest. It allows for the distributed processing of the measured data and introduces further flexibility by employing a probabilistic approach for the selection of the data blocks used at a given iteration. We study the reconstruction performance with respect to the data distribution and we propose the use of nonuniform probabilities for the randomised updates. Our simulations show the feasibility of the randomisation given a limited computing infrastructure as well as important computational advantages when compared to state-of-the-art algorithmic structures.Comment: 5 pages, 3 figures, Proceedings of the European Signal Processing Conference (EUSIPCO) 2016, Related journal publication available at https://arxiv.org/abs/1601.0402

Decentralized Constrained Optimization: Double Averaging and Gradient Projection

In this paper, we consider the convex, finite-sum minimization problem with explicit convex constraints over strongly connected directed graphs. The constraint is an intersection of several convex sets each being known to only one node. To solve this problem, we propose a novel decentralized projected gradient scheme based on local averaging and prove its convergence using only local functions' smoothness

Catching Cheats: Detecting Strategic Manipulation in Distributed Optimisation of Electric Vehicle Aggregators

Given the rapid rise of electric vehicles (EVs) worldwide, and the ambitious targets set for the near future, the management of large EV fleets must be seen as a priority. Specifically, we study a scenario where EV charging is managed through self-interested EV aggregators who compete in the day-ahead market in order to purchase the electricity needed to meet their clients' requirements. With the aim of reducing electricity costs and lowering the impact on electricity markets, a centralised bidding coordination framework has been proposed in the literature employing a coordinator. In order to improve privacy and limit the need for the coordinator, we propose a reformulation of the coordination framework as a decentralised algorithm, employing the Alternating Direction Method of Multipliers (ADMM). However, given the self-interested nature of the aggregators, they can deviate from the algorithm in order to reduce their energy costs. Hence, we study the strategic manipulation of the ADMM algorithm and, in doing so, describe and analyse different possible attack vectors and propose a mathematical framework to quantify and detect manipulation. Importantly, this detection framework is not limited the considered EV scenario and can be applied to general ADMM algorithms. Finally, we test the proposed decentralised coordination and manipulation detection algorithms in realistic scenarios using real market and driver data from Spain. Our empirical results show that the decentralised algorithm's convergence to the optimal solution can be effectively disrupted by manipulative attacks achieving convergence to a different non-optimal solution which benefits the attacker. With respect to the detection algorithm, results indicate that it achieves very high accuracies and significantly outperforms a naive benchmark

Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age

Simultaneous Localization and Mapping (SLAM)consists in the concurrent construction of a model of the environment (the map), and the estimation of the state of the robot moving within it. The SLAM community has made astonishing progress over the last 30 years, enabling large-scale real-world applications, and witnessing a steady transition of this technology to industry. We survey the current state of SLAM. We start by presenting what is now the de-facto standard formulation for SLAM. We then review related work, covering a broad set of topics including robustness and scalability in long-term mapping, metric and semantic representations for mapping, theoretical performance guarantees, active SLAM and exploration, and other new frontiers. This paper simultaneously serves as a position paper and tutorial to those who are users of SLAM. By looking at the published research with a critical eye, we delineate open challenges and new research issues, that still deserve careful scientific investigation. The paper also contains the authors' take on two questions that often animate discussions during robotics conferences: Do robots need SLAM? and Is SLAM solved