Luca Schenato

In this work we focus on the problem of minimizing the sum of convex cost functions in a distributed fashion over a peer-to-peer network. In particular we are interested in the case in which communications between nodes are lossy and the agents are not synchronized among themselves. We address this problem by proposing a modified version of the relaxed ADMM (R-ADMM), which corresponds to the generalized Douglas-Rachford operator applied to the dual of our problem. By exploiting results from operator theory we are then able to prove the almost sure convergence of the proposed algorithm under i.i.d. random packet losses and asynchronous operation of the agents. By further assuming the cost functions to be strongly convex, we are able to prove that the algorithm converges exponentially fast in mean square in a neighborhood of the optimal solution. Moreover, we provide an upper bound to the convergence rate. Finally, we present numerical simulations of the proposed algorithm over random geometric graphs in the aforementioned lossy and asynchronous scenario.

In this paper we propose a distributed implementation
of the relaxed Alternating Direction Method of Multipliers algorithm
(R-ADMM) for optimization of a separable convex cost
function, whose terms are stored by a set of interacting agents,
one for each agent. Specifically  the local cost stored by each node is in
general a function of both the state of the node and the states of its
neighbors, a framework that we refer to as `partition-based' optimization.
This framework presents a great flexibility and can be adapted to a large
number of different applications.
By recasting the problem into an operator theoretical framework, the proposed
algorithm is shown to be provably robust against random packet losses that
might occur in the communication between
neighboring nodes. Finally, the effectiveness of the proposed algorithm is
confirmed by  a set of compelling numerical simulations run over random
geometric graphs subject to i.i.d. random packet losses.

In this work we address the problem of distributed optimization of the sum of convex cost functions in the context of multi-agent systems over lossy communication networks. Building upon operator theory, first, we derive an ADMM-like algorithm, referred to as relaxed ADMM (R-ADMM) via a generalized Peaceman-Rachford Splitting operator on the Lagrange dual formulation of the original optimization problem. This algorithm depends on two parameters, namely the averaging coefficient $\alpha$ and the augmented Lagrangian coefficient $\rho$ and we show that by setting $\alpha=1/2$ we recover the standard ADMM algorithm as a special case. Moreover, first, we reformulate our R-ADMM algorithm into an implementation that presents reduced complexity in terms of memory, communication and computational requirements. Second, we propose a further reformulation which let us provide the first ADMM-like algorithm with guaranteed convergence properties even in the presence of lossy communication. Finally, this work is complemented with a set of compelling numerical simulations of the proposed algorithms over random geometric graphs subject to i.i.d. random packet losses.

We consider the problem of controlling a smart lighting system of multiple luminaires with collocated occupancy and light sensors. The objective is to attain illumination levels higher than specified values (possibly changing over time) at the workplace by adapting dimming levels using sensor information, while minimizing energy consumption. We propose to estimate the daylight illuminance levels at the workplace based on the daylight illuminance measurements at the ceiling. More specifically, this daylight estimator is based on a model built from data collected by light sensors placed at workplace reference points and at the luminaires in a training phase. Three estimation methods are considered: Regularized least squares, locally weighted regularized least squares, and cluster-based regularized least squares. This model is then used in the operational phase by the lighting controller to compute dimming levels by solving a linear programming problem, in which power consumption is minimized under the constraint that the estimated illuminance is higher than a specified target value. The performance of the proposed approach with the three estimation methods is evaluated using an open-office lighting model with different daylight conditions. We show that the proposed approach offers reduced under-illumination and energy consumption in comparison to existing alternative approaches.

In this paper, we study the problem of real-time optimal distributed partitioning for perimeter patrolling in the context of multicamera networks for surveillance, where each camera has limited mobility range and speed, and the communication is unreliable. The objective is to coordinate the cameras in order to minimize the time elapsed between two different visits of each point of the perimeter. We address this problem by casting it into a convex problem in which the perimeter is partitioned into nonoverlapping segments, each patrolled by a camera that sweeps back and forth at the maximum speed. We then propose an asynchronous distributed algorithm that guarantees that these segments cover the whole patrolling perimeter at any time and asymptotically converge to the optimal centralized solution under reliable communication. We finally modify the proposed algorithm in order to attain the same convergence and covering properties even in the more challenging scenario, where communication is lossy and there is no channel feedback, i.e., the transmitting camera is not aware whether a packet has been received or not by its neighbors.