Saghar Hosseini

Online distributed optimization via dual averaging

This paper presents a regret analysis on a distributed online optimization problem computed over a network of agents. The goal is to distributively optimize a global objective function which can be decomposed into the summation of convex cost functions associated with each agent. Since the agents face uncertainties in the environment, their cost functions change at each time step. We extend a distributed algorithm based on dual subgradient averaging to the online setting. The proposed algorithm yields an upper bound on regret as a function of the underlying network topology, specifically its connectivity. The regret of an algorithm is the difference between the cost of the sequence of decisions generated by the algorithm and the performance of the best fixed decision in hindsight. A model for distributed sensor estimation is proposed and the corresponding simulation results are presented.

Online Distributed Convex Optimization on Dynamic Networks

This note presents a distributed optimization scheme over a network of agents in the presence of cost uncertainties and over switching communication topologies. Inspired by recent advances in distributed convex optimization, we propose a distributed algorithm based on dual sub-gradient averaging. A convergence rate analysis for the offline optimization, and a regret analysis for the online case, as a function of the underlying dynamic network topology are then presented for both classes of uncertainties. Application of the proposed setup is then discussed for uncertain sensor networks.

Optimal path planning and power allocation for a long endurance solar-powered UAV

In this paper the problem of optimal path planning and power allocation for an Unmanned Aerial Vehicle (UAV) is explored. The UAV is equipped with photovoltaic cells on top of its wings and its energy sources are solar power and rechargeable batteries. The Sun incidence angle on the photovoltaic cells, which subsequently affects energy harvesting, is determined by the attitude of the UAV and the Sun position. The desired optimal path between two given boundary points, is aimed at increasing the amount of energy storage at the final point. Meanwhile, the charging state of the battery, resulting from the power allocation, needs to be determined along with the path planning procedure. Two approaches, nonlinear programming and model reduction, are proposed and their corresponding simulation results are presented and compared.

Optimal path planning for solar-powered UAVs based on unit quaternions

In this paper, we examine a unit quaternion based method to design the optimal paths with maximum sun exposure for unmanned aerial vehicles (UAVs) equipped with photovoltaic cells on their wings. The mission of traveling between two specified boundary points with fixed flying time and constant speed is considered. Since the solar power is the sole source of energy for these UAVs during the flight, we consider the problem of maximizing the incoming solar radiation throughout their trajectory. As the attitude of the UAV directly determines solar intensity normal to the vertical surface of the wing, we use a unit quaternion based method to control the attitude maneuver during the flight interval. Subsequently, the aircraft kinematics are expressed as quadratic functions in terms of unit quaternions which can be solved by a branch and bound approach. Simulation results in two and three dimensions are presented.

Scaling Up Stochastic Dual Coordinate Ascent

Stochastic Dual Coordinate Ascent (SDCA) has recently emerged as a state-of-the-art method for solving large-scale supervised learning problems formulated as minimization of convex loss functions. It performs iterative, random-coordinate updates to maximize the dual objective. Due to the sequential nature of the iterations, it is typically implemented as a single-threaded algorithm limited to in-memory datasets. In this paper, we introduce an asynchronous parallel version of the algorithm, analyze its convergence properties, and propose a solution for primal-dual synchronization required to achieve convergence in practice. In addition, we describe a method for scaling the algorithm to out-of-memory datasets via multi-threaded deserialization of block-compressed data. This approach yields sufficient pseudo-randomness to provide the same convergence rate as random-order in-memory access. Empirical evaluation demonstrates the efficiency of the proposed methods and their ability to fully utilize computational resources and scale to out-of-memory datasets.

Energy-Aware Aerial Surveillance for a Long-Endurance Solar-Powered Unmanned Aerial Vehicles

In this paper, energy optimal surveillance trajectories for unmanned aerial vehicles (UAV) are explored. The main objective is to have maximum sensor coverage range while maintaining a perpetual flight in the presence of uncertainties. A solar-powered UAV is equipped with photovoltaic cells mounted on its wings and rechargeable batteries. The photovoltaic cells generate solar energy based on the position of the sun, attitude of the UAV, and sky clarity. The vehicle aims to optimize the energy storage in the batteries and coverage during the day while the availability of solar radiation is uncertain and the sensor resolution diminishes because of altitude gain. A model for optimal coverage, path planning, and power allocation in a solar-powered UAV is proposed and the corresponding simulation results are presented. In addition, the effect of maximum altitude gain on the energy storage is studied based on a reduced hybrid model. An online setting is proposed to represent the solar radiation uncertainties. T...

Online distributed ADMM via dual averaging

This paper presents a convergence analysis on a distributed Alternating Direction Method of Multipliers (ADMM) algorithm which solves online convex optimization problems under linear constraints. The goal is to distributively optimize a global objective function over a network of decision makers. The global objective function is composed of convex cost functions associated with each agent. The local cost functions can be broken down into two convex functions, one of which is revealed over time to the decision makers and one known a priori. We extend an online ADMM algorithm to a distributed setting based on dual-averaging. We then explore the rate of convergence of the performance of the sequence of decisions generated by the algorithm to the best fixed decision in hindsight. This performance metric is called regret. An upper bound on the regret of the proposed algorithm is presented as a function of the underlying network topology and linear constraints. The online distributed ADMM algorithm is then applied to a formation acquisition problem.