Chenguang Xi

On the distributed optimization over directed networks

In this paper, we propose a distributed algorithm, called Directed-Distributed Gradient Descent (D-DGD), to solve multi-agent optimization problems over directed graphs. Existing algorithms mostly deal with similar problems under the assumption of undirected networks, i.e., requiring the weight matrices to be doubly-stochastic. The row-stochasticity of the weight matrix guarantees that all agents reach consensus, while the column-stochasticity ensures that each agents local gradient contributes equally to the global objective. In a directed graph, however, it may not be possible to construct a doubly-stochastic weight matrix in a distributed manner. We overcome this difficulty by augmenting an additional variable for each agent to record the change in the state evolution. In each iteration, the algorithm simultaneously constructs a row-stochastic matrix and a column-stochastic matrix instead of only a doubly-stochastic matrix. The convergence of the new weight matrix, depending on the row-stochastic and column-stochastic matrices, ensures agents to reach both consensus and optimality. The analysis shows that the proposed algorithm converges at a rate of

Optimization over directed graphs: Linear convergence rate

O(\frac{\ln k}{\sqrt{k}})

Distributed dynamic optimization over directed graphs

, where

On the impact of low-rank interference on distributed multi-agent optimization

k

Source localization in complex networks using a frequency-domain approach

is the number of iterations.

Distributed Subgradient Projection Algorithm Over Directed Graphs

This paper considers distributed multi-agents optimization problems where agents collaborate to minimize the sum of locally known convex functions. We focus on the case when the communication between agents is described by a directed graph. The proposed algorithm achieves the best known rate of convergence for this class of problems, O(μk) for 0 < μ < 1, given that the objective functions are strongly-convex, where k is the number of iterations. Moreover, it provides a wider and more realistic range of step-size compared with existing methods.

Distributed Gradient Descent over Directed Graphs

This paper considers distributed convex optimization problems over a multi-agent network, with each agent possessing a dynamic objective function. The agents aim to collectively track the minimum of the sum of locally known time-varying convex functions by exchanging information between the neighbors. We focus on scenarios when the communication among the agents is described by a directed network. We devise an algorithm with a discrete time-sampling scheme such that the distance between any agent estimate and time-varying optimal solutions converges to a steady state error bound whose size is related to the constant step-size and the sampling interval. The convergence rate is shown to be linear given that the objective function is strongly-convex. Numerical simulations demonstrate the practical utility of the proposed approach.

ADD-OPT: Accelerated Distributed Directed Optimization

In this paper, we study the impact of low-rank interference on the problem of optimizing a sum of convex objective functions corresponding to multiple agents. We prove that the impact of interference can mathematically be regarded as additional constraints to original unconstrained optimization. The proposed analysis uses the notion of interference alignment where the agent transmissions are aligned in either the null space or range space of interference. We consider two cases: (i) when the interference is uniquely determined by the transmitter; and, (ii) when the interference is only determined by the receiver. The former requires the null space of the interference while the latter requires the range space. Experiments on distributed source localization demonstrate good performance of our interference cancellation strategy.

DEXTRA: A Fast Algorithm for Optimization Over Directed Graphs

In this paper, we provide a novel frequency-domain approach to locate an arbitrary number of sources in a large number of zones. In typical source localization methods, the sources are assumed to be acoustic or RF; sensors are placed in different zones to listen to these sources where each zone-to-sensor has a unique path loss and delay. Since each zone has a path loss and delay to each sensor, the sensing matrix is full and the problem of source localization effectively reduces to a sparse signal recovery problem. On the contrary, we are interested in scenarios where the sources may not have an acoustic or RF signature, e.g., locating a vehicle with cameras or a rumor in a social network; and a very few sensors may be able to sense the sources due to obstacles/occlusions. In other words, instead of having a full sensing matrix (as in sparse recovery), the sensing matrix is now highly sparse. To this aim, we provide a protocol for the sensors to collaborate among each other and devise a frequency-domain approach to assist an interrogator to locate the source. In particular, an interrogator (e.g., a UAV) analyzes the Frequency-Response (FR) of the collaborated statistic at an arbitrary sensor, and moves to a neighboring sensor whose FR magnitude is the largest among all the neighbors. With carefully designed collaboration, we show that the FR magnitude at any sensor increases in the direction of the source. In order to locate multiple sources, we characterize the diversity in the sources to arrive at their successful identification.