Asynchronous Distributed Optimization Research Articles

Triggered Gradient Tracking for asynchronous distributed optimization

This paper proposes Asynchronous Triggered Gradient Tracking, i.e., a distributed optimization algorithm to solve consensus optimization over networks with asynchronous communication. As a building block, we devise the continuous-time counterpart of the recently proposed (discrete-time) distributed gradient tracking called Continuous Gradient Tracking. By using a Lyapunov approach, we prove exponential stability of the equilibrium corresponding to agents’ estimates being consensual to the optimal solution, with arbitrary initialization of the local estimates. Then, we propose two triggered versions of the algorithm. In the first one, the agents continuously integrate their local dynamics and exchange with neighbors their current local variables in a synchronous way. In Asynchronous Triggered Gradient Tracking, we propose a totally asynchronous scheme in which each agent sends to neighbors its current local variables based on a triggering condition that depends on a locally verifiable condition. The triggering protocol preserves the linear convergence of the algorithm and avoids the Zeno behavior, i.e., an infinite number of triggering events over a finite interval of time is excluded. By using the stability analysis of Continuous Gradient Tracking as a preparatory result, we show exponential stability of the equilibrium point holds for both triggered algorithms and any estimate initialization. Finally, the simulations validate the effectiveness of the proposed methods on a data analytics problem, showing also improved performance in terms of inter-agent communication.

Momentum extrapolation prediction-based asynchronous distributed optimization for power systems

Iterative distributed optimization algorithms usually need synchronization of subproblems at each iteration. An iteration index is defined, and subproblems are solved once at each iteration. This degrades distributed optimization scalability and computational resource under-utilization, particularly if subproblems are heterogeneous. To address these limitations for solving optimal power flow, this paper proposes a prediction-correction-based asynchronous alternating direction method of multipliers (A-ADMM). At the end of each iteration, an OPF subproblem no longer needs to wait for its neighbors’ most updated shared variable information. A momentum-based extrapolation method is developed to predict shared variable values. A correction step is designed using momentum to prevent predicted values from becoming far from the possible solution and avoid divergence. These predictions are integrated into distributed optimization to allow subproblems to be solved continuously with no need for synchronization at each iteration. The proposed A-ADMM reduces the unproductive time and computational resource under-utilization if subproblems are computationally heterogeneous. A-ADMM potentially enhances the solution speed even if subproblems are homogeneous as every iteration k is carried out using a good forecast of shared variable values in iteration k+1. Numerical results show the promising performance of the proposed algorithm.

Event-triggered asynchronous distributed optimization algorithm with heterogeneous time-varying step-sizes

This paper concerns distributed convex optimization problems over time-varying undirected graphs, in which the global objective function is expressed as the sum of individual objective functions of the agents. Each agent only knows its local objective functions. To figure out such problems, an event-triggered asynchronous distributed optimization algorithm (termed as EV-ADOA) with time-varying heterogeneous step-sizes is proposed, which is suitable for undirected graphs changing over time. Under two standard assumptions on strongly convex and smoothness of local objective functions, the EV-ADOA can achieve linear convergence with a proper upper bound of the heterogeneous time-varying step-sizes. EV-ADOA with event-triggered scheme can decrease network communication, and the Zeno-like behavior strictly is excluded. The efficiency of EV-ADOA is demonstrated by experiments.

ADMM Optimization Strategies for Wide-Area Oscillation Monitoring in Power Systems Under Asynchronous Communication Delays

In this paper, we present a suite of asynchronous distributed optimization algorithms for wide-area oscillation estimation in power systems using alternating direction method of multipliers (ADMMs). We first pose the estimation problem as a real-time, iterative, and distributed consensus problem. Thereafter, we consider a probabilistic traffic model for modeling delays in any typical wide-area communication network, and study how the delays enter the process of information exchange between distributed phasor data concentrators that are employed to execute this consensus algorithm in a coordinated fashion. Finally, we propose four different strategies by which the convergence rate and accuracy of this consensus algorithm can be made immune to the asynchrony resulting from the network traffic. We carry out extensive simulations to show possible numerical instabilities and sensitivities of the ADMM convergence on our proposed strategies. Our results exhibit a broad view of how the convergence of any distributed estimation algorithm in a generic cyber-physical system depends strongly on the uncertainties of the underlying communication models.

Target to sensor allocation: A hierarchical dynamic Distributed Constraint Optimization approach

Distributed target allocation and tracking is an important research problem. This problem is complex but has many applications in various domains, including, pervasive computing, surveillance and military systems. In this paper we propose a technique to solve the target to sensor allocation problem by modeling the problem as a hierarchical Distributed Constraint Optimization Problem (HDCOP). Distributed Constrain Optimization Problems (DCOPs) tend to be computationally expensive and often intractable, particularly in large problem spaces such as Wireless Sensor Networks (WSNs). To address this challenge we propose changing the sensor to target allocation as a hierarchical set of smaller DCOPs with a shared system of constraints. Thus, we avoid significant computational and communication costs. Furthermore, in contrast to other DCOP modeling methods, a non-binary variable modeling is employed to reduce the number of intra-agent constraints. To evaluate the performance of the proposed approach, we use the surveillance system of the Regional Waterloo Airport as a test case. Two DCOP solution algorithms are considered, namely, the Distributed Breakout Algorithm (DBA) and the Asynchronous Distributed Optimization (ADOPT). We evaluate the computational and communication costs of these two algorithms for solving the target to sensor allocation problem using the proposed hierarchical formulation. We compare the performance of these algorithms with respect to the incurred computational and communication costs.

ADOPT-ing: unifying asynchronous distributed optimization with asynchronous backtracking

This article presents an asynchronous algorithm for solving distributed constraint optimization problems (DCOPs). The proposed technique unifies asynchronous backtracking (ABT) and asynchronous distributed optimization (ADOPT) where valued nogoods enable more flexible reasoning and more opportunities for communication, leading to an important speed-up. While feedback can be sent in ADOPT by COST messages only to one predefined predecessor, our extension allows for sending such information to any relevant agent. The concept of valued nogood is an extension by Dago and Verfaille of the concept of classic nogood that associates the list of conflicting assignments with a cost and, optionally, with a set of references to culprit constraints. DCOPs have been shown to have very elegant distributed solutions, such as ADOPT, distributed asynchronous overlay (DisAO), or DPOP. These algorithms are typically tuned to minimize the longest causal chain of messages as a measure of how the algorithms will scale for systems with remote agents (with large latency in communication). ADOPT has the property of maintaining the initial distribution of the problem. To be efficient, ADOPT needs a preprocessing step consisting of computing a Depth-First Search (DFS) tree on the constraint graph. Valued nogoods allow for automatically detecting and exploiting the best DFS tree compatible with the current ordering. To exploit such DFS trees it is now sufficient to ensure that they exist. Also, the inference rules available for valued nogoods help to exploit schemes of communication where more feedback is sent to higher priority agents. Together they result in an order of magnitude improvement.