Distributed Online Convex Optimization on Time-Varying Directed Graphs

Akbari, Mohammad; Gharesifard, Bahman; Linder, Tamás

doi:10.1109/tcns.2015.2505149

Cited by 143 publications

(120 citation statements)

References 21 publications

Supporting

Mentioning

119

Contrasting

Order By: Relevance

“…We consider a network of agents without a central coordination unit that is tasked with solving a global optimization problem in which the objective function is the sum of local costs of the agents, that is, F (x) = fuse and aggregate local information-a process which can be represented through a weight matrix that is in accordance with the network structure. In particular, a common assumption in this line of research is the availability of a doubly stochastic weight matrix (i.e., each row and each column sum up to 1) or a column stochastic one (i.e., each column sums up to 1); see, e.g., [9,17,19,23,24,31,32,38,41] for the former case and [1,29,41,42,46,48] for the latter. Here, the latter case is clearly weaker and, more importantly, allows one to employ the Push-Sum protocol [18] or the technique in [27] in order to asymptotically "balance the graph," thereby achieving exact convergence as a doubly stochastic matrix does in many distributed algorithms.…”

Section: Introductionmentioning

confidence: 99%

Distributed optimization over directed graphs with row stochasticity and constraint regularity

Abed

2019

Automatica

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 99%

Distributed optimization over directed graphs with row stochasticity and constraint regularity

Abed

2019

Automatica

View full text Add to dashboard Cite

“…proper convex extended real-valued function. Let y ⋆ be the minimizer of (5). Suppose that in Algorithm 2 each local step-size α i is chosen such that 0 < α i ≤ 1 Li with…”

Section: Asynchronous Distributed Dual Proximal Gradientmentioning

confidence: 99%

Randomized dual proximal gradient for large-scale distributed optimization

Notarnicola

Notarstefano

2015

2015 54th IEEE Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

In this paper we consider distributed optimization problems in which the cost function is separable (i.e., a sum of possibly non-smooth functions all sharing a common variable) and can be split into a strongly convex term and a convex one. The second term is typically used to encode constraints or to regularize the solution. We propose an asynchronous, distributed optimization algorithm over an undirected topology, based on a proximal gradient update on the dual problem. We show that by means of a proper choice of primal variables, the dual problem is separable and the dual variables can be stacked into separate blocks. This allows us to show that a distributed gossip update can be obtained by means of a randomized block-coordinate proximal gradient on the dual function.

show abstract

“…2) Unlike most consensus-based approaches in [17], [19]- [23], this algorithm does not require the weighting matrix to be doubly-stochastic, which makes it applicable in any directed graphs, since finding a doubly-stochastic weighting matrix for a directed graph is not a trivial task [34], [35]. In addition, this algorithm is allowed to take any positive and non-increasing step-size as compared to those using diminishing and square summable stepsize [17], [18]. The wider range of step-size selection implies a wider range of stability.…”

Section: Introductionmentioning

confidence: 99%

Randomized Gradient-Free Distributed Online Optimization with Time-Varying Cost Functions

Pang

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

This paper presents a randomized gradient-free distributed online optimization algorithm, with a group of agents whose local objective functions are time-varying. It is worth noting that the value of the local objective function is only revealed to the corresponding agent after the decision is made at each time-step. Thus, each agent updates the decision variable using the local objective function value of its last decision and the information collected from its immediate in-neighbors. A randomized gradient-free oracle is built locally in replacement of the true gradient information in guiding the updates of the decision variable. The notion of dynamic regret is brought forward to measure the difference between the total cost incurred by the agent's state estimation and the offline centralized optimal solution where the objective functions are available a priori. Under the assumptions of strongly connected communication graph and bounded subgradients of the local objective functions, we characterize the dynamic regret associated with each agent as a function of the time duration T and the deviation of the minimizer sequence. Averaging the dynamic regret over the time duration, we establish the asymptotic convergence to a small neighborhood of zero with a rate of O(ln T / √ T ). The effectiveness of this algorithm is illustrated through numerical simulations.

show abstract

Distributed Online Convex Optimization on Time-Varying Directed Graphs

Cited by 143 publications

References 21 publications

Distributed optimization over directed graphs with row stochasticity and constraint regularity

Distributed optimization over directed graphs with row stochasticity and constraint regularity

Randomized dual proximal gradient for large-scale distributed optimization

Randomized Gradient-Free Distributed Online Optimization with Time-Varying Cost Functions

Contact Info

Product

Resources

About