Distributed optimization over directed graphs with row stochasticity and constraint regularity

A Privacy-Masking Learning Algorithm for Online Distributed Optimization over Time-Varying Unbalanced Digraphs

“…) as the methods in [15,16] with no DP scheme, coinciding with best theoretical regrets obtained by state-of-the-art methods. Moreover, our analysis discloses a trade-off between optimization accuracy and privacy degree by adaptively adjusting the amount of Laplace noises injected.…”

“…However, it requires that each node must acquire its out-degree for restructuring outgoing weights, which is difficult to be completed in a distributed scenario, especially when broadcast-based networks are adopted. In comparison with column-stochastic weight matrices, rowstochastic weight matrices are more practicable and easier to be satisfied, since each node can allocate these weights on messages by itself when received [13,15,16].…”

Distributed Primal-Dual Perturbation Algorithm Over Unbalanced Directed Networks

“…, π N ] ∈ R N be the normalized left eigenvector corresponding to the eigenvalue 1 of W . We note that, under Assumption 1, π is a positive vector [6]. We here consider the following auxiliary variables:…”

“…Let µ be a constant such that µ ∈ (|µ 2 (W )|, 0), where µ 2 (W ) is the second largest eigenvalue of W in modulus. In the following lemma, it is stated that the i-th element of v (k) i computed by (10) converges geometrically to π i (Proposition 1 in [6]). Lemma 3.…”

Distributed gradient descent method with edge‐based event‐driven communication for non‐convex optimization

“…In [2], the authors revealed that consensus control plays a key role in distributed optimization over multi-agent networks. Over the past few years, a wide range of extensions for consensus-based optimization algorithms have been conducted such as optimization for time-varying and directed communication networks [3][4][5], constrained optimization by the ADMM algorithm [6], and gradient tracking algorithms for fast convergence [7].…”