An Asynchronous Distributed Proximal Gradient Method for Composite Convex Optimization
Authors: Necdet Aybat, Zi Wang, Garud Iyengar
ICML 2015 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we compared DFAL with an ADMM method proposed in (Makhdoumi & Ozdaglar, 2014) on the sparse group LASSO problem with Huber loss: P i=1 β1 x 1+β2 x Gi+ P j=1 hδ a T i (j)x bi , (13) where β1, β2 > 0, Ai Rmi n, bi Rmi, a T i (j) denotes the j-th row of Ai, the Huber loss function hδ(x) := max{tx t2/2 : t [ δ, δ]}, and x Gi := PK k=1 xgi(k) 2 denotes the group norm with respect to the partition Gi of [1, n] := {1, , n} for all i N, i.e., Gi = {gi(k)}K k=1 such that SK k=1 gi(k) = [1, n], and gi(j) gi(k) = for all j = k. In this case, γi(x) := Pmi j=1 hδ a T i (j)x bi and ρi(x) := β1 x 1 + β2 x Gi. Next, we briefly describe the ADMM algorithm in (Makhdoumi & Ozdaglar, 2014), and propose a more efficient variant, SADMM, for (13). |
| Researcher Affiliation | Academia | N. S. Aybat NSA10@PSU.EDU Z. Wang ZXW121@PSU.EDU Penn State University, University Park, PA 16802 USA G. Iyengar GARUD@IEOR.COLUMBIA.EDU Columbia University, New York, NY 10027 USA |
| Pseudocode | Yes | Figure 1. First-order Augmented Lagrangian algorithm; Figure 2. Multi Step Accelerated Prox. Gradient (MS-APG) alg.; Figure 3. Dist. First-order Aug. Lagrangian (DFAL) alg.; Figure 4. Randomized Block Coordinate Descent (RBCD) alg.; Figure 5. Split ADMM algorithm |
| Open Source Code | No | The paper does not provide any explicit statements about open-source code availability or links to repositories for the described methodology. |
| Open Datasets | No | The paper describes how the data for the experiments was generated (e.g., "For test problems in CASE 1, we created a single partition G..."; "For the test problems in CASE 2, we created a different partition Gi...") but does not provide access information (link, DOI, repository, or formal citation) for a publicly available or open dataset. |
| Dataset Splits | No | The paper does not provide specific dataset split information (exact percentages, sample counts, or citations to predefined splits) for training, validation, and test sets. It mentions "test problems" but not in the context of data partitioning splits for reproduction. |
| Hardware Specification | No | The paper does not explicitly describe the hardware used to run its experiments, such as specific CPU/GPU models, memory, or cloud resources. |
| Software Dependencies | Yes | Therefore, in order to be fair, we computed them using an efficient interior point solver MOSEK (ver. 7.1.0.12). |
| Experiment Setup | Yes | In our experiments, the network was either a star tree or a clique with either 5 or 10 nodes. The remaining problem parameters defining {ρi, γi}i N were set as follows. We set β1 = β2 = 1 N , δ = 1, and K = 10. Let n = Kng for ng {100, 300}, i.e., n {1000, 3000}. We generated partitions {Gi}i N in two different ways. For test problems in CASE 1, we created a single partition G = {g(k)}K k=1 by generating K groups uniformly at random such that |g(k)| = ng for all k; and set Gi = G for all i N, i.e., ρi(x) = ρ(x) := β1 x 1 + β2 x G for all i N. For the test problems in CASE 2, we created a different partition Gi for each node i, in the same manner as in Case 1. For all i N, mi = n 2N , and the elements of Ai Rmi n are i.i.d. with standard Gaussian, and we set bi = Ai x for xj = ( 1)je (j 1)/ng for j [1, n]. ... All the algorithms are terminated when the relative suboptimality, |F (k) F |/|F |, is less then 10 3, and consensus violation, CV(k), is less than 10 4... |