arXiv subjects

Diyako Ghaderyan

Publications and source records attributed to Diyako Ghaderyan.

4 recordsLinked to original sources

arXiv2026

AdGT: Decentralized Gradient Tracking with Adaptive Per-Agent Stepsizes

In decentralized optimization, gradient-tracking methods typically rely on a single global stepsize. This choice can be conservative when agents have local objectives with different smoothness constants, since the stepsize must remain stable for the agent with the largest smoothness constant. This paper proposes AdGT, a decentralized gradient-tracking method in which each agent adapts its own stepsize using local gradient variation and a single global safety factor. The method reduces fixed-stepsize tuning effort and allows agents to exploit local smoothness information during the iterations. For smooth and strongly convex local objectives over undirected networks, we prove that the analyzed AdGT update converges linearly to the exact consensus optimizer. We also study two adaptive stepsize updates that use changes in the gradient-tracking direction. We characterize when the corresponding candidate determines the stepsize and prove conditional lower and upper stepsize bounds and linear convergence under an additional relative tracking-disagreement condition. Experiments on logistic regression, ridge regression, synthetic quadratic problems, and a linear-regression benchmark against state-of-the-art decentralized solvers show that AdGT often reaches a given accuracy in fewer iterations or gradient evaluations than tuned fixed-stepsize GT and the tested baselines, especially under heterogeneous local smoothness. In the topology experiments, each tested AdGT update uses one common safety factor across all graphs, whereas the fixed GT stepsize is tuned separately for each graph and seed.

math.OC↗

arXiv2024

Federated Smoothing Proximal Gradient for Quantile Regression with Non-Convex Penalties

Distributed sensors in the internet-of-things (IoT) generate vast amounts of sparse data. Analyzing this high-dimensional data and identifying relevant predictors pose substantial challenges, especially when data is preferred to remain on the device where it was collected for reasons such as data integrity, communication bandwidth, and privacy. This paper introduces a federated quantile regression algorithm to address these challenges. Quantile regression provides a more comprehensive view of the relationship between variables than mean regression models. However, traditional approaches face difficulties when dealing with nonconvex sparse penalties and the inherent non-smoothness of the loss function. For this purpose, we propose a federated smoothing proximal gradient (FSPG) algorithm that integrates a smoothing mechanism with the proximal gradient framework, thereby enhancing both precision and computational speed. This integration adeptly handles optimization over a network of devices, each holding local data samples, making it particularly effective in federated learning scenarios. The FSPG algorithm ensures steady progress and reliable convergence in each iteration by maintaining or reducing the value of the objective function. By leveraging nonconvex penalties, such as the minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD), the proposed method can identify and preserve key predictors within sparse models. Comprehensive simulations validate the robust theoretical foundations of the proposed algorithm and demonstrate improved estimation precision and reliable convergence.

cs.LG↗

arXiv2024

Decentralized Smoothing ADMM for Quantile Regression with Non-Convex Sparse Penalties

In the rapidly evolving internet-of-things (IoT) ecosystem, effective data analysis techniques are crucial for handling distributed data generated by sensors. Addressing the limitations of existing methods, such as the sub-gradient approach, which fails to distinguish between active and non-active coefficients effectively, this paper introduces the decentralized smoothing alternating direction method of multipliers (DSAD) for penalized quantile regression. Our method leverages non-convex sparse penalties like the minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD), improving the identification and retention of significant predictors. DSAD incorporates a total variation norm within a smoothing ADMM framework, achieving consensus among distributed nodes and ensuring uniform model performance across disparate data sources. This approach overcomes traditional convergence challenges associated with non-convex penalties in decentralized settings. We present theoretical proofs and extensive simulation results to validate the effectiveness of the DSAD, demonstrating its superiority in achieving reliable convergence and enhancing estimation accuracy compared with prior methods.

cs.LG↗

arXiv2023

A Fast Row-Stochastic Decentralized Method for Distributed Optimization Over Directed Graphs

In this paper, we introduce a fast row-stochastic decentralized algorithm, referred to as FRSD, to solve consensus optimization problems over directed communication graphs. The proposed algorithm only utilizes row-stochastic weights, leading to certain practical advantages in broadcast communication settings over those requiring column-stochastic weights. Under the assumption that each node-specific function is smooth and strongly convex, we show that the FRSD iterate sequence converges with a linear rate to the optimal consensus solution. In contrast to the existing methods for directed networks, FRSD enjoys linear convergence without employing a gradient tracking (GT) technique explicitly, rather it implements GT implicitly with the use of a novel momentum term, which leads to a significant reduction in communication and storage overhead for each node when FRSD is implemented for solving high-dimensional problems over small-to-medium scale networks. In the numerical tests, we compare FRSD with other state-of-the-art methods, which use row-stochastic and/or column-stochastic weights.

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