arXiv subjects

Songyi Dian

Publications and source records attributed to Songyi Dian.

3 recordsLinked to original sources

arXiv2026

Stochastic Momentum Tracking Push-Pull for Decentralized Optimization over Directed Graphs

Decentralized optimization over directed networks is frequently challenged by asymmetric communication and the inherent high variance of stochastic gradients, which collectively cause severe oscillations and hinder algorithmic convergence. To address these challenges, we propose the Stochastic Momentum Tracking Push-Pull (SMTPP) algorithm, which tracks the momentum term rather than raw stochastic gradients within the Push-Pull architecture. This design successfully decouples the variance reduction capacity from the algebraic connectivity of the graph.Although the inherent topology mismatch of directed graphs precludes exact convergence under persistent stochastic noise, SMTPP rigorously compresses this unavoidable steady-state error floor into a minimal neighborhood determined by network connectivity and gradient variance. Furthermore, SMTPP guarantees convergence on any strongly connected directed graph. Extensive experiments on non-convex logistic regression demonstrate that the algorithm is highly robust to network connectivity. By effectively dampening topology-induced oscillations, SMTPP achieves convergence rates and overall performance that closely match those of centralized baselines, regardless of whether the network is sparse or dense.

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arXiv2026

Improved Convergence for Decentralized Stochastic Optimization with Biased Gradients

Decentralized stochastic optimization has emerged as a fundamental paradigm for large-scale machine learning. However, practical implementations often rely on biased gradient estimators arising from communication compression or inexact local oracles, which severely degrade convergence in the presence of data heterogeneity. To address the challenge, we propose Decentralized Momentum Tracking with Biased Gradients (Biased-DMT), a novel decentralized algorithm designed to operate reliably under biased gradient information. We establish a comprehensive convergence theory for Biased-DMT in nonconvex settings and show that it achieves linear speedup with respect to the number of agents. The theoretical analysis shows that Biased-DMT decouples the effects of network topology from data heterogeneity, enabling robust performance even in sparse communication networks. Notably, when the gradient oracle introduces only absolute bias, the proposed method eliminates the structural heterogeneity error and converges to the exact physical error floor. For the case of relative bias, we further characterize the convergence limit and show that the remaining error is an unavoidable physical consequence of locally injected noise. Extensive numerical experiments corroborate our theoretical analysis and demonstrate the practical effectiveness of Biased-DMT across a range of decentralized learning scenarios.

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arXiv2025

Geometric Iterative Approach for Efficient Inverse Kinematics and Planning of Continuum Robots with a Floating Base Under Environment Constraints

Continuum robots with floating bases demonstrate exceptional operational capabilities in confined spaces, such as those encountered in medical surgeries and equipment maintenance. However, developing low-cost solutions for their motion and planning problems remains a significant challenge in this field. This paper investigates the application of geometric iterative strategy methods to continuum robots, and proposes the algorithm based on an improved two-layer geometric iterative strategy for motion planning. First, we thoroughly study the kinematics and effective workspace of a multi-segment tendon-driven continuum robot with a floating base. Then, generalized iterative algorithms for solving arbitrary-segment continuum robots are proposed based on a series of problems such as initial arm shape dependence exhibited by similar methods when applied to continuum robots. Further, the task scenario is extended to a follow-the-leader task considering environmental factors, and further extended algorithm are proposed. Simulation comparison results with similar methods demonstrate the effectiveness of the proposed method in eliminating the initial arm shape dependence and improving the solution efficiency and accuracy. The experimental results further demonstrate that the method based on improved two-layer geometric iteration can be used for motion planning task of a continuum robot with a floating base, under an average deviation of about 4 mm in the end position, an average orientation deviation of no more than 1 degree, and the reduction of average number of iterations and time cost is 127.4 iterations and 72.6 ms compared with similar methods, respectively.

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