近期，实验室博士生熊永阳作为第一作者、导师吴立刚教授作为通讯作者的论文“Distributed Online Optimization in Time-Varying Unbalanced Networkswithout Explicit Subgradients”被国际权威期刊IEEE Transactions on Signal Processing录用。

该论文针对时变非平衡有向网络的在线优化问题，提出了基于一致性协议的分布式在线优化算法。与现有相关算法依赖双随机权重矩阵不同，该算法通过动态地构造行随机矩阵并且对零阶梯度信息进行尺度变换，从而解决了时变有向网络中信息传递不平衡的问题，同时移除了算法对真实次梯度信息的需求。论文严格刻画了所提算法的动态Regret界，并且进一步揭示了零阶梯度信息并没有在本质上削弱算法的收敛性能。所提算法拓展了现有分布式在线学习算法的适用范围。论文通过传感器网络中的动态多目标追踪问题和动态稀疏信号恢复问题验证了所提算法的有效性。

Abstract

This paper studies a distributed online constrained optimization problem over time-varying unbalanced digraphs without explicit subgradients. In sharp contrast to the existing algorithms, we design a novel consensus-based distributed online algorithm with a local randomized zeroth-order oracle and then rescale the oracle by constructing row-stochastic matrices, which aims to address the unbalancedness of time-varying digraphs. Under mild conditions, the average dynamic regret over a time horizon is shown to asymptotically converge at a sublinear rate provided that the accumulated variation grows sublinearly with a specific order. Moreover, the counterpart of the proposed algorithm when subgradients are available is also provided, along with its dynamic regret bound, which reflects that the convergence of our algorithm is essentially not affected by the zeroth-order oracle. Simulations on distributed targets tracking problem and dynamic sparse signal recovery problem in sensor networks are employed to demonstrate the effectiveness of the proposed algorithm.