发表机构
University of California Irvine（加州大学尔湾分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种与维度无关的标量通信机制，通过共享种子刷新随机方向传输内积，实现分布式优化，保证强凸成本下指数收敛且无残余误差。
AI 中文摘要
网络上的分布式优化要求智能体反复与邻居交换决策变量。当决策维度 $d$ 较大时，这些交换主导通信成本，这对带宽受限的智能体至关重要。现有解决方案对交换向量进行量化或稀疏化，但每条消息仍随 $d$ 缩放，且压缩误差必须由额外状态补偿。为解决此局限，我们提出一种标量通信机制，其中每条邻居消息携带一个实数，与 $d$ 无关。智能体从共享种子重新生成公共随机方向，仅传输其状态与该方向的内积，并基于邻居状态的秩一代理进行行动，同时保留完整局部梯度。我们针对现有连续时间分布式优化算法开发并分析该机制。对于具有 Lipschitz 梯度的强凸局部成本，我们证明优化器仍是唯一共识均衡，固定方向存在伪均衡，且以足够高频率刷新方向可实现指数均方和几乎必然收敛，具有恒定增益且无残余误差。该框架允许任何各向同性固定范数方向分布，包括 Rademacher、缩放坐标和球面归一化高斯方向；三者均比未归一化高斯方向实现更低的刷新编码方差。方向分布和刷新间隔的影响在仿真中得以展示。
英文摘要
Distributed optimization over networks requires agents to repeatedly exchange decision variables with their neighbors. When the decision dimension $d$ is large, these exchanges dominate the communication cost, which is critical for bandwidth-constrained agents. Existing remedies quantize or sparsify the exchanged vectors, yet each message still scales with $d$ and the compression error must be compensated by additional states. To address this limitation, we propose a scalar-communication mechanism in which every neighbor message carries a single real number regardless of $d$. Agents regenerate a common random direction from a shared seed, transmit only the inner product of their state with that direction, and act on the resulting rank-one surrogate of their neighbors' states while retaining full local gradients. We develop and analyze the mechanism for an existing continuous-time distributed optimization algorithm. For strongly convex local costs with Lipschitz gradients, we show that the optimizer remains the unique consensus equilibrium, that a fixed direction admits spurious equilibria, and that refreshing the direction at a sufficiently high rate yields exponential mean-square and almost-sure convergence with constant gains and no residual error. The framework admits any isotropic fixed-norm direction distribution, including Rademacher, scaled-coordinate, and sphere-normalized Gaussian directions; all three attain lower fresh-encoding variance than unnormalized Gaussian directions. The effects of the direction distribution and the refresh interval are illustrated in~simulations.
