AI 中文总结
本文针对分布式系统的不确定性问题，提出零阶算法实现智能体协作最小化局部CVaR目标平均值，仿真验证了方法的有效性。
AI 中文摘要
分布式系统常运行于不确定性环境中，最小化期望损失可能忽略罕见但严重的事件。本文研究分布式风险厌恶凸优化问题，智能体在时变网络上协作最小化局部条件风险价值（CVaR）目标的平均值。每个智能体仅能获取其局部损失函数的带噪评估，无法获取其CVaR目标或梯度，因此本文开发了一种零阶算法，利用采样损失构造经验CVaR估计及其梯度估计。每次迭代中，智能体结合邻域决策并执行局部更新。在凸性和Lipschitz连续性假设下，本文证明智能体达到精确渐近共识，还建立了加权遍历迭代的有限时间期望次优性界。在递减步长和固定样本量下，局部最后迭代几乎必然收敛到共同最优解，其极限期望CVaR间隙由平滑误差和有限样本误差界定，该分布式界与本文提供的集中式基准的参数依赖匹配。最后，在分布式传感器网络估计问题上的仿真验证了该方法的有效性。
英文摘要
Distributed systems often operate under uncertainty, where minimizing expected loss may overlook rare but severe events. This paper studies a distributed risk-averse convex optimization problem in which agents cooperatively minimize the average of local conditional value-at-risk (CVaR) objectives over a time-varying network. Each agent has access only to noisy evaluations of its local loss function, rather than to its CVaR objective or gradient. We therefore develop a zeroth-order algorithm that uses sampled losses to construct empirical CVaR estimates and their gradient estimates. At each iteration, agents combine neighboring decisions and perform a local update. Under convexity and Lipschitz continuity assumptions, we prove that the agents reach exact asymptotic consensus. We also establish a finite-time expected suboptimality bound for the weighted ergodic iterate. With diminishing step sizes and fixed sample sizes, the local last iterates converge almost surely to a common optimum, and their limiting expected CVaR gap is bounded in terms of the smoothing and finite-sample errors. This distributed bound matches the parameter dependence of the centralized benchmark provided in this paper. Finally, simulations on a distributed sensor network estimation problem illustrate the efficacy of the method.
