We consider the measurement model $Y = AX,$ where $X$ and, hence, $Y$ are random variables and $A$ is an a priori known tall matrix. At each time instance, a sample of one of $Y$'s coordinates is available, and the goal is to estimate $\mu := \mathbb{E}[X]$ via these samples. However, the challenge is that a small but unknown subset of $Y$'s coordinates are controlled by adversaries with infinite power: they can return any real number each time they are queried for a sample. For such an adversarial setting, we propose the first asynchronous online algorithm that converges to $\mu$ almost surely. We prove this result using a novel differential inclusion based two-timescale analysis. Two key highlights of our proof include: (a) the use of a novel Lyapunov function for showing that $\mu$ is the unique global attractor for our algorithm's limiting dynamics, and (b) the use of martingale and stopping time theory to show that our algorithm's iterates are almost surely bounded.

该论文提出了一种在对抗性场景下的异步在线算法，利用差分包含和鞅论证了算法的收敛性和界限性，证明了该算法可以稳定地估计随机矩阵模型下的期望值，避免了在小部分噪声下的表现问题。

带对手的在线学习：微分包容分析