Tight Convergence Rates for Online Distributed Linear Estimation with Adversarial Measurements
We study mean estimation of a random vector $X$ in a distributed parameter-server-worker setup. Worker $i$ observes samples of $a_i^\top X$, where $a_i^\top$ is the $i$th row of a known sensing matrix $A$. The key challenges are adversarial measurements and asynchrony: a fixed subset of workers may transmit corrupted measurements, and workers are activated asynchronously--only one is active at any time. In our previous work, we proposed a two-timescale $\ell_1$-minimization algorithm and established asymptotic recovery under a null-space-property-like condition on $A$. In this work, we establish tight non-asymptotic convergence rates under the same null-space-property-like condition. We a...
| Authors | Nibedita Roy, Vishal Halder, Gugan Thoppe et al. |
|---|---|
| Primary category | stat.ML |
| Published | 7 April 2026 |
| Last updated at source | 7 April 2026 |
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