Abstract: Byzantine-robust learning has emerged as a prominent fault-tolerant distributed machine learning framework. However, most techniques consider the *static* setting, wherein the identity of Byzantine machines remains fixed during the learning process. This assumption does not capture real-world *dynamic* Byzantine behaviors, which may include transient malfunctions or targeted temporal attacks. Addressing this limitation, we propose $\textsf{DynaBRO}$ -- a new method capable of withstanding $\mathcal{O}(\sqrt{T})$ rounds of Byzantine identity alterations (where $T$ is the total number of training rounds), while matching the asymptotic convergence rate of the static setting. Our method combines a multi-level Monte Carlo (MLMC) gradient estimation technique with robust aggregation of worker updates and incorporates a fail-safe filter to limit bias from dynamic Byzantine strategies. Additionally, by leveraging an adaptive learning rate, our approach eliminates the need for knowing the percentage of Byzantine workers.