| Abstract: |
| In this talk, we consider how the learning rate affects the performance of a relaxed randomized Kaczmarz algorithm for solving $Ax \approx b + \varepsilon$, where $Ax=b$ is a consistent linear system and $\varepsilon$ has independent mean zero random entries. We derive a learning rate schedule that optimizes a bound on the expected error that is sharp in certain cases; in contrast to the exponential convergence of the standard randomized Kaczmarz algorithm, our optimized bound involves the reciprocal of the Lambert-$W$ function of an exponential. |
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