Dona Sarkar posted an update to the known issues section of the announcement last night on the Windows Blog confirming the issue and fortunately, the workaround doesn't require much more than simply being patient. She explains:
IMPORTANT: You may see “Initializing…” when attempting to download this build and the download progress indicator shown when downloading this build may seem broken under Settings > Update & security > Windows Update. It may look like you’re getting stuck at 0% or at other percentages. Ignore the indicator and be patient. The build should download fine, and the installation should kick off.
Dona also linked to a forum post, originally started for issues updating to Build 15019, which did require a bit more work to kick off the update, such as disabling the Windows Update service. This go around however, it is suggested to just be patient until the Update service does its thing.
As of writing, the ISOs for build 15031 haven't yet been made available on the Microsoft download site, but if you are stuck on build 15019 and don't feel like waiting around, you can download build 15025, mount the ISO in Windows Explorer and upgrade that way.
Source: Windows Blog