Republishing, by definition, is using existing audiences, or updating additional Devices, and/or updating the date ranges in the publish schedule. In about 90% cases, simply choose the Regular audience, Extensions, or both and then hit publish. Leave the defaults (i.e., Renew) as-is. However, we have some great options available for certain circumstances. Note: some options may not be available for all DSPs.

(Default) Publishes the exact audience as created on a schedule to keep it from expiring. Republishes the same exact audience again. Some DSPs flush their audiences periodically and this prevents the audience from being removed and it will continue serving as per the schedule you set up.
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Adds additional Devices to the same audience within the DSP. You set the date range you would like to add when setting up the schedule. No need to reassign the audience to the campaign in the DSP. Original audience minus any Devices we detect as inactive and adding any new Devices seen at the original location(s.) This function takes the same Geoframes, refreshes to the selected lookback period and publishes the new audience. NOTE: Not available for all DSPs.

Similar to Refresh but publishes the new date range as a separate audience in the DSP so you will need to manually assign the new audience for the specified date range to the campaign. This publishes only the "Net New" Devices based on the look back you set up.