The majority of the driver work is carried out by Microsoft's Xbox One OS driver team in Redmond (or wherever they are based these days) and they work alongside a select team from AMD as and when needed (seeing as they obviously produced the GPU for the system). It is Microsoft that drives the evolution of the drivers and incremental updates may be released to address serious bugs, performance issues, security vulnerabilities, housekeeping, new features, and so forth. At a higher level, it's analogous to the PC world in many ways (e.g. updated driver from X to support new features exposed by DirectX version Y.Z). The beauty, if you can call it that, is the nature of the system and the fact that it's a fixed platform... which causes less headaches for the developers. If, for example, Microsoft were to support DirectX12 on Xbox One then there would be an update to the drivers to support new features made available in that new version of the API. However, legacy and backwards support is essential as they must absolutely not break what worked before.