Implementations can reduce the time required to obtain responses from an automated assistant through proactive caching, locally at a client device, of proactive assistant cache entries - and through on-device utilization of the proactive assistant cache entries. Different proactive cache entries can be provided to different client devices, and various implementations relate to technique(s) utilized in determining which proactive cache entries to provide to which client devices. In some of those implementations, in determining which proactive cache entries to provide (proactively or in response to a request) to a given client device, a remote system selects, from a superset of candidate proactive cache entries, a subset of the cache entries for providing to the given client device.