I wouldn't go so far as to say that there's an engineering solution to the question, yet, but there are some hard facts that suggest which way the answer lies.

Until we figure out superluminal communications, c is going to severely limit what we can accomplish using robots as proxies for humans. Our local "sphere of interest" could be as small as a few tens of lightyears in radius, its size determined by c and the length of a human lifespan (or the human attention span). The bubble grows if we lengthen the human lifespan, or develop the ability to reliably plan and execute multigenerational projects.

c imposes constraints on decision-making latency, and c plus energy requirements limit bandwidth. (Remember how the early deep solar system probes had bit rates in the single digits? That's the energy/bandwidth tradeoff) Those two constraints mean that our ability to monitor a robot and effectively control its actions degrades rapidly with distance.

The obvious solution is one we've been using since the beginning of time: Deploy a human brain close to the action, to drink information directly through high-bandwidth senses, and to make decisions on-the-spot. We figured out distributed intelligence millennia before computers came along. I think that the most effective strategy for interstellar exploration will be a blend of robots and humans, with robots at the leading edge of our sphere of exploration, in a thin shell <100 lightyears beyond the sphere of human exploration. Robots are the cheap pioneers you use in the early stages, but the whole point is to blaze a path for humans to follow.

(The notion of sending an AI is the same strategy implemented in silicon. We're nowhere close to that level of AI, and if we accomplish it, then I'd ask if it isn't six of one half dozen of another? Doesn't that just validate the need for on-site intelligence?)

That's all fine and dandy, but the objections about cost and complexity are certainly valid. Human-crewed starships could be orders of magnitude more expensive than robots. But maybe not as expensive as we're assuming.

There are hidden costs to the way we do spaceflight at our current level of technology, that may skew our evaluation of the scope of effort and cost of interstellar exploration. Fact is, we teleoperate manned missions as well as robotic missions: We fly only a small part of the spacecraft, and leave the bridge on the ground and call it "Mission Control". This works in near-Earth space because c is a negligible consideration. But I think that to explore even our own Solar System effectively, we have to bite the bullet and begin to deploy autonomous spacecraft. We have to fly Mission Control, too.

Looking at the whole picture, then, flying an autonomous spacecraft with its own bridge requires the information processing and decision-making capabilities of several hundred human-level intelligences. I'd keep that in mind when speculating about sending AIs on interstellar missions: We're talking about not one silicon sentient, but the equivalent of hundreds, which reduces the cost advantage of silicon (even if we had human-equivalent AI, and the jury's still out over whether we ever will).

A strategy of exploration through teleoperating interstellar robot probes requires that we maintain a central mission control infrastructure that must last for centuries, and I'm doubtful that we know how to do that yet. The social problem is more daunting the engineering challenges: The support structure must be immune to changes in the political wind and economic fortune and public interest in the mission, and must maintain perfect continuity of record-keeping to match questions and answers separated by decades. It might require designing some sort of quasi-religious order devoted to carrying out the multigenerational mission.

Bottom line, I suspect that the cost differential between human and robotic interstellar missions isn't as wide as we automatically assume, if we take into account all of the cost and effort required to operate a spacecraft. Mostly what we can do is just move the costs around, either front-loading the cost by biting the bullet and building autonomous manned starships; or try to do it on the installment plan through teleoperation of robots, and hope we can keep up the payments down through the centuries.

If we build autonomous human-crewed starships, we could send them off with a clear conscience, knowing that the mission and crew could survive whatever happens here, independent of an umbilical lightyears long. That seems philopsophically correct, considering the argument that we should expand into the galaxy for the security of not having all our eggs in one basket. An interstellar exploration program based on autonomous crewed starships would be not only inherently more robust, it would accomplish the greater purpose of dispersal that, in the long run, will guarantee survival of our species.