Could there be "natural impact regularization" or "impact regularization by default"?

I think, like a lot of things in agent foundations, this is just another consequence of natural abstractions [? · GW].

The universe naturally decomposes into a hierarchy of subsystems; molecules to cells to organisms to countries. Changes in one subsystem only sparsely interact with the other subsystems, and their impact may vanish entirely at the next level up. A single cell becoming cancerous may yet be contained by the immune system, never impacting the human. A new engineering technique pioneered for a specific project may generalize to similar projects, and even change all such projects' efficiency in ways that have a macro-economic impact; but it will likely not. A different person getting elected the mayor doesn't much impact city politics in neighbouring cities, and may literally not matter at the geopolitical scale.

This applies from the planning direction too. If you have a good map of the environment, it'll decompose into the subsystems reflecting the territory-level subsystems as well. When optimizing over a specific subsystem, the interventions you're considering will naturally limit their impact to that subsystem: that's what subsystemization does, and counteracting this tendency requires deliberately staging sum-threshold attacks [LW · GW] on the wider system, which you won't be doing.

In the Rubik's Cube example, this dynamic is a bit more abstract, but basically still applies. In a way similar to how the "maze" here [LW · GW] kind-of decomposes into a top side and a bottom side.

A complication is that any one agent can only have so much bandwidth, which would sometimes incentivize more blunt control. I've been thinking bandwidth is probably going to become a huge area of agent foundations

I agree. I currently think "bandwidth" in terms like "what's the longest message I can 'inject' into the environment per time-step?" is what "resources" are in information-theoretic terms [LW(p) · GW(p)]. See the output-side bottleneck in this formulation [LW · GW]: resources are the action bandwidth, which is the size of the "plan" into which you have to "compress" your desired world-state if you want to "communicate" it to the environment.

really the instrumental incentive is often to search for "precise" methods of influencing the world, where one can push in a lot of information to effect narrow change

I disagree. I've given it a lot of thoughts (none published yet), but this sort of "precise influence" is something I call "inferential control". It allows you to maximize your impact given your action bottleneck, but this sort of optimization is "brittle". If something unknown unknown happens, the plan you've injected breaks instantly and gracelessly, because the fundamental assumptions on which its functionality relied – the pathways by which it meant to implement its objective – turn out to be invalid.

It sort of naturally favours arithmetic utility maximization over geometric utility maximization [? · GW]. By taking actions that'd only work if your predictions and models are true, you're basically sacrificing your selves living in the timelines that you're predicting to be impossible, and distributing their resources to the timelines you expect to find yourself in.

And this applies more and more the more "optimization capacity" you're trying to push through a narrow bottleneck. E. g., if you want to change the entire state of a giant environment through a tiny action-pinhole, you'd need to do it by exploiting some sort of "snowball effect"/"butterfly effect". Your tiny initial intervention would need to exploit some environmental structures to increase its size, and do so iteratively. That takes time (for whatever notion of "time" applies). You'd need to optimize over a longer stretch of environment-state changes, and your initial predictions need to be accurate for that entire stretch, because you'd have little ability to "steer" a plan that snowballed far beyond your pinhole's ability to control.

By contrast, increasing the size of your action bottleneck is pretty much the definition of "robust" optimization, i. e. geometric utility maximization. It improves your ability to control the states of all possible worlds you may find yourself in, minimizing the need for "brittle" inferential control. It increases your adaptability, basically, letting you craft a "message" comprehensively addressing any unpredicted crisis the environment throws at you, right in the middle of it happening.

See my post Requirements for a STEM-capable AGI Value Learner [LW · GW] for a suggestion of a natural impact regularizer on any approximately-Bayesian agent: large impact actions that could take it out-of-distribution decrease the certainty of its predictions, generally making the results its optimization worse, and anything sufficiently smart will be cautious about doing that.