Homework vs. research
On this video by Phanimations, keeping my own experience in mind but not referring to it directly.
There is a crucial difference between problems that behave like homework and those that behave like research. A homework problem has a precise setup and well-specified conditions for success and failure which leak many bits about the solution space. Even if the setup isn't entirely precise or conditions well-specified, they were created by a human, which greatly constrains possibility-space. A research problem, on the other hand, has no such things.
We might say that the fundamental difference between a homework problem and a research problem in this dichotomy is that a homework problem has a prior for which answers are correct, and which are incorrect. Even if you can't backpropagate from that prior to the step-by-step-solution-space, you have something to measure your step-by-step solution's progress against. This makes homework problems much easier, as a class. (Interestingly, this implies that difficulty in evaluation is core to agentic work - which matches my experience with LLM agents.)
Almost all single-player video games are about homework problems. Some exceptions are parts of The Witness, Minecraft, and Factorio. Improving at most multi-player video games is a research problem.
Ideally, you should seek to turn research problems into homework problems. Have something to measure your work against that is as close to individual steps as possible. It's especially helpful if this can tell you whether you might be far off from the solution (requiring rethinking deep into the chain of logic, +explore) or nearby (requiring further progress past this point, +exploit). Some priors that seem useful:
- Direct empirical results. See the Wright Brothers.
- A deep prior about what-a-solution-should-look-like. Often aesthetic, like Einstein's strong priors around locality, determinism, symmetries, etc. See Einstein's Speed.
- Experience from similar work or other fields that you can translate into such a prior.
- A strong model of the core problems that need to be solved, so you can notice when progress is groping towards either solving them or dissolving them.