What are "mesa-optimizers"?
Machine learning
An approach to AI in which, instead of designing an algorithm directly, we have the system search through possible algorithms based on how well they do on some training data.
"Mesa" is Greek for inner/within/inside. "Optimizer
Something that can improve some process or physical artifact so that it is fit for a certain purpose or fulfills some set of requirements.
In this context, the "outer problem-solver" is the machine learning process that created the mesa-optimizer.
For example, a human being can be thought of as a mesa-optimizer of evolution. Evolution is an optimizer, which fine-tunes creatures for reproductive fitness. Most creatures have a set program which helps them survive and reproduce, but human beings developed intelligence, itself an optimizing power. While intelligence initially emerged as a solution of the optimization problem of evolution, humans now use intelligence to optimize their own goals, sometimes at the expense of reproductive success.