I've been thinking more about how to teach writing at this moment where AI models have gotten to a level where for most writing that we don’t care that much about, we probably immediately start with them.

From the instructor’s perspective, the design of an assignment can be thought of as “solving” a bi-level optimization problem — something similar to the problems that we would have seen in intermediate microeconomics.

Let’s begin with the “inner” optimization problem. That of the student writing the assignment so as to achieve a relative high grade. Roughly, the objective function consists of the grade — which is a function of the final draft of the paper ($w_n$), and the expectations for the assignment $(p)$ — and the effort of producing the final draft of the paper — here some function associated with the entire sequence of writing.

$$ \underset{\{w\}{t=1}^n}{\text{maximize}} \ G(w_n, p) + \lambda \|\{w_t\}{t=1}^n \| $$

In this viewpoint, students differ in that they apply their own solver to this problem.

$$ \underset{p}{\text{maximize}} \ E_i\big[E_{\varepsilon}[\{w_t^*(\varepsilon, p)\}_{t=1}^{n(i,\varepsilon, p)}] \big] $$