I recently wrote a post about myopia, and one thing I found difficult when writing the post was in really justifying its usefulness. So eventually I mostly gave up, leaving just the point that it can be used for some general analysis (which I still think is true), but without doing any optimality proofs.
But now I’ve been thinking about it further, and I think I’ve realized—don’t we lack formal proofs of the usefulness of myopia in general? Myopia seems to mostly be justified by the observation that we’re already being myopic in some ways, e.g. when training prediction models. But I don’t think anybody has formally proven that training prediction models myopically rather than nonmyopically is a good idea for any purpose?
So that seems like a good first step. But that immediately raises the question, good for what purpose? Generally it’s justified with us not wanting the prediction algorithms to manipulate the real-world distribution of the data to make it more predictable. And that’s sometimes true, but I’m pretty sure one could come up with cases where it would be perfectly fine to do so, e.g. I keep some things organized so that they are easier to find.
It seems to me that it’s about modularity. We want to design the prediction algorithm separately from the agent, so we do the predictions myopically because modifying the real world is the agent’s job. So my current best guess for the optimality criterion of myopic optimization of predictions would be something related to supporting a wide variety of agents.
Yeah, I think usually when people are interested in myopia, it’s because they think there’s some desired solution to the problem that is myopic / local, and they want to try to force the algorithm to find that solution rather than some other one. E.g. answering a question based only on some function of its contents, rather than based on the long-term impact of different answers.
I think that once you postulate such a desired myopic solution and its non-myopic competitors, then you can easily prove that myopia helps. But this still leaves the question of how we know this problems statement is true—if there’s a simpler myopic solution that’s bad, then myopia won’t help (so how can we predict if this is true?) and if there’s a simpler non-myopic solution that’s good, myopia may actively hurt (this one seems a little easier to predict though).
I recently wrote a post about myopia, and one thing I found difficult when writing the post was in really justifying its usefulness. So eventually I mostly gave up, leaving just the point that it can be used for some general analysis (which I still think is true), but without doing any optimality proofs.
But now I’ve been thinking about it further, and I think I’ve realized—don’t we lack formal proofs of the usefulness of myopia in general? Myopia seems to mostly be justified by the observation that we’re already being myopic in some ways, e.g. when training prediction models. But I don’t think anybody has formally proven that training prediction models myopically rather than nonmyopically is a good idea for any purpose?
So that seems like a good first step. But that immediately raises the question, good for what purpose? Generally it’s justified with us not wanting the prediction algorithms to manipulate the real-world distribution of the data to make it more predictable. And that’s sometimes true, but I’m pretty sure one could come up with cases where it would be perfectly fine to do so, e.g. I keep some things organized so that they are easier to find.
It seems to me that it’s about modularity. We want to design the prediction algorithm separately from the agent, so we do the predictions myopically because modifying the real world is the agent’s job. So my current best guess for the optimality criterion of myopic optimization of predictions would be something related to supporting a wide variety of agents.
Yeah, I think usually when people are interested in myopia, it’s because they think there’s some desired solution to the problem that is myopic / local, and they want to try to force the algorithm to find that solution rather than some other one. E.g. answering a question based only on some function of its contents, rather than based on the long-term impact of different answers.
I think that once you postulate such a desired myopic solution and its non-myopic competitors, then you can easily prove that myopia helps. But this still leaves the question of how we know this problems statement is true—if there’s a simpler myopic solution that’s bad, then myopia won’t help (so how can we predict if this is true?) and if there’s a simpler non-myopic solution that’s good, myopia may actively hurt (this one seems a little easier to predict though).