The type 1 vs. type 2 feedback distinction here seems really central. I'm interested if this seems like a fair characterization to both of you.

Type 1: Feedback which we use for training (via gradient descent)
Type 2: Feedback which we use to decide whether to deploy trained agent. 

(There's a bit of gray between Type 1 and 2, since choosing whether to deploy is another form of selection, but I'm assuming we're okay stating that gradient descent and model selection operate in qualitatively distinct regimes.)

The key disagreement is whether we expect type 1 feedback will be closer to type 2 feedback, or whether type 2 feedback will be closer to our true goals. If the former, our agents generalizing from type 1 to type 2 is relatively uninformative, and we still have Goodhart. In the latter case, the agent is only very weakly optimizing the type 2 feedback, and so we don't need to worry much about Goodhart, and should expect type 2 feedback to continue track our true goals well.

Main argument for type 1 ~ type 2: by definition, we design type 1 feedback (+associated learning algorithm) so that resulting agents perform well under type 2
Main argument for type 1 !~ type 2: type 2 feedback can be something like 1000-10000x more expensive, since we only have to evaluate it once, rather than enough times to be useful for gradient descent

I'd also be interested to discuss this disagreement in particular, since I could definitely go either way on it. (I plan to think about it more myself.)

Okay, that makes sense (and seems compelling, though not decisive, to me). I'm happy to leave it here - thanks for the answers!

It seems like you should either run separate models for D and D*, or jointly train the model on both D and D*, definitely you shouldn't train on D then run on D* (and you don't need to!).

Sorry yes, you're completely right. (I previously didn't like that there's a model trained on $E_{z\sim Z,D}\left[P_{H^A}\right(y|x,z\left)\right]$ which only gets used for finding z*, but realized it's not a big deal.)

The goal is to be as good as an unaligned ML system though, not just to be better than humans. And the ML system updates on D, so we need to update on D too.

I agree - I mean for the alternative to be running IDA on D*, using D as an auxiliary input (rather than using indirection through Mz). In other words, if we need IDA to access a large context Mz, we could also use IDA to access a large context D? Without something like the distilled core assumption, I'm not sure if there are major advantages one way or the other?

OTOH, with something like the distilled core assumption, it's clearly better to go through Mz, because Mz is much smaller than D (I think of this as amortizing the cost of distilling D).

Thanks. This is helpful. I agree that LTP with the distilled core assumption buys us a lot, both theoretically and probably in practice too.

> The distilled core assumption seems right to me because the neural network weights are already a distilled representation of D, and we only need to compete with that representation... My main reservation is that this seems really hard... If we require competitiveness then it seems like z has to look quite a lot like the weights of a neural network

Great, agreed with all of this.

> In writing the original post I was imagining z* being much bigger than a neural network but distilled by a neural network in some way. I've generally moved away from that kind of perspective, partly based on the kinds of considerations in this post

I share the top-line view, but I'm not sure what issues obfuscated arguments present for large z*, other than generally pushing more difficulty onto alignment/debate. (Probably not important to respond to, just wanted to flag in case this matters elsewhere.)

> That said, I'm not sure we require OOD generalization even if we represent z via a model Mz. E.g. suppose that Mz(i) is the ith word of the intractably-large z.

I agree that Mz (= z*) does not require OOD generalization. My claim is that the amplified model using Mz involves a ML model which must generalize OOD. On D, our y-targets are $P_{H^A}(y|x,Mz)$ where $H^A$ is an amplified human. On D*, our y-targets are similarly $P_{H^A}(y\ast |x\ast ,Mz)$. The key question for me is whether our y-targets on D* are good. If we use the distilled core assumption, they are - they're exactly the predictions the human makes after updating on D. Without it, our y-targets depend on $H^A$, which involves a ML model. 

In particular, I'm assuming H^A is something like human + policy $P_M(y|x,Mz)$, where $P_M$ was optimized to imitate H on D (with z sampled), but is making predictions on D* now. Maybe the picture is that we instead run IDA from scratch on D*? E.g. for amplification, this involves ignoring the models/policies we already have, starting with the usual unaided human supervision on D* at first, and bootstrapping all the way up. I suppose this works, but then couldn't we just have run IDA on D* without access to Mz (which itself can still access superhuman performance)?

I'm trying to get a better handle on what the benefits coming from LTP are. Here's my current picture - are there points here where I've misundersood?
_________

The core problem: We have a training distribution (x, y) ~ D and a deployment distribution (x*, y*) ~ D*, where D != D*. We would rather not rely on ML OOD generalization from D to D*. Instead, we would rather have a human label D*, train an ML model on those labels, and only rely on IID generalization. Suppose D is too large for a human to process. If the human knows how to label D* without learning from D, that’s fine. But D* might be very hard for humans. In particular we need to outperform prosaic ML: the human (before updating on D) needs to outperform an ML model (after updating on D).

Insight from LTP: Ideally, we can compress D into something more manageable: some latent variable z*. Then the human can use z* to predict P_H(y* | x*, z*) instead of just P_H(y* | x*), and can now hopefully outperform the prosaic ML model. The benefit is we can now rely on IID generalization while remaining competitive.

At first, this seems to assume that it is possible to compress the key information in D into a much smaller core z* containing the main insights (distilled core assumption). For example, if D were movements of planets, z* might be the laws of physics. This post argues this is not necessary: by using amplification or debate, the amplified human can use a very large z*. But since the amplification/debate models are ML models, and we’re running these models to aid human decisions on x*, aren’t we back to relying on ML OOD generalization, and so back where we started?