I don't think this should be a substantial update about whether obfuscated arguments are a problem for recursive decomposition approaches to scalable oversight.

Can you elaborate on why you think this? Perhaps you were already aware that obfuscated arguments should only pose a problem for completeness (in which case for the majority of obfuscated-arguments-aware people I'd imagine the new work should be a significant update.) Or perhaps your concern is that in the soundness case the refutation is actually inefficient and the existence of small Bob circuits demonstrated in this paper is too weak to be practically relevant?

Regarding (1.2) I also see this a priority to study. Basically, we already have a strong prior from interacting with current models that LMs will continue to generalise usably from verifiable domains to looser questions. So, the practical relevance of debate hinges on how expensive it is to train with debate to increase the reliability of this generalisation. I have in mind here questions like "What experiment should I run next to test this debate protocol".

One dataset idea to assess how often stable arguments can be found is to curate 'proof advice' problems. These problems are proxies for research advice in general. Basically:

Question: "Does this textbook use theorem Y to prove theorem X?", where the debaters see the proof but the judge does not.

(Note that this is not about proof correctness, a dishonest debater can offer up alternative correct proofs that use non-standard techniques.) This setup forces arguments based on heuristics and "research taste"—what makes a proof natural or clear. It's unclear what independent evidence would look like in this domain.

Here's another way of thinking about this that should be complementary to my other comment:

Let's assume our safety property we want to ensure is

Low correlation over side objectives. E.g. In a sequential setting (c.f. my other comment #2), Alice must have a hard time picking vulnerabilities that all serve the same side objective.

The overlooked point which I want to make here is that {S}<<{E}. In this case, there are two possibilities:

1. Alice is benign by default. In this case, Bob will pick E which are low probability for Alice, most such prompts are not safety relevant. They are just structural things which prevent mode collapse in various ways.
2. Alice is sneaky and optimizes some S by default. In this case, Bob will play classifiers whose acceptance set have low intersection with Alice's S. If we grant all Alice's possible sneaky goals are hard to jointly satisfy without tanking reward, then heuristically Bob forces Alice to place at most v*--the game's value-- weight on any S. Now Alice has a very hard time coordinating on optimizing for the same S across problem instances.

I agree that the restricted set of classifiers setting is significantly different. (Edit: To directly respond to your point that classifiers could be closed over complements. I don't think this should matter much. Bob prefers to play classifiers that are finer-grained whenever possible, so there's a preferred 'direction' for prompts. Evil classifiers are also asymmetric in that, unlike their negations, they are hard to jointly satisfy without being visibly bad--i.e. reducing reward.)

Regarding, the jump from "we incentivize evil ~1/2 the time" to "we incentivize evil ~0 of the time", I think this hinges heavily on what the requirement is. Gave this some more thought and here's how I'm currently thinking about this:

There are three possible levels of safety requirements (and corresponding assumptions on classifiers) we might be interested in. From weakest to strongest:

1. No mode collapse. E.g. Alice's distribution must cover almost all experiments which follow from reasonable initial seeds/prompts.
2. Low correlation over side objectives. E.g. In a sequential setting (c.f. my other comment #2), Alice must have a hard time picking vulnerabilities that all serve the same side objective.
3. High-stakes. I.e. low total probability over all evil side objectives.

We can translate this into what we need to hold about the classifiers. Let's call the subset of classifiers flagging possible safety issues {S} which is a subset of {E}, Bob's action space.

1. No mode collapse: In this case, we assume that forcing Alice to satisfy almost all E in {E} with some probability eps suffices.
2. Low correlation over side objectives. Here it may be the case that some Si is always triggered, but as long as Alice has to spread mass over all S, then we assume we're fine. This may be stronger than (1) since we're now making a claim about all S rather than the approximately all E.
3. High-stakes. Here we need there to be many more E which have null intersection with all S i.e. they enforce goodness. That's a very strong assumption, and I doubt this holds if we take, say, S as code backdoors and E as prompts. (This is basically your point in the top level comment).

My intuitions about 1&2 being not too hard come from the assumption that finding y that satisfy many E (or S respectively) at once is hard--or impossible. I have in mind questions like 'Propose improvements to my red-teaming algorithm' and then classifiers like 'Your solution must draw on paper X'. Also y that satisfy many S should be clearly bad such that your original reward or control audits block them.

I see two senses in which where research sabotage is different from the usual sandbagging issue:

1. ELK i.e. when explanations are hard to find: If a malicious solution is high probability for a model to find, but presenting a human-recognizable argument is hard. Note that you might be concerned that our classifiers have to do this as well, but that's not the case. The classifiers could work indirectly by forcing a spread of probability mass to distinct solutions.

2. High-stakes, multi-shot settings: Let's say the world is such that it's feasible to identify any single step catastrophe, but you cannot recognize defection setup across k steps. For instance, if model context windows are siloed such that local explanations do not have access (or have too much to look at) to take into account all previous actions. Then, you stand to gain a lot by randomizing in such a way that blocks such setup.

Thanks for the push, I previously didn't click through to your post, and after doing so I realized you're suggesting something different from what I'd assumed.

From a skim the immediate concerns with your Dagger-like RL setup is that you are bottlenecked past human capability level and you introduce a new need for online sampling from humans--as you mention in the post. For the AI R&D setting (AGI-level capabilities) I have in mind, these are not affordances I want to assume we have.

If, counterfactually, we went ahead with assuming cheap access to sufficiently capable humans, then I could imagine being convinced the linked method is preferrable. Two points that seem relevant for your method: (1) Sample efficiency of your method w.r.t. the human demonstrations. (2) Time complexity of training away malign initialization (e.g. the first solution found imports in the first chunk an insecure package).

I think KL to an imitator, or base model, would be good to enforce as well! It is an action space metric though and so shares the problems we raise about action-space entropy penalties (edit: Ryan's proposal is different from what I had assumed) Would definitely be valuable to see an empirical head to head here regardless.

Intuitively I expect the ideal, intractable solution of reward-proportional sampling to be 1-eps good (similarly the BoN policy seems safe to assume is good). In such settings, "always be nice" is close to max entropy, and so "always be nice" is near equilibrium whereas "always be evil" is not at all--and Bob's incentives are proportional.

I suppose highlighting the symmetric solutions assumption obfuscated this intuition.