I am not sure what you mean by “meets the LIC or similar” in this context. If we consider a predictor which is a learning algorithm in itself (i.e., it predicts by learning from the agent’s past choices),

Yeah, that’s what I meant.

, then the agent will converge to one-boxing. This is because a weak predictor will be fully inside the agent’s prior, so the agent will know that one-boxing for long enough will cause the predictor to fill the box.

Suppose the interval between encounters with the predictor is long enough that, due to the agent’s temporal discounting, the immediate reward of two-boxing outweighs the later gains which one-boxing provides. In any specific encounter with the predictor, the agent may prefer to two-box, but prefer to have been the sort of agent who predictably one-boxes, and also preferring to pre-commit to one-box on the next example if a commitment mechanism exists. (This scenario also requires a carefully tuned strength for the predictor, of course.)

But I wasn’t sure this would be the result for your agent, since you described the agent using the hypothesis which gives the best picture about achievable utility.

As I discussed in Do Sufficiently Advanced Agents Use Logic, what I tend to think about is the case where the agent doesn’t literally encounter the predictor repeatedly in its physical history. Instead, the agent must learn what strategy to use by reasoning about similar (but “smaller”) scenarios. But we can get the same effect by assuming the temporal discounting is steep enough, as above.

I was never convinced that “logical ASP” is a “fair” problem. I once joked with Scott that we can consider a “predictor” that is just the single line of code “return DEFECT” but in the comments it says “I am defecting only because Iknowyou will defect.” It was a joke, but it was half-serious. The notion of “weak predictor” taken to the limit leads to absurdity, and if you don’t take it to the limit it might still lead to absurdity. Logical inductors in one way to try specifying a “weak predictor”, but I am not convinced that settings in which logic is inserted ad hoc should be made into desiderata.

Yeah, it is clear that there has to be a case where the predictor is so weak that the agent should not care. I’m fine with dropping the purely logical cases as desiderata in favor of the learning-theoretic versions. But, the ability to construct analogous problems for logic and for learning theory is notable. Paying attention to that analogy more generally seems like a good idea.

I am not sure we need anarbitrarycutoff. There might be a good solution where the agent can dynamically choose any finite cutoff.

Yeah, I guess we can do a variety of things:

Naming a time limit for the commitment.

Naming a time at which a time limit for the commitment will be named.

Naming an ordinal (in some ordinal notation), so that a smaller ordinal must be named every time-step, until a smaller ordinal cannot be named, at which point the commitment runs out

I suspect I want to evaluate a commitment scheme by asking whether it helps achieve a nice regret-bound notion, rather than defining the regret notion by evaluating regret-with-respect-to-making-commitments.

Thinking about LI policy selection where we choose a slow-growing function * f(n)* which determines how long we think before we choose the policy to follow on day

*–– there’s this weird trade-off between how (apparently) “good” the updatelessness is vs how long it takes to be any good at all. I’m fine with notions of rationality being parameterized by an ordinal or some such if it’s just a choose-the-largest-number game. But in this case, choosing too slow-growing a function makes you worse off; so the fact that the rationality principle is parameterized (by the slow-growing function) is problematic. Choosing a commitment scheme seems similar.*

**n**So it would be nice to have a rationality notion which clarified this situation.

My main concern here is: the case for empirical updatelessness seems strong in realizable situations where the prior is meaningful. Things aren’t as nice in the non-realizable cases such as logical uncertainty. But it doesn’t make sense to abandon updateless principles altogether because of this!

Backwards, thanks!