So does that mean a GLUT in the zombie world cannot be conscious, but a GLUT in our world (assuming infinite storage space, since apparently we were able to assume that for the zombie world) can be conscious?

suppose that we (or Omega, since we're going to assume nigh omniscience) asked the person whether JFK was murdered by Lee Harvey Oswald or not, and if they get it wrong, then they are killed/tortured/dust-specked into oblivion/whatever.

Okay, but what is the utility function Omega is trying to optimize?

Let's say you walk up to Omega, tell it "was JFK murdered by Lee Harvey Oswald or not? And by the way, if you get this wrong, I am going to kill you/torture you/dust-spec you."

Unless we've figured out how to build safe oracles, with very high probability, Omega is not a safe oracle. Via https://arbital.com/p/instrumental_convergence/, even though Omega may or may not care if it gets tortured/dust-speced, we can assume it doesn't want to get killed. So what is it going to do?

Do you think it's going to tell you what it thinks is the true answer? Or do you think it's going to tell you the answer that will minimize the risk of it getting killed?

I also inferred rape from the story. It was the part about how in desperation, he reached out and grabbed at her ankle. And then he was imprisoned in response to that.

But what then makes it recommend a policy that we will actually want to implement?

First of all, I'm assuming that we're taking as axiomatic that the tool "wants" to improve itself (or else why would it have even bothered to consider recommending that it be modified to improve itself?); i.e. improving itself is favorable according to its utility function.

Then: It will recommend a policy that we will actually want to implement, because its model of the universe includes our minds and it can see that if it recommends a policy we will actually want to implement leads it to a higher ranked state in its utility function.

To steelman the parent argument a bit, a simple policy can be dangerous, but if an agent proposed a simple and dangerous policy to us, we probably would not implement it (since we could see that it was dangerous), and thus the agent itself would not be dangerous to us.

If the agent were to propose a policy that, as far as we could tell, appears safe, but was in fact dangerous, then simultaneously:

1. We didn't understand the policy.
2. The agent was dangerous to us.

Can you be a bit more specific in your interpretation of AIXI here?

Here are my assumptions, let me know where you have different assumptions:

• Traditional-AIXI is assumed to exists in the same universe as the human who wants to use AIXI to solve some problem.
• Traditional-AIXI has a fixed input channel (e.g. it's connected to a webcam, and/or it receives keyboard signals from the human, etc.)
• Traditional-AIXI has a fixed output channel (e.g. it's connected to a LCD monitor, or it can control a robot servo arm, or whatever).
• The human has somehow pre-provided Traditional-AIXI with some utility function.
• Traditional-AIXI operates in discrete time steps.
• In the first timestep that elapses since Traditional-AIXI is activated, Traditional-AIXI examines the input it receives. It considers all possible programs that take pair (S, A) and emits an output P, where S is the prior state, A is an action to take, and P is the predicted output of taking the action A in state S. Then it discards all programs that would not have produced the input it received, regardless of what S or A it was given. Then it weighs the remaining program according to their Kolmorogov complexity. This is basically the Solomonoff induction step.
• Now Traditional-AIXI has to make a decision about an output to generate. It considers all possible outputs it could produce, and feeds it to the programs under consideration, to produce a predicted next time step. Traditional-AIXI then calculates the expected utility of each output (using its pre-programmed utility function), picks the one with the highest utility, and emits that output. Note that it has no idea how any of its outputs would the universe, so this is essentially a uniformly random choice.
• In the next timestep, Traditional-AIXI reads its inputs again, but this time taking into account what output it has generated in the previous step. It can now start to model correlation, and eventually causation, between its input and outputs. It has a previous state S and it knows what action A it took in its last step. It can further discard more programs, and narrow the possible models that describes the universe it finds itself in.

How does Tool-AIXI work in contrast to this? Holden seems to want to avoid having any utility function pre-defined at all. However, presumably Tool-AIXI still receives inputs and still produces outputs (probably Holden intends not to allow Tool-AIXI to control a robot servo arm, but he might intend for Tool-AIXI to be able to control an LCD monitor, or at the very least, produce some sort of text file as output).

Does Tool-AIXI proceed in discrete time steps gathering input? Or do we prevent Tool-AIXI from running until a user is ready to submit a curated input to Tool-AIXI? If the latter, how quickly to we expect Tool-AIXI to be able to formulate an reasonable model of our universe?

How does Tool-AIXI choose what output to produce, if there's no utility function?

If we type in "Tool-AIXI, please give me a cure for cancer" onto a keyboard attached to Tool-AIXI and submit that as an input, do we think that a model that encodes ASCII, the English language, bio-organisms, etc. has a lower kolmogorov complexity than a model that says "we live in a universe where we receive exactly this hardcoded stream of bytes"?

Does Tool-AIXI model the output it produces (whether that be pixels on a screen, or bytes to a file) as an action, or does it somehow prevent itself from modelling its output as if it were an action that had some effect on the universe that it exists in? If the former, then isn't this just an agenty Oracle AI? If the latter, then what kind of programs is it generate for its model (surely not programs that take (S, A) pairs as inputs, or else what would it use for A when evaluating its plans and predicting the future)?

I think LearnFun might be informative here. https://www.youtube.com/watch?v=xOCurBYI_gY

LearnFun watches a human play an arbitrary NES games. It is hardcoded to assume that as time progresses, the game is moving towards a "better and better" state (i.e. it assumes the player's trying to win and is at least somewhat effective at achieving its goals). The key point here is that LearnFun does not know ahead of time what the objective of the game is. It infers what the objective of the game is from watching humans play. (More technically, it observes the entire universe, where the entire universe is defined to be the entire RAM content of the NES).

I think there's some parallels here with your scenario where we don't want to explicitly tell the AI what our utility function is. Instead, we're pointing to a state, and we're saying "This is a good state" (and I guess either we'd explicitly tell the AI "and this other state, it's a bad state" or we assume the AI can somehow infer bad states to contrast the good states from), and then we ask the AI to come up with a plan (and possibly execute the plan) that would lead to "more good" states.

So what happens? Bit of a spoiler, but sometimes the AI seems to make a pretty good inference for what the utility function a human would probably have had for a given NES game, but sometimes it makes a terrible inference. It never seems to make a "perfect" inference: the even in its best performance, it seems to be optimizing very strange things.

The other part of it is that even if it does have a decent inference for the utility function, it's not always good at coming up with a plan that will optimize that utility function.

The analogy with cryptography is an interesting one, because...

In cryptography, even after you've proven that a given encryption scheme is secure, and that proof has been centuply (100 times) checked by different researchers at different institutions, it might still end up being insecure, for many reasons.

Examples of reasons include:

• The proof assumed mathematical integers/reals, of which computer integers/floating point numbers are just an approximation.
• The proof assumed that the hardware the algorithm would be running on was reliable (e.g. a reliable source of randomness).
• The proof assumed operations were mathematical abstractions and thus exist out of time, and thus neglected side channel attacks which measures how long a physical real world CPU took to execute a the algorithm in order to make inferences as to what the algorithm did (and thus recover the private keys).
• The proof assumed the machine executing the algorithm was idealized in various ways, when in fact a CPU emits heat other electromagnetic waves, which can be detected and from which inferences can be drawn, etc.

Also, if you're going to measure information content, you really need to fix a formal language first, or else "the number of bits needed to express X" is ill-defined.

Basically, learn model theory before trying to wield it.

I don't know model theory, but isn't the crucial detail here whether or not the number of bits needed to express X is finite or infinite? If so, then it seems we can handwave the specific formal language we're using to describe X, in the same way that we can handwave what encoding for Turing Machines generally when talking about Kolmogorov complexity, even though to actually get a concrete integer K(S) representing the Kolmogorovo complexity of a string S requires us to use a fixed encoding of Turing Machines. In practice, we never actually care what the number K(S) is.

I can't directly observe Eliezer winning or losing, but I can make (perhaps very weak) inferences about how often he wins/loses given his writing.

As an analogy, I might not have the opportunity to play a given videogame ABC against a given blogger XYZ that I've never met and will never meet. But if I read his blog posts on ABC strategies, and try to apply them when I play ABC, and find that my win-rate vastly improves, I can infer that XYZ also probably wins often (and probably wins more often than I do).