Even granting that it is possible for cosmic rays to flip any given bit, or any sequence of bits, in a computer's memory, it is far from clear to me that the probability of this happening approaches 1 over the lifetime of the universe. It isn't very hard to come up with cases where an event is both completely possible, and has probability 0: for instance, if I pick a number at random with uniform distribution from the closed interval [0,1], the probability I will pick 1 is 0 even though 1 is as likely a choice as any other option on the interval. And in the concrete case you're referring to, the universe has finite time to flip these bits before it sinks into entropy. Moreover, I wouldn't expect the sequence of datapoints needed to convince an AI that humans are hostile (or whatever) to be invariant across time: as the AI accrued more data, it would plausibly require more data to persuade it to change its mind.
I showed recently, predicated on a few assumptions, that a certain agent was asymptotically “benign” with probability 1. (That term may be replaced by something like “domesticated” in the next version, but I’ll use “benign” for now).
This result leaves something to be desired: namely an agent which is safe for its entire lifetime. It seems very difficult to formally show such a strong result for any agent. Suppose we had a design for an agent which did value learning properly. That is, suppose we somehow figured out how to design an agent which understood what constituted observational evidence of humanity’s reflectively-endorsed utility function.
Presumably, such an agent could learn (just about) any utility function depending on what observations it encounters. Surely, there would be a set of observations which caused it to believe that every human was better off dead.
In the presence of cosmic rays, then, one cannot say that agent is safe for its entire lifetime with probability 1 (edited for clarity). For any finite sequence of observations that would cause the agent to conclude that humanity was better off dead, this sequence has strictly positive probability, since with positive probability, cosmic rays will flip every relevant bit in the computer’s memory.
This agent is presumably still asymptotically safe. This is a bit hard to justify without a concrete proposal for what this agent looks like, but at the very least, the cosmic ray argument doesn’t go through. With probability 1, the sample mean of a Bernoulli(θ) random variable (like the indicator of whether a bit was flipped) approaches θ, which is small enough that a competent value learner should be able to deal with it.
This is not to suggest that the value learner is unsafe. Insanely inconvenient cosmic ray activity is a risk I’m willing to take. The takeaway here is that it complicates the question of what we as algorithm designers should aim for. We should definitely be writing down sets assumptions from which we can derive formal results about the expected behavior of an agent, but is there anything to aim for that is stronger than asymptotic safety?