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by Vadim Kosoy 77 days ago | Alex Appel likes this | link | parent | on: Musings on Exploration

A few comments.

Traps are a somewhat bigger issue than you seem to think, when you take acausal attack into account. Your prior contains low complexity hypotheses that intentionally produce good predictions until some critical pivot point at which they switch to something manipulative. So, every time your reach such a pivot point you are facing a decision with irreversible consequences and there is no prior evidence to help you. Delegative learning gets around this my having the agent delegate precisely at the pivot point.

Even disregarding that, “Once the agent has figured out some of how the world works, most environments/hypotheses where there is a trap have evidential clues elsewhere to rule them out” is not quite true.

The notion of a “trap” is relative to the way you organize your uncertainty about the world. Saying that the environment might contain traps is saying that the class of environments you consider is unlearnable. However, the specification of a Bayesian agent only depends on the prior that you get by “averaging” the environments in this class. Different ways of decomposing the prior into hypotheses might yield learnable or unlearnable classes.

For example, consider an environment in which taking action A leads to heaven with probability 70% and hell with probability 30% whereas taking action B leads to heaven with probability 50% and hell with probability 50%. In this environment, taking action A is the better choice and there is no problem. However, if you decompose it into a mixture of deterministic environments then, from that perspective, you have a trap.

To give a “realistic” example, imagine that, we think that quantum random is truly random, but actually there is an underlying theory which allows predicting quantum events deterministically. Then, a strategy that seems optimal from the perspective of an agent that only knows quantum theory might be “suicidal” (permanently sacrificing value) from the perspective of an agent that knows the deeper underlying theory.

As another example, imagine that (i) the only way to escape the heat death of our universe is by controlled vacuum collapse and (ii) because we don’t know in which string vacuum we are, there is no way to be certain about the outcome of a controlled vacuum collapse without high energy experiments that have a significant chance of triggering an uncontrolled vacuum collapse. AFAIK this situation is consistent with our knowledge of physics. So, if you consider the different string vacua to be different hypotheses, we are facing a trap. On the other hand, if you have some theory that gives you a probability distribution over these vacua then there is a well-defined optimal strategy.

The point is, it is probably not meaningful/realistic to claim that we can design an agent that will almost certainly successfully deal with all traps, but it is meaningful and realistic to claim that we can design an agent that will be optimal relatively to our own posterior belief state (which is, more or less by definition, the sort of agent that it is a good idea to build).

The reason “explorative” algorithms such as PSRL (Posterior Sampling Reinforcement Learning) cannot be trivially replaced by the Bayes optimal policy, is that the Bayes optimal policy is (more) computationally intractable. For example, if you consider a finite set of finite MDP hypotheses then PSRL can be implemented in polynomial time but the Bayes optimal policy cannot (in fact I am not 100% sure about this, but I think that hole can be patched using the PCP theorem).

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Delegative Reinforcement Learning solves this problem by keeping humans in the loop while preserving consequentialist reasoning. Ofc currently the theory is based on a lot of simplification and the ultimate learning protocol will probably look differently, but I think that the basic mechanism (delegation combined with model-based reasoning) is sound.

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This is somewhat related to what I wrote about here. If you consider only what I call convex gamblers/traders and fix some weighting (“prior”) over the gamblers then there is a natural convex set of dominant forecasters (for each history, it is the set of minima of some convex function on \(\Delta\mathcal{O}^\omega\).)

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Hi Alex!

The definition of \(h^{!k}\) makes sense for any \(h\), that is, the superscript \(!k\) in this context is a mapping from finite histories to sets of pairs as you said. In the line in question we just apply this mapping to \(x_{:n}\) where \(x\) is a bound variable coming from the expected value.

I hope this helps?

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Indeed there is some kind of length limit in the website. I moved Appendices B and C to a separate post.

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by Vadim Kosoy 211 days ago | link | parent | on: Hyperreal Brouwer

Very nice. I wonder whether this fixed point theorem also implies the various generalization of Kakutani’s fixed point theorem in the literature, such as Lassonde’s theorem about compositions of Kakutani functions. It sounds like it should because the composition of hypercontinuous functions is hypercontinuous, but I don’t see the formal argument immediately since if we have \(x \in *X,\ y \in *Y\) with standard parts \(x_\omega,\ y_\omega\) s.t. \(f(x)=y\), and and \(y' \in *Y,\ z \in *Z\) with standard parts \(y'_\omega=y_\omega,\ z_\omega\) s.t. \(g(y')=z\) then it’s not clear why there should be \(x'\in X,\ z'\in Z\) s.t. with standard parts \(x'_\omega=x_\omega,\ z'_\omega=z_\omega\) s.t. \(g(f(x'))=z'\).

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Freezing the reward seems like the correct answer by definition, since if I am an agent following the utility function \(R\) and I have to design a new agent now, then it is rational for me to design the new agent to follow the utility function I am following now (i.e. this action is usually rated as the best according to my current utility function).

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Unfortunately, it’s not just your browser. The website truncates the document for some reason. I emailed Matthew about it and ey are looking into it.

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I think technical research should be posted here. Moreover, I think that merging IAFF and LW is a bad idea. We should be striving to attract people from mainstream academia / AI research groups rather than making ourselves seem even more eccentric / esoteric.

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Note that the problem with exploration already arises in ordinary reinforcement learning, without going into “exotic” decision theories. Regarding the question of why humans don’t seem to have this problem, I think it is a combination of

  • The universe is regular (which is related to what you said about “we can’t see any plausible causal way it could happen”), so a Bayes-optimal policy with a simplicity prior has something going for it. On the other hand, sometimes you do need to experiment, so this can’t be the only explanation.

  • Any individual human has parents that teach em things, including things like “touching a hot stove is dangerous.” Later in life, ey can draw on much of the knowledge accumulated by human civilization. This tunnels the exploration into safe channels, analogously to the role of the advisor in my recent posts.

  • One may say that the previous point only passes the recursive buck, since we can consider all of humanity to be the “agent”. From this perspective, it seems that the universe just happens to be relatively safe, in the sense that it’s pretty hard for an individual human to do something that will irreparably damage all of humanity… or at least it was the case during most of human history.

  • In addition, we have some useful instincts baked in by evolution (e.g. probably some notion of existing in a three dimensional space with objects that interact mechanically). Again, you could zoom further out and say evolution works because it’s hard to create a species that will wipe out all life.

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