Kolmogorov complexity makes reward learning worse
discussion post by Stuart Armstrong 107 days ago | discuss

A putative new idea for AI control; index here.

In a previous post, I argued that Kolmogorov complexity/simplicity priors do not help when learning human values - that some extreme versions of the reward or planners were of roughly equal complexity.

Here I’ll demonstrate that it’s even worse than that: the extreme versions are likely simpler than a “reasonable” one would be.

Of course, as with any statement about Kolmogorov complexity, this is dependent on the computer language used. But I’ll aim to show that for a “reasonable” language, the result holds.

So let $$(p, R)$$ be a reasonable pair that encodes what we want to encode in human rationality and reward. It is compatible with the human policy $$\pi_H$$, in that $$p(R)=\pi_H$$.

Let $$(p_r, R_r)$$ be the compatible pair where $$p_r$$ is the rational Bayesian expected reward maximiser, with $$R_r$$ the corresponding reward so that $$p_r(R_r)=\pi_H$$.

Let $$(p_i, 0)$$ be the indifferent planner (indifferent to the choice of reward), chosen so that $$p_i(R')=\pi_H$$ for all $$R'$$. The reward $$0$$ is the trivial reward.

# Information content present in each pair

The planer $$p_i$$ is simply a map to $$\pi_H$$, so the only information in $$p_i$$ (and $$(p_i, 0)$$) is the definition of $$\pi_H$$.

The policy $$\pi_H$$ and the brief definition of an expected reward maximiser $$p_r$$ are the only information content in $$(p_r, R_r)$$.

On the other hand, $$(p, R)$$ defines not only $$\pi_H$$, but, at every action, it defines the bias or inefficiency of $$\pi_H$$, as the difference between the value of $$\pi_H$$ and the ideal $$R$$-maximising policy $$\pi_R$$. This is a large amount of information, including, for instance, every single human bias and example of bounded rationality.

None of the other pairs have this information (there’s no such thing as bias for the flat reward $$0$$, nor for the expected reward maximiser $$p_r$$), so $$(p, R)$$ contains a lot more information than the other pairs, so we expect it to have higher Kolmogorov complexity.

### NEW DISCUSSION POSTS

[Delegative Reinforcement
 by Vadim Kosoy on Stable Pointers to Value II: Environmental Goals | 1 like

Intermediate update: The
 by Alex Appel on Further Progress on a Bayesian Version of Logical ... | 0 likes

Since Briggs [1] shows that
 by 258 on In memoryless Cartesian environments, every UDT po... | 2 likes

This doesn't quite work. The
 by Nisan Stiennon on Logical counterfactuals and differential privacy | 0 likes

I at first didn't understand
 by Sam Eisenstat on An Untrollable Mathematician | 1 like

This is somewhat related to
 by Vadim Kosoy on The set of Logical Inductors is not Convex | 0 likes

This uses logical inductors
 by Abram Demski on The set of Logical Inductors is not Convex | 0 likes

Nice writeup. Is one-boxing
 by Tom Everitt on Smoking Lesion Steelman II | 0 likes

Hi Alex! The definition of
 by Vadim Kosoy on Delegative Inverse Reinforcement Learning | 0 likes

A summary that might be
 by Alex Appel on Delegative Inverse Reinforcement Learning | 1 like

I don't believe that
 by Alex Appel on Delegative Inverse Reinforcement Learning | 0 likes

This is exactly the sort of
 by Stuart Armstrong on Being legible to other agents by committing to usi... | 0 likes

When considering an embedder
 by Jack Gallagher on Where does ADT Go Wrong? | 0 likes

The differences between this
 by Abram Demski on Policy Selection Solves Most Problems | 1 like

Looking "at the very
 by Abram Demski on Policy Selection Solves Most Problems | 0 likes