Intelligent Agent Foundations Forumsign up / log in
Kolmogorov complexity makes reward learning worse
discussion post by Stuart Armstrong 202 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 LINKS

NEW POSTS

NEW DISCUSSION POSTS

RECENT COMMENTS

Note: I currently think that
by Jessica Taylor on Predicting HCH using expert advice | 0 likes

Counterfactual mugging
by Jessica Taylor on Doubts about Updatelessness | 0 likes

What do you mean by "in full
by David Krueger on Doubts about Updatelessness | 0 likes

It seems relatively plausible
by Paul Christiano on Maximally efficient agents will probably have an a... | 1 like

I think that in that case,
by Alex Appel on Smoking Lesion Steelman | 1 like

Two minor comments. First,
by Sam Eisenstat on No Constant Distribution Can be a Logical Inductor | 1 like

A: While that is a really
by Alex Appel on Musings on Exploration | 0 likes

> The true reason to do
by Jessica Taylor on Musings on Exploration | 0 likes

A few comments. Traps are
by Vadim Kosoy on Musings on Exploration | 1 like

I'm not convinced exploration
by Abram Demski on Musings on Exploration | 0 likes

Update: This isn't really an
by Alex Appel on A Difficulty With Density-Zero Exploration | 0 likes

If you drop the
by Alex Appel on Distributed Cooperation | 1 like

Cool! I'm happy to see this
by Abram Demski on Distributed Cooperation | 0 likes

Caveat: The version of EDT
by 258 on In memoryless Cartesian environments, every UDT po... | 2 likes

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

RSS

Privacy & Terms