by Alex Appel 21 days ago | link | parent I don’t believe that $$x_{:n}^{!k}$$ was defined anywhere, but we “use the definition” in the proof of Lemma 1. As far as I can tell, it’s a set of (j,y) pairs, where j is the index of a hypothesis, and y is an infinite history string, rather like the set $$h^{!k}$$. How do the definitions of $$h^{!k}$$ and $$x^{!k}_{:n}$$ differ?

 by Vadim Kosoy 21 days ago | link 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? reply

### NEW DISCUSSION POSTS

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

 by Paul Christiano on Policy Selection Solves Most Problems | 1 like

>policy selection converges
 by Stuart Armstrong on Policy Selection Solves Most Problems | 0 likes

Indeed there is some kind of
 by Vadim Kosoy on Catastrophe Mitigation Using DRL | 0 likes

Very nice. I wonder whether
 by Vadim Kosoy on Hyperreal Brouwer | 0 likes

Freezing the reward seems
 by Vadim Kosoy on Resolving human inconsistency in a simple model | 0 likes