$5.000: Clarifying the Agent-Like Structure Problem

A few months ago, Thomas Kwa put together a statement of a potential “holy grail” of Selection Theorems and put a prize on it:

The ultimate goal of John Wentworth’s sequence "Basic Foundations for Agent Models" is to prove a selection theorem of the form:

Premise (as stated by John): “a system steers far-away parts of the world into a relatively-small chunk of their state space”Desired conclusion: The system is very likely (probability approaching 1 with increasing model size / optimization power / whatever) consequentialist, in that it has an internal world-model and search process. Note that this is a structural rather than behavioral property.

John has not yet proved such a result and it would be a major advance in the selection theorems agenda. I also find it plausible that someone without specific context could do meaningful work here. As such, I’ll offer a $5000 bounty to anyone who finds a precise theorem statement and beats John to the full proof (or disproof + proof of a well-motivated weaker statement). This bounty will decrease to zero as the sequence is completed and over the next ~12 months. Partial contributions will be rewarded proportionally.

I’ll call this the Agent-Like Structure Problem for purposes of this post (though I’ll flag that other researchers might prefer a different formulation of the agent-like structure problem). For some background on why we might expect a theorem like this, see What’s General-Purpose Search, And Why Might We Expect To See It In Trained ML Systems?.

Since Thomas’ prize announcement, I’ve had a couple other people ask me about potential prize problems. Such people usually want me to judge submissions for their prize, which is a big ask - good alignment problems are usually not fully formalized, which means judging will inevitably involve explaining to people how their “solution” isn’t really solving the intended problem. That’s a lot of stressful work.

The goal of this post is to explain the Agent-Like Structure Problem (as I see it) in enough detail that I’d be willing-in-principle to judge submissions for a prize on the problem (see final section for terms and conditions). In particular, I’ll talk about various ways in which I expect people will solve the wrong problem.

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