Imperfect World Models are Exploitable

TL;DR

This paper introduces a formal framework for understanding and analyzing model exploitation in reinforcement learning, revealing fundamental limits and proposing a safe horizon for avoiding exploitation.

Contribution

It develops a general theory linking reward hacking and model exploitation, showing exploitation's inevitability on large policy sets and proposing a notion of safe planning horizon.

Findings

Exploitation is unavoidable on large policy sets.

Conditions for unhackability in finite sets do not prevent exploitation.

A safe horizon can be derived to avoid exploitation within certain limits.

Abstract

We propose a novel definition of model exploitation in reinforcement learning. Informally, a world model is exploitable if it implies that one policy should be strictly preferred over another while the environment's true transition model implies the reverse. We analogize our definition with a prior characterization of reward hacking but show that the associated proof of inevitability does not transfer to exploitation. To overcome this obstruction, we develop a general theory of reward hacking and model exploitation that proves that exploitation is essentially unavoidable on large policy sets and yields the corresponding claim for hacking as a special case. Unfortunately, we also find that the conditions that guarantee unhackability in finite policy sets have no counterpart that precludes exploitation. Consequently, we introduce a relaxed notion of exploitation and derive a safe horizon within which it can be avoided. Taken together, our results establish a formal bridge between reward hacking and model exploitation and elucidate the limits of safe planning in world models.