Johannes Treutlein and Rubi Hudson worked on this post as part of SERI MATS, under the mentorship of Evan Hubinger. Rubi has also received mentorship from Leo Gao. We thank Erik Jenner for helpful discussions and Alexander Pan for bringing the performative prediction literature to our attention.

Update 30 May 2023: We have now published a paper based on our previous post and this post (the material from this post is in Appendix D).

1. Introduction

In our previous post, we analyzed a setting in which an oracle AI is maximizing a strictly proper scoring rule while it can influence the world with its predictions about the probabilities of possible outcomes. In this setting, a prediction is called a fixed point if it accurately reflects the oracle's beliefs about the world, after having made that prediction. We showed that an oracle AI that is maximizing a strictly proper scoring rule may choose to misrepresent its beliefs and not output a fixed point, even if one exists. This is bad since, all else equal, we expect better outcomes when decisions are based on accurate rather than inaccurate reports.

In our previous analysis, we assumed that the oracle jointly optimizes both its prediction and the effect of its prediction on the world. In contrast, in this post we examine cases in which the AI only optimizes its prediction—there is a stop-gradient (Foerster et al., 2018; Demski, 2019) in front of the oracle's model of the world, which prevents optimizing outcomes directly.

This type of cognition could result, for instance, from self-supervised training on historical data. In that case, the AI may learn a robust world model, and it may learn to match its predictions to its beliefs about the world. However, the AI may never learn to optimize outcomes through its prediction, since this yields no advantage on the training data, which cannot be influenced by the AI.

Consider a situation where this oracle makes a prediction that can influence the world, and assume it models this influence correctly. Then this could put the AI in a game in which it is trying to make a prediction to match its world model, while the world model updates its beliefs conditional on the AI's prediction. What happens in this game depends on the cognition learned by the AI during training. However, we show that, in contrast to the incentives discussed in our previous post, the only equilibria of this...

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