by Abram Demski 19 days ago | link | parent I’m not convinced exploration doesn’t tile. Exploration steps would not be self-modified away if they’re actually useful/important, and if the agent can recognize this. In the case of chicken-rule, it’s unclear how to make a decision at all without it. Plus, the exploration never needs to occur – though, subjectively, the agent can’t know that, so that doesn’t really effect the question of tiling. But, the agent could see that removing the chicken step removes the ability of the agent to reason about the consequences of alternate actions. I think it’s somewhat plausible that you can get something which needs chicken rule as a foundation, but which can decide not to use it in cases like troll bridge, because it is deciding whether to use the chicken rule for sensible reasons (where “sensible” includes the chicken rule itself). Deciding to use the chicken rule is a transparent-Newcomb-like problem: your behavior in the case that you do see a proof of your own action affects your ability to reason in the case that you don’t. The same things seem to apply to exploration. Given our current level of understanding, chicken rule and true exploration seem closely analogous. However, it’s quite plausible that this will stop being the case with a better understanding. In particular, Sam recently pointed out to me that Löb’s theorem doesn’t go through for $$\Box \phi := \mathbb{P}(\phi) \geq 0.95$$. We have a decent picture of what tiling looks like in pure logical settings, but that’s shaped very highly by Löb’s theorem. So, tiling considerations for exploration could look very different from those for chicken-rule.

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