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1.A Loophole for Self-Applicative Soundness
discussion post by Alex Appel 137 days ago | Abram Demski likes this | 4 comments
2.Logical Inductor Tiling and Why it's Hard
post by Alex Appel 135 days ago | Sam Eisenstat and Abram Demski like this | discuss

(Tiling result due to Sam, exposition of obstacles due to me)

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3.Logical Inductor Lemmas
discussion post by Alex Appel 146 days ago | discuss
4.Two Notions of Best Response
post by Alex Appel 146 days ago | discuss

In game theory, there are two different notions of “best response” at play. Causal best-response corresponds to standard game-theoretic reasoning, because it assumes that the joint probability distribution over everyone else’s moves remains unchanged if one player changes their move. The second one, Evidential best-response, can model cases where the actions of the various players are not subjectively independent, such as Death in Damascus, Twin Prisoner’s Dilemma, Troll Bridge, Newcomb, and Smoking Lesion, and will be useful to analyze the behavior of logical inductors in repeated games. This is just a quick rundown of the basic properties of these two notions of best response.

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5.Logical Inductors Converge to Correlated Equilibria (Kinda)
post by Alex Appel 146 days ago | Sam Eisenstat and Jessica Taylor like this | 1 comment

Logical inductors of “similar strength”, playing against each other in a repeated game, will converge to correlated equilibria of the one-shot game, for the same reason that players that react to the past plays of their opponent converge to correlated equilibria. In fact, this proof is essentially just the proof from Calibrated Learning and Correlated Equilibrium by Forster (1997), adapted to a logical inductor setting.

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6.Doubts about Updatelessness
discussion post by Alex Appel 169 days ago | Abram Demski likes this | 3 comments
7.Resource-Limited Reflective Oracles
discussion post by Alex Appel 191 days ago | Sam Eisenstat, Abram Demski and Jessica Taylor like this | 1 comment
8.No Constant Distribution Can be a Logical Inductor
discussion post by Alex Appel 195 days ago | Sam Eisenstat, Vadim Kosoy, Abram Demski, Jessica Taylor and Stuart Armstrong like this | 1 comment
9.Musings on Exploration
discussion post by Alex Appel 199 days ago | Vadim Kosoy likes this | 4 comments
10.A Difficulty With Density-Zero Exploration
discussion post by Alex Appel 206 days ago | 1 comment
11.Distributed Cooperation
post by Alex Appel 215 days ago | Abram Demski and Scott Garrabrant like this | 2 comments

Reflective oracles can be approximated by computing Nash equilibria. But is there some procedure that produces a Pareto-optimal equilibrium in a game, aka, a point produced by a Cooperative oracle? It turns out there is. There are some interesting philosophical aspects to it, which will be typed up in the next post.

The result is not original to me, it’s been floating around MIRI for a while. I think Scott, Sam, and Abram worked on it, but there might have been others. All I did was formalize it a bit, and generalize from the 2-player 2-move case to the n-player n-move case. With the formalism here, it’s a bit hard to intuitively understand what’s going on, so I’ll indicate where to visualize an appropriate 3-dimensional object.

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12.Passing Troll Bridge
discussion post by Alex Appel 238 days ago | Abram Demski likes this | discuss
13.Further Progress on a Bayesian Version of Logical Uncertainty
post by Alex Appel 260 days ago | Scott Garrabrant likes this | 1 comment

I’d like to credit Daniel Demski for helpful discussion.

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14.Strategy Nonconvexity Induced by a Choice of Potential Oracles
discussion post by Alex Appel 265 days ago | Abram Demski likes this | discuss
15.Open Problems Regarding Counterfactuals: An Introduction For Beginners
link by Alex Appel 458 days ago | Vadim Kosoy, Tsvi Benson-Tilsen, Vladimir Nesov and Wei Dai like this | 2 comments

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