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Bounded Oracle Induction — AI Alignment Forum

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Because logical induction relies on the Brouwer fixed-point theorem, and reflective oracles rely on the Kakutani fixed-point theorem which Brouwer is a special case of, it's possible that logical induction could have been derived for the first time from reflective oracles. Attempting to do this in the most obvious way by having traders output a circuit that takes a binary-search approximation of the market as input doesn't produce any insights in particular. However, by attempting to redevelop the logical induction algorithm from scratch with the aid of a bounded reflective oracle, we arrive at a new way of looking at logical induction, with the following interesting features. 1: It collapses the distinction between the algorithm outputting the trading circuit, and the trading circuit itself. 2: All trades can be naturally interpreted as probability measures over bitstrings, with the reward given by a simple betting game, instead of shares that pay off if some boolean combination is tr

x Bounded Oracle Induction — AI Alignment Forum Logical Induction Logical Uncertainty Oracle AI Frontpage 14 Bounded Oracle Induction by Diffractor 28th Nov 2018 11 min read 0 14 Introduction: Because logical induction relies on the Brouwer fixed-point theorem, and reflective oracles rely on the Kakutani fixed-point theorem which Brouwer is a special case of, it's possible that logical induction could have been derived for the first time from reflective oracles. Attempting to do this in the most obvious way by having traders output a circuit that takes a binary-search approximation of the mark

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