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# AIXI

## Basic idea

A theoretical mathematical formalism for artificial general intelligence (Marcus Hutter, 2000). Combines Solomonoff induction (universal prior over environments) with sequential decision theory: the agent picks the action that maximises expected future reward summed over all computable environments, weighted by Kolmogorov complexity.

## Key formulas

* $a\_k = \arg\max\_{a\_k} \sum\_{o\_k r\_k} \cdots \max\_{a\_m} \sum\_{o\_m r\_m} (r\_k + \cdots + r\_m) \sum\_{q : U(q,a\_{1..m}) = o\_1 r\_1 \cdots o\_m r\_m} 2^{-|q|}$
* Universal prior: $\xi(x) = \sum\_{p : U(p)=x\*} 2^{-|p|}$
* Uncomputable, but $\varepsilon$-approximable.

Is a theoritical mathematical formalism for artificial general intelligence. AIXI was first proposed by Marcus Hutter.

## Resources

<https://en.wikipedia.org/wiki/AIXI>