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# ai

## Basic idea

Construction of agents that perceive and act to maximise some objective. Modern AI is dominated by gradient-based learning on differentiable models.

## Key formulas

* Bayes: $P(h|d) = P(d|h)P(h)/P(d)$
* Expected utility: $\mathbb{E}\[U] = \sum\_a P(a) U(a)$
* Solomonoff prior: $M(x) = \sum\_{p : U(p)=x\*} 2^{-|p|}$