Universal artificial intelligence, AIXI

AIXI [’ai̯k͡siː] is a thought experiment about “universal intelligence”. Think of it as “AI if compute were no object”, or, if we’d prefer, “AI at the asymptotic limit of the scaling laws”. It’s basically the most super-possible superintelligence.

It’s not meant to be implemented directly (it’s uncomputable); it’s a gold-standard reference model: “what would a perfectly rational agent look like if it had unlimited computing power?”

The construction is simple in spirit: it combines Solomonoff induction (a universal Bayesian prior over all computable environments) with sequential decision theory (choose actions that maximize expected future reward).

Formally, the value of an action sequence \(a_{1:m}\), given history \(h_t = a_1 o_1 r_1 \dots a_{t-1} o_{t-1} r_{t-1}\), is

\[ V^{\pi}(h_t) \;=\; \mathbb{E}_{\mu \sim \xi} \Bigg[ \sum_{k=t}^{\infty} r_k \;\Big|\; h_t, a_{t:\infty} \sim \pi \Bigg], \]

where:

• \(r_k\) are the rewards,
• \(\pi\) is the policy,
• \(\mu\) ranges over all computable environment distributions,
• \(\xi\) is the Solomonoff mixture prior, weighting each \(\mu\) by \(2^{-K(\mu)}\) with \(K(\mu)\) the Kolmogorov complexity of the environment.

At each step, AIXI chooses the action that maximizes this universal expectation of future reward.

So in words: AIXI is the policy that, in every possible computable world, maximizes expected total reward, weighted by how simple the world’s description is. This makes AIXI maximally intelligent in a precise, technical sense.

But since Kolmogorov complexity is uncomputable, AIXI is uncomputable too. People study approximations such as AIXItl (time- and length-limited), but AIXI’s main role is theoretical: it’s a yardstick for general intelligence, and a source of theorems about what such agents would do.