# AIXI

AIXI is an algorithm for a maximally intelligent agent, developed by Marcus Hutter.

The agent model in which AIXI works is as follows: There is an *agent*, and an *environment*, which is a computable function unknown to the agent. So, the agent will need to have a probability distribution on the range of possible environments. On each clock tick, the agent receives an *observation* (a bitstring/number) from the environment, as well as a reward (another number). The agent then outputs an *action* (another number). Then again, on each iteration, the environment provides an observation and reward as a function of the full history of the interaction, and agent outputs its action likewise. The agent's intelligence is defined by its expected reward across all environments.

AIXI uses Solomonoff induction, a formalization of Occam's Razor, to guess about the nature of its environment. It guesses that less complex environments are more likely than more complex ones. Complexity is measured by the sum of lengths of all programs (in a Turing machine) that would produce a given environment; more complex environments get exponentially less weight. AIXI then calculates the expected reward of each action it might choose and chooses the best one. It does so by extrapolating its actions into the future, using the assumption that at each step into the future it will again choose the best possible action using the same procedure.

AIXI is provably more intelligent than any other possible agent. However, it is not a feasible AI, as Solomonoff induction is not computable; and it evaluates expected value over an infinite set of possible choices. Thus, it does not serve not as a design for a real AI. But is its valuable as a theoretical model of intelligence, as it abstracts away resource limitations that limit the intelligence of and complicate the analysis of real-world AI.

AIXI has also served to inspire a computable variant, AIXItl, which is provably more intelligent within time and space constraints than any other agent with the same constraints. AIXItl too is intractable, but implementable variants such as the Monte Carlo approximation by Veness et al. have shown promising results in simple general-intelligence test problems.

Eliezer Yudkowsky and others have pointed out that AIXI lacks a self-model: It extrapolates its own actions into the future indefinitely, on the assumption that it will keep working in the same way in the future. Though AIXI is an abstraction, any real AI would have a physical embodiment that could be damaged, and an implementation which could change its behavior due to bugs; and the AIXI formalism completely ignores these possibilities. This is called the Anvil problem.

## References

- M. Hutter (2010) Universal Algorithmic Intelligence: A mathematical top->down approach. In Goertzel & Pennachin (eds.), Artificial General Intelligence, 227-287. Berlin: Springer.
- M. Hutter, (2005) Universal Artificial Intelligence: Sequential decisions based on algorithmic probability. Berlin: Springer.
- J. Veness, K.S. Ng, M. Hutter, W. Uther and D. Silver (2011) A Monte-Carlo AIXI Approximation, *Journal of Artiﬁcial Intelligence Research* 40, 95-142]

## Blog posts

- AIXI and Existential Despair by paulfchristiano
- [video] Paul Christiano's impromptu tutorial on AIXI and TDT