# Marcus Hutter

Marcus Hutter
Born 1967
Website
http://www.hutter1.net

Marcus Hutter (born 1967) is a German computer scientist and professor at the Australian National University. Hutter was born and educated in Munich, where he studied physics and computer science at the Technical University of Munich. In 2000 he joined Jürgen Schmidhuber's group at the Swiss Artificial Intelligence lab IDSIA, where he developed the first mathematical theory of optimal Universal Artificial Intelligence, based on Kolmogorov complexity and Ray Solomonoff's theory of universal inductive inference. In 2006 he also accepted a professorship at the Australian National University in Canberra.

Hutter's notion of universal AI describes the optimal strategy of an agent that wants to maximize its future expected reward in some unknown dynamic environment, up to some fixed future horizon. This is the general reinforcement learning problem. Solomonoff/Hutter's only assumption is that the reactions of the environment in response to the agent's actions follow some unknown but computable probability distribution.

## Universal artificial intelligence (AIXI)

Hutter uses Solomonoff's inductive inference as a mathematical formalization of Occam's razor.[1] Hutter adds to this formalization the expected value of an action: shorter (Kolmogorov complexity) computable theories have more weight when calculating the expected value of an action across all computable theories which perfectly describe previous observations.[2]

At any time, given the limited observation sequence so far, what is the Bayes-optimal way of selecting the next action? Hutter proved that the answer is to use Solomonoff's universal prior to predict the probability of each possible future, and execute the first action of the best policy [3] (a policy is any program that will output all the next actions and input all the next perceptions up to the horizon). A policy is the best if, on a weighted average of all the possible futures, it will maximize the predicted reward up to the horizon. He called this universal algorithm AIXI.

This is mainly a theoretical result. To overcome the problem that Solomonoff's prior is incomputable, in 2002 Hutter also published an asymptotically fastest algorithm for all well-defined problems. Given some formal description of a problem class, the algorithm systematically generates all proofs in a sufficiently powerful axiomatic system that allows for proving time bounds of solution-computing programs. Simultaneously, whenever a proof has been found that shows that a particular program has a better time bound than the previous best, a clever resource allocation scheme will assign most of the remaining search time to this program. Hutter showed that his method is essentially as fast as the unknown fastest program for solving problems from the given class, save for an additive constant independent of the problem instance. For example, if the problem size is $n$, and there exists an initially unknown program that solves any problem in the class within $n^7$ computational steps, then Hutter's method will solve it within $5n^7 + O(1)$ steps. The additive constant hidden in the $O()$ notation may be large enough to render the algorithm practically infeasible despite its useful theoretical properties.

Several algorithms approximate AIXI to make usable on a modern computer. The more computing power they are given, the more they behave like AIXI (their limit is AIXI).[4][5][6]

## Hutter Prize for Lossless Compression of Human Knowledge

On August 6, 2006, Hutter announced the Hutter Prize for Lossless Compression of Human Knowledge with an initial purse of 50,000 Euros, the intent of which is to encourage the advancement of artificial intelligence through the exploitation of Hutter's theory of optimal universal artificial intelligence.

## References

1. ^ Hutter, M. (2003). "On the existence and convergence of computable universal priors". Algorithmic Learning Theory. Lecture Notes in Computer Science 2842: 298–312. arXiv:cs/0305052. doi:10.1007/978-3-540-39624-6_24. ISBN 978-3-540-20291-2.
2. ^ Hutter 2004
3. ^ Hutter, M. "Principles of Solomonoff induction and AIXI" (PDF).
4. ^ Veness, Joel; Kee Siong Ng; Hutter, Marcus; Uther, William; Silver, David (2009). "A Monte Carlo AIXI Approximation". arXiv:0909.0801 [cs.AI].
5. ^ Veness, Joel; Kee Siong Ng; Hutter, Marcus; Silver, David (2010). "Reinforcement Learning via AIXI Approximation". Proc. 24th AAAI Conference on Artificial Intelligence (AAAI 2010): 605–611. arXiv:1007.2049v1.
6. ^ Pankov, S. (2008). "A computational approximation to the AIXI model". In Pei Wang. Artificial General Intelligence, 2008: Proceedings of the First AGI Conference. IOS Press. pp. 256–267. ISBN 978-1-58603-833-5.