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  1. Reward-Punishment Symmetric Universal Intelligence.Samuel Allen Alexander & Marcus Hutter - 2021 - In Samuel Allen Alexander & Marcus Hutter (eds.), AGI.
    Can an agent's intelligence level be negative? We extend the Legg-Hutter agent-environment framework to include punishments and argue for an affirmative answer to that question. We show that if the background encodings and Universal Turing Machine (UTM) admit certain Kolmogorov complexity symmetries, then the resulting Legg-Hutter intelligence measure is symmetric about the origin. In particular, this implies reward-ignoring agents have Legg-Hutter intelligence 0 according to such UTMs.
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  2. Universal Agent Mixtures and the Geometry of Intelligence.Samuel Allen Alexander, David Quarel, Len Du & Marcus Hutter - 2023 - Aistats.
    Inspired by recent progress in multi-agent Reinforcement Learning (RL), in this work we examine the collective intelligent behaviour of theoretical universal agents by introducing a weighted mixture operation. Given a weighted set of agents, their weighted mixture is a new agent whose expected total reward in any environment is the corresponding weighted average of the original agents' expected total rewards in that environment. Thus, if RL agent intelligence is quantified in terms of performance across environments, the weighted mixture's intelligence is (...)
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  3. One decade of universal artificial intelligence.Marcus Hutter - 2012 - In Pei Wang & Ben Goertzel (eds.), Theoretical Foundations of Artificial General Intelligence. Springer. pp. 67--88.
    The first decade of this century has seen the nascency of the first mathematical theory of general artificial intelligence. This theory of Universal Artificial Intelligence (UAI) has made significant contributions to many theoretical, philosophical, and practical AI questions. In a series of papers culminating in book (Hutter, 2005), an exciting sound and complete mathematical model for a super intelligent agent (AIXI) has been developed and rigorously analyzed. While nowadays most AI researchers avoid discussing intelligence, the award-winning PhD thesis (Legg, 2008) (...)
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  4. Probabilities on Sentences in an Expressive Logic.Marcus Hutter, John W. Lloyd, Kee Siong Ng & William T. B. Uther - 2013 - Journal of Applied Logic 11 (4):386-420.
    Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability of being (...)
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  5.  61
    Classification by decomposition: a novel approach to classification of symmetric $$2\times 2$$ games.Mikael Böörs, Tobias Wängberg, Tom Everitt & Marcus Hutter - 2022 - Theory and Decision 93 (3):463-508.
    In this paper, we provide a detailed review of previous classifications of 2 × 2 games and suggest a mathematically simple way to classify the symmetric 2 × 2 games based on a decomposition of the payoff matrix into a cooperative and a zero-sum part. We argue that differences in the interaction between the parts is what makes games interesting in different ways. Our claim is supported by evolutionary computer experiments and findings in previous literature. In addition, we provide a (...)
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