Universal Intelligence: A Definition of Machine Intelligence (0712.3329v1)

Abstract: A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we approach this problem in the following way: We take a number of well known informal definitions of human intelligence that have been given by experts, and extract their essential features. These are then mathematically formalised to produce a general measure of intelligence for arbitrary machines. We believe that this equation formally captures the concept of machine intelligence in the broadest reasonable sense. We then show how this formal definition is related to the theory of universal optimal learning agents. Finally, we survey the many other tests and definitions of intelligence that have been proposed for machines.

• The paper introduces a formal definition of machine intelligence as an agent’s capacity to maximize rewards across a wide range of environments.
• It employs a reinforcement learning framework combined with Kolmogorov complexity to weight environments by simplicity.
• The approach establishes a scalable, objective method for comparing agents, laying the groundwork for future practical intelligence tests.

An Essay on "Universal Intelligence: A Definition of Machine Intelligence" by Shane Legg and Marcus Hutter

Shane Legg and Marcus Hutter address a core issue in the field of machine intelligence: the lack of a unified, formal definition of intelligence applicable to both biological and artificial systems. In their paper, they propose a mathematical formulation of machine intelligence grounded in existing theories of human intelligence, complexity theory, and reinforcement learning. This essay aims to provide an expert-level summary and analysis of their work.

Overview of the Definition

Legg and Hutter's approach begins with the derivation of an informal definition of intelligence informed by expert interpretations. Their refined definition states:

"Intelligence measures an agent’s ability to achieve goals in a wide range of environments."

This definition incorporates three essential elements: agents, environments, and goals. Agents interact with their environments through actions and perceptions, with environments sending rewards to agents based on their actions. The goal of an agent is to maximize these rewards. This setup naturally leads to a reinforcement learning framework, which the authors argue is general enough to encompass various aspects of intelligence.

Formal Agent-Environment Framework

The interaction model is formalized by defining the agent and environment as probability measures within a basic agent-environment framework. The agent's intelligence is formalized using the notion of expected future rewards, discounted appropriately. Notably, the paper adopts a universal approach by aiming for a discount-free value by bounding the total reward sum.

Here, the complexity of environments plays a pivotal role. The authors advocate for leveraging Kolmogorov complexity as a measure to weigh different environments, thereby integrating the principle of Occam's razor. The probability of an environment in this framework is inversely proportional to its complexity, encapsulated in the measure $2^{-K(\mu)}$, where $K(\mu)$ represents the complexity of environment $\mu$.

Universal Intelligence (Υ)

The culmination of these elements is the definition of universal intelligence:

$$\Upsilon(\pi) := \sum_{\mu \in E} 2^{-K(\mu)} V^\pi_\mu$$

In this formula, $V^\pi_\mu$ represents the expected value of the sum of rewards an agent $\pi$ receives in environment $\mu$, and $2^{-K(\mu)}$ embodies the complexity-weighted distribution over all computable environments $E$.

Properties and Implications

Through theoretical analysis, the authors demonstrate that universal intelligence possesses several desirable properties:

• Validity and Informativeness: The measure effectively ranks agents by their ability to achieve goals across a diverse set of environments.
• Scalability: The definition spans the intelligence spectrum from simple agents up to theoretically optimal agents such as AIXI.
• Formalism and Objectivity: The definition is expressed mathematically, leaving little room for ambiguity.

Moreover, the broader implication suggests that achieving high values of $\Upsilon$ requires agents to be capable of dealing with a multitude of environments effectively, echoing human-like adaptability and learning.

Addressing Criticisms and Future Work

Legg and Hutter anticipate several criticisms of their work. They defend against the "No Free Lunch" theorem by emphasizing that their environmental distribution is complexity-weighted, not uniform. They also address philosophical concerns, such as the Blockhead argument, by reaffirming their stance on functionalism: performance, not internal mechanism, is what ultimately constitutes intelligence.

A significant challenge remains: developing a practical intelligence test based on their theoretical foundations. This involves approximating the non-computable elements, such as Kolmogorov complexity. Future work, potentially leveraging Levin’s complexity or Schmidhuber’s Speed prior, may address these computational issues, leading to viable intelligence tests that approximate $\Upsilon$ effectively.

Conclusion

Legg and Hutter's paper lays a robust theoretical foundation for defining and measuring machine intelligence. By integrating elements from complexity theory, reinforcement learning, and human intelligence studies, they provide a nuanced, mathematically rigorous definition. While practical applications will require further development, their work offers a universal framework that could transform our understanding and measurement of machine intelligence, extending beyond anthropocentric biases towards a more inclusive, scalable, and functional conception of intelligence.