• Aishwarya Pothula

Universal Intelligence: A measure of Machine Intelligence ?

In our weekly lab session, our professor asked " What do you think is intelligence?".


Student 1: Ability to learn, professor.

Professor: Is a circus lion intelligent then?

Student 2: I think all animals are intelligent. In fact all living things. Any living being which is able to survive in its environment is intelligent.

Professor: So, if something survives in its environment, can you call it intelligent?

Student 4: Ability to apply knowledge to achieve a goal

Professor: What is the goal? Who gave the goal? Where is the goal being achieved? What is the motivation?


The rest of the afternoon's discussion continued along similar lines, with our professor playing the Devil's advocate and while we were trying to come up with definitions of intelligence. Like any smart student would do, we googled for a definition and were inundated with numerous definitions.


Definition of Intelligence

Faced with multiple definitions themselves, the authors Shane Legg and Marcus Hutter in their paper, Universal intelligence: A definition of Machine Intelligence, attempt to define intelligence.

The authors have perused definitions given by several experts, extracting the common themes of to arrive at a definition of intelligence in the broadest terms. The common themes expressed are that intelligence is seen as a property of an individual who is interacting with an external environment. Another common notion is that an individual's intelligence is related to their ability to succeed in achieving a goal. Other common ideas stress on the ability to learn, adapt to unforeseen situations and environments. These prevailing themes are evidenced by definitions such as

“Ability to adapt oneself adequately to relatively new situations in life.” -R. Pinter
“A global concept that involves an individual’s ability to act purposefully, think rationally, and deal effectively with the environment.” D. Wechsler

Combining these common threads in the studied descriptions, the authors have proposed the following definition.

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

Formalization of Definition for Machine Intelligence

Using this definition as a starting point, the authors formalize the definition of machine intelligence in the following way.



This equation defines the Universal intelligence of an agent $π$ to be the weighted average of its value function over all environments in the environment space $E$.


Components of the equation Υ(π) is the universal intelligence of an agent π μ ∈ E indicates individual environment μ belongs to the environment space E V_{μ}^π is the value function of π in each environment μ 2^{−K(μ)} is the probability such an environment μ existing in the universe −K(μ) is the kolmogorov complexity of an environment


Reinforcement Learning Framework

For the formalization, the authors depend on the Reinforcement Learning framework. In this framework, as represented in the figure below, an agent, by performing some actions in an environment, tries to solve a goal communicated through rewards and observations from the environment. In the framework, an expected future value V_{μ}^π is the discounted sum of future rewards obtained by an agent π in an environment μ.



In my opinion, the contribution of the Universal Intelligence equation is two-fold. One, the authors have mathematically formalized a way to estimate the probability of an environment existing. Two, the equation also provides a way to grade experiments according to their complexity. Both contribution are possible because of the use of kolmogorov's complexity to model the probability distribution of the environment space.


Kolmogorov's complexity

But, what is kolmogorov's complexity? In simple terms, it is the length of the shortest program from which the desired output can be produced given by K(x) := min_p {l(p) :U(p) =x}. Here p is the program generated by Turing Machine U to generate desired output x. The length of the shortest program is chosen, indicated by min_p, to be the kolmogorov complexity of x. The rationale behind using kolgomorov's complexity to quantify an environment's complexity is that easy environments can be represented using short programs while more complex environments have to be represented using longer programs.


Given the formal definition for universal intelligence, the authors have used it to compare the intelligences of various agents such as

  • A random agent

  • A very specialized agent

  • A general but simple agent

  • A simple agent with more history

  • A simple forward looking agent

  • A very intelligent agent

  • A super intelligent agent

  • A Human

The authors have also conducted a survey of existing test for intelligence and rated then across various factors . The picture below is a summary of the tests surveyed and the factors against which they are compared.


Survey of Tests for Intelligence



My Thoughts

I have two main reservations with regards to the paper. One is that, though machine intelligence has a formal definition, it is not practicable. The reason for impracticability lies in the issue that Kolgomorov's complexity is incomputable. My second reservation lies with their use of rewards-based mechanism to communicate goals to the agents. Firstly, not every goal can be communicated through rewards. Secondly, I feel that the agent should have at least some motivation that is internally generated such as hunger, curiosity etc. This is not possible when goals are designed by the programmer and communicated through rewards. In the author's words, " If we gave the agent complete control over rewards, then our framework would become meaningless".


What I find useful for my research in the paper is a working definition that I can use for intelligence. The survey of existing tests for intelligence and their comparison is very useful.


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