in the set E. Occam's razor is given by the term 2−K(µ) which weights the agent's performance in each environment inversely proportional to its complexity. The definition is very general in terms of which sensors or actuators the agent might have as all information exchanged between the agent and the environment takes place over very general communication channels. Finally, the formal definition places no limits on the internal workings of the agent. Thus, we can apply the definition to any system that is able to receive and generate information with view to achieving goals. The main drawback, however, is that the Kolmogorov complexity function K is not computable and can only be approximated.

This is an important point that we will return to later.

## 3.4 Universal Intelligence Of Various Agents

In order to gain some intuition for our definition of universal intelligence, in this subsection we will consider a range of different agents and their relative degrees of universal intelligence. A random agent. The agent with the lowest intelligence, at least among those that are not actively trying to perform badly, would be one that makes uniformly random actions. We will call this π rand. Although this is clearly a weak agent, we cannot simply conclude that the value of V
π rand µ will always be low as some environments will generate high reward no matter what the agent does. Nevertheless, in general such an agent will not be very successful as it will fail to exploit any regularities in the environment, no matter how simple they are. It follows then that the values of V
π rand µ will typically be low compared to other agents, and thus Υ(π rand) will be low. Conversely, if Υ(π rand) is very low, then the equation for Υ implies that for simple environments, and many complex environments, the value of V
π rand µ must also be relatively low. This kind of poor performance in general is what we would expect of an unintelligent agent. A very specialised agent. From the equation for Υ, we see that an agent could have very low universal intelligence but still perform extremely well at a few very specific and complex tasks. Consider, for example, IBM's Deep Blue chess supercomputer, which we will represent by π dblue. When µ chess describes the game of chess, V
π dblue µchess is very high.

However 2−K(µ chess)is small, and for µ 6= µ chess the value function will be low as π dblue only plays chess. Therefore, the value of Υ(π dblue) will be very low. Intuitively, this is because Deep Blue is too inflexible and narrow to have general intelligence; a characteristic weakness of specialised artificial intelligence systems. A general but simple agent. Imagine an agent that performs very basic learning by building up a table of observation and action pairs and keeping statistics on the rewards that follow. Each time an observation that it has been seen before occurs, the agent takes the action with highest estimated expected reward in the next cycle with 90% probability, or a random action with 10% probability. We will call this agent π basic. It is immediately clear that many environments, both complex and very simple, will have at least some structure that such an agent would take advantage of. Thus, for almost all µ we will have V
π basic µ > V π rand µ and so Υ(π basic) > Υ(π rand). Intuitively, this is what we would expect as π basic, while very simplistic, is surely more intelligent than π rand
.