# ARTIFICIAL INTELLIGENCE: The Ideal Mapping From Precept Sequences To Actions

Once we realize that an agent's behavior depends only on its percept sequence to date, then we can
describe any particular agent by making a table of the action it takes in response to each possible
percept sequence. (For most agents, this would be a very long list—infinite, in fact, unless we
place a bound on the length of percept sequences we want to consider.) Such a list is called
a mapping from percept sequences to actions. We can, in principle, find out which mapping
correctly describes an agent by trying out all possible percept sequences and recording which
actions the agent does in response. (If the agent uses some randomization in its computations,
then we would have to try some percept sequences several times to get a good idea of the agent's
average behavior.) And if mappings describe agents, then ideal mappings describe ideal agents.

Specifying which action an agent ought to take in response to any given percept sequence provides
a design for an ideal agent.
This does not mean, of course, that we have to create an explicit table with an entry
for every possible percept sequence. It is possible to define a specification of the mapping
without exhaustively enumerating it. Consider a very simple agent: the square-root function
on a calculator. The percept sequence for this agent is a sequence of keystrokes representing a
number, and the action is to display a number on the display screen. The ideal mapping is that
when the percept is a positive number x, the right action is to display a positive number z such
that z
2
« x, accurate to, say, 15 decimal places.

This specification of the ideal mapping does
not require the designer to actually construct a table of square roots. Nor does the square-root
function have to use a table to behave correctly: Figure 2.2 shows part of the ideal mapping and
a simple program that implements the mapping using Newton's method.
The square-root example illustrates the relationship between the ideal mapping and an
ideal agent design, for a very restricted task. Whereas the table is very large, the agent is a nice,;
compact program. It turns out that it is possible to design nice, compact agents that implement part of the ideal mapping for the square-root problem (accurate to 1 5 digits), and a
corresponding program that implements the ideal mapping.

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