CI as optimization

In this lecture, we focus on a common mathematical basis for CI techniques…

• specifically: the idea that we are somehow optimizing a function which corresponds to intelligent behavior.

For instance, things that you will see later in this course:

• Learning with MLP’s by backpropagation.
• Search and optimization with a Genetic Algorithm.
• Search and optimization with an ant colony or a swarm.
• Optimization of action selection with Reinforcement Learning.

Both learning and evolution can be thought of as a form of ‘optimization’: we try to improve something (behavior or organisms) in order to get “better”.

This function we are trying to optimize is given by some parameter $\theta$:

In a mathematical sense, we denote optimizing as: Maximize $F(θ)$. Alternatively, we could also call it: Minimize $–F(θ)$.

In the example, the result could be:

However, we need to be careful when maximizing. How far should we go? When is enough?

Another important question is: we may use optimization techniques if we know what function we are trying to optimize… but, what is this function?

Fitness functions and fitness landscapes

Per definition the fitness of a candidate, $\theta$, defines how “good” (how well $\theta$ configures $\gamma$ to solve the problem) that state is in solving the “problem”: