Understanding the Monte Carlo method
Before understanding how the Monte Carlo method is useful in reinforcement learning, first, let's understand what the Monte Carlo method is and how it works. The Monte Carlo method is a statistical technique used to find an approximate solution through sampling.
For instance, the Monte Carlo method approximates the expectation of a random variable by sampling, and when the sample size is greater, the approximation will be better. Let's suppose we have a random variable X and say we need to compute the expected value of X; that is E(X), then we can compute it by taking the sum of the values of X multiplied by their respective probabilities as follows:
But instead of computing the expectation like this, can we approximate it with the Monte Carlo method? Yes! We can estimate the expected value of X by just sampling the values of X for some N times and compute the average value of X as the expected value of X as follows:...