# Summary

In this chapter, we looked at the two most commonly used techniques to solve DP problems. The first method, memoization, also called the top-bottom method uses a dictionary (or HashMap-like structure) to store intermediate results in a natural (unordered) manner. While the second method, the tabular method, also called the bottom-up method, sequentially solves problems from small to large and usually saves the result in a matrix-like structure.

Next, we also looked at how to use DP to solve RL problems using policy and value iteration, and how we overcome the disadvantage of policy iteration by using the modified Bellman equation. We implemented policy and value iteration in two very popular environments: Taxi-v3 and FrozenLake-v0.

In the next chapter, we will be studying Monte Carlo methods, which are used to simulate real-world scenarios and are some of the most widely used tools in domains such as finance, mechanics, and trading.