Don’t worry if you don’t know what these are, because I’m here to break it down for you in the most casual way possible.

Before anything else, MDPs. An MDP is a fancy math model that helps us make decisions based on probabilities and rewards. It’s like playing a game of chess but with more numbers and less kings getting taken. In an MDP, we have a set of states (like the position of all the pieces in chess), actions (moving your pawn or knight), and rewards (getting a point for capturing an opponent’s piece). The goal is to find the best sequence of actions that will lead us to the highest possible reward.

Now, POMDPs. A POMDP is like an MDP but with one big twist we can’t see all the states at once! Instead, we have a set of observations (like seeing which pieces are on your side and which ones aren’t), and we use these to make decisions based on probabilities and rewards. It’s like playing chess in the dark but with more numbers and less kings getting taken.

So why do we care about MDPs and POMDPs? Well, they have a ton of applications in real life! For example, you can use them to optimize traffic flow or design better robots that can navigate through complex environments. They’re also used in finance for portfolio management and risk analysis.

But here’s the thing MDPs and POMDPs are notoriously difficult to solve. In fact, they’re so hard that even the smartest computers struggle with them! But don’t worry, we have some tricks up our sleeves to make things easier for us. One of these tricks is called “policy iteration,” which involves iteratively improving a policy (a sequence of actions) until it converges to an optimal solution.

Another trick is called “value iteration,” which involves finding the expected value of each state and using that information to guide our decisions. This can be done by solving a system of linear equations, but it’s not always easy or efficient!

If you want to learn more about these topics, check out some of the references at the end. And if you ever need help with your homework or research project, don’t hesitate to reach out!