If you don’t know what this means, congratulations on being a normal human. But if you do, then you probably already hate me for writing this guide because it’s going to be filled .

So, let’s start by defining POMDPs in the most simplistic way possible: they are like Markov Decision Processes (MDPs), but instead of having full information about the state, you only have partial observations. This means that your agent has to make decisions based on imperfect knowledge and uncertainty.

Now, how we can solve POMDPs using dynamic programming algorithms. The most popular algorithm for solving POMDPs is called Point-Based Value Iteration (PBVI), which involves iteratively computing the value of each state in a given policy. This sounds like a lot of work, but don’t worry, I’ll explain it to you as if we were having a casual conversation over drinks at a bar.

First, let’s define what we mean by “value” in this context. In POMDPs, the value is not just the immediate reward that your agent receives for taking an action, but also includes the expected future rewards and costs associated with each state. This means that you have to take into account the long-term consequences of your actions, which can be challenging because you don’t know exactly what will happen in the future.

Now, how PBVI works. The algorithm involves iteratively computing the value function for each state and policy pair using a set of equations that are based on dynamic programming principles. These equations involve calculating the expected reward for taking an action from a given state, as well as the probability of transitioning to another state after taking that action.

The basic idea behind PBVI is to start with a random initial value function and then iteratively improve it by computing the values for each state in a given policy. This process involves updating the value function based on the expected rewards and costs associated with each state, as well as the probability of transitioning to another state after taking an action.

The algorithm works by first selecting a set of states that are considered “relevant” or “important”. These states are typically those that have high uncertainty or high reward potential. The algorithm then computes the value function for each relevant state and policy pair, using a set of equations that involve calculating the expected rewards and costs associated with each action.

The process involves iteratively updating the value function based on the current estimates of the transition probabilities and reward functions. This is done by computing the expected reward for taking an action from a given state, as well as the probability of transitioning to another state after taking that action. The algorithm then updates the value function for each relevant state and policy pair using these new estimates.

The process continues until convergence is reached or a predefined number of iterations has been completed. At this point, the optimal policy can be computed by selecting the action with the highest expected reward from each state in the final value function.

So, there you have it ! A casual guide to solving POMDPs using dynamic programming algorithms. If this sounds like too much work for your liking, don’t worry AI researchers are working on developing more efficient and scalable methods for solving these problems in the future. But until then, we can all enjoy a nice cold drink while our agents struggle through uncertain environments!