But don’t be scared, bro! In this tutorial, we’ll break down POMDPs into their simplest form: solving a maze without seeing it.

To start what is a POMDP? It’s essentially a decision-making problem where you have incomplete information about the environment. You can think of it as playing chess blindfolded, or navigating through a dark room with only your sense of touch to guide you. In other words, you don’t know what’s happening around you at any given time.

Now let’s apply this concept to our maze problem. Imagine you have a robot that needs to navigate through a complex maze to reach the end goal (let’s say it’s a delicious piece of cake). But there are obstacles and dead ends in the way, and your robot can only move one step at a time without knowing exactly where it is or what’s ahead.

To solve this problem using POMDPs, we need to break down our decision-making process into three steps: observation, action, and belief update. Let’s go through each of these in detail.

Observation: The robot can only sense its immediate surroundings (i.e., the walls or obstacles it touches). It cannot see where it is or what’s ahead. So we need to define a set of possible observations that our robot might encounter, and assign probabilities to each one based on the current state of the maze.

For example, if our robot is in a corner with walls on both sides, there are only two possible observations: “wall left” or “wall right”. If it’s in an open space, there could be multiple observations depending on which direction it faces (e.g., “open ahead”, “open to the left”, etc.).

Action: The robot can move one step at a time in any of four directions: up, down, left or right. But again, we don’t know exactly where our robot is, so we need to define a set of possible actions based on its current belief (i.e., what it thinks the maze looks like).

For example, if our robot believes that there’s an open space ahead and no walls to the left or right, it might choose to move forward. But if it believes that there are walls in all directions, it might choose to turn around instead.

Belief update: This is where things get interesting (and a bit complicated). Our robot needs to maintain a belief about what the maze looks like based on its observations and actions. In other words, it’s constantly updating its mental map of the environment as it moves through it.

To do this, we need to define a set of possible states for our maze (i.e., all the different configurations that could exist), and assign probabilities to each one based on the current observations and actions. We can then use Bayes’ theorem to update these probabilities as new information becomes available.

For example, if our robot moves forward and encounters a wall, it might revise its belief about what lies ahead by increasing the probability of certain states (i.e., those that include walls in that location) and decreasing the probability of others (i.e., those that don’t).

Of course, this is a simplified version of how POMDPs work in real-world applications like robotics or autonomous vehicles. But hopefully, this tutorial has given you a basic understanding of the concepts and helped demystify some of the jargon.

In terms of resources for learning more about POMDPs, I highly recommend checking out the book “Partially Observable Markov Decision Processes: Solving the Planning Under Uncertainty” by Stuart Russell and Peter Norvig (the same authors who wrote the classic AI textbook “Artificial Intelligence: A Modern Approach”). It’s a bit dense at times, but it covers everything from theory to implementation in great detail.

Until next time, happy maze-solving!