Markov Decision Processes (MDPs) represent the mathematical foundation of intelligent AI decision-making under uncertainty. These powerful frameworks enable autonomous systems to evaluate actions, predict outcomes, and optimize behavior through strategic reward maximization, making them essential for building truly adaptive artificial intelligence that thrives in complex, real-world environments.

Markov Decision Processes (MDPs) serve as powerful mathematical frameworks for modeling sequential decision-making under uncertainty.

In practical applications, MDPs act as the strategic brain of autonomous systems, enabling them to evaluate different actions based on current states and expected future rewards. This makes them particularly valuable for creating adaptive AI agents that can learn and optimize their behavior over time.

Now, just before jumping in, for those of you who don’t know. We’re Nebulum. We teach visionaries like you how to create deep tech applications, like applications in the AI or machine learning space, without having to know how to code. So if you want to surprise yourself in terms of what you’re able to build, check out our program links in the description below. Okay, let’s get back to it.

So I want to explore the topic of Markov Decision Processes today because as AI advances, we must embed stronger reasoning and decision-making capabilities into our systems — capabilities that extend beyond the limits of an AI model’s context window. The real world is messy, complex, and constantly changing. Teaching machines to operate in that dynamic space is where the magic really begins. In fact, something even potentially beautiful and philosophical starts to happen when we start building out these models, which I’ll explore at the end of this video.

Let’s dive in.

Why Use Markov Decision Processes in AI Systems?

We use Markov Decision Processes to model problems. Here’s a simple example: a robot must collect medicine from this “pick-up state” and deliver it to a machine in the upper right corner, which distributes it to patients. If optimizing for efficiency, we’d want the fewest moves possible – this route takes only 4 moves versus 6 the other way. In a deterministic world, in this case, we’d select the 4 move algorithm.

We could select that option because deterministic systems always produce identical outputs from identical inputs. Tell the robot “move up one” and it moves up one.

Stochastic systems on the other hand incorporate randomness to capture uncertainty and build realistic complexity into applications. In a deterministic system, I’d simply tell you to hit the like button (that is my input), and you’d subscribe (that would be the output). Essentially, moving you from that unsubscribed state to this subscribed state. But as a system designer, I face reality: there’s only a certain probability you’ll actually like and subscribe. For you, there are other paths forward, with their own probabilities. This makes it a stochastic model.

This terminology matters because it’s our world’s unpredictable nature that makes Markov Decision Processes so valuable.

“The real world is messy, complex, and constantly changing. Teaching machines to operate in that dynamic space is where the magic really begins.”

Understanding Stochastic Decision Making with MDPs

Okay, let’s jump back to our robot. Think of each of these squares as a state. Now imagine that we build some complexity into this model. Imagine that we said that every time we asked our robot to move up or down into a new state, there was a 10% chance it would move unpredictably right or left. And imagine that in this more complex world, we also baked in a reward system. For instance, the robot will gain 100 points for making a successful delivery. However, it will lose 10 points for hitting a wall or an outside boundary and it will lose 5000 points for falling down the stairs. So we bake this into our algorithm to disincentivize it from moving close to these stairs.

With this new system, the shortest path creates high risk of massive point loss. To maximize rewards, the robot must avoid positions left of the stairs. Now the optimal path becomes the longer route because of the uncertainty in this world.

This simple example illustrates why we use Markov Decision Processes: to create systems that maximize cumulative rewards through optimal policy selection. A policy is simply a strategy that tells the agent which action to take in each state.

The 5 Essential Components of Markov Decision Processes

To understand how this works, let’s examine the 5 main components of a Markov Decision Process.

The 5 components are:

• States (S)
• Actions (A)
• Transition Probabilities (P) – P(s’|s,a)
• Rewards (R) – R(s,a,s’)
• Discount Factor (γ)

States: The Foundation of MDP Decision Making

First, let’s discuss states.

States represent everything you know about your world at a given moment. The state contains all information needed to make optimal decisions moving forward. States can be simple, like coordinates or positions – for example, “I’m currently in State A.”

States can also be more complex, containing important attributes or factors. In our robot example, we might need the robot’s battery level or inventory status. However, I won’t elaborate on attributes within states because this leads to what Richard E. Bellman, in his book Dynamic Programming called “the curse of dimensionality” – where machine reasoning becomes exponentially more complex as we add layers.

I mention this only so you understand that states can be as simple or complex as you design them to be.

Another important note about states is that they are memoryless. Let me give you an example of what a memoryless state actually looks like because this concept is hard for some people to understand. Let’s look at this chess board for example. Because right now we can look at this chess board and we can build a model to move forward without having to know how we got to this current board configuration. The previous moves don’t matter. The present configuration of the board is all we need to know. This is similar to how memoryless states work. We don’t need to know the past in order to be able to optimally move towards the future.

Actions: Defining Available Choices in Each State

Now, let’s talk about Actions.

Actions are the available choices we have in any given state. For example, we might have an up, down, left, right move action. We might also have a delivery action or a charging action. The set of actions available to us may vary by state. For example, from this position the robot can’t move left and obviously the robot can only be charged if it were near the charging station.

Transition Probabilities: Modeling Uncertainty in MDP Systems

The third component is transition probabilities. Let’s switch to a new model with some directionality to it. In this example, we’ll use a student as an agent, because understanding how this logic works in the human world, helps us understand how to program this logic in a mechanical world. In this example, a student makes study choices, passes or fails, then loops back to the next grade if they pass.

The agent starts here as a student, then chooses between three states: not studying, studying moderately, or studying hard. After choosing, we introduce uncertainty through transition probabilities.

Each state under the study decision represents a professor. We’ll call them professor A, B and C. However, when you submit your final exam, you have no control over who grades your paper. Professor A is the toughest to impress and loves to give out low grades. Professor B fairly grades papers and professor C loves giving out good grades. With this setup, if you don’t study, you definitely fail (100% probability) no matter which professor grades your paper. If you study moderately, you have only a 1% chance of failing but no chance of graduating with honors. If you study hard, you have no chance of failing and a 20% chance of graduating with honors.

From our starting point, if our objective is graduating with honors, we should choose the hard study state. While success isn’t guaranteed, it’s the only state with above-zero probability for honors while avoiding failure.

Now, remember states can have variables. Imagine this student has a “mental health” variable. We only allow entering the hard study state if mental health exceeds 70%. Each hard study cycle decreases mental health by 35 points, while moderate study recharges it by 35 points.

This means each school year starting in State A, our algorithm only allows hard studying every other year when mental health is sufficient.

Similarly, in our robot example, energy might decrease 1% per move. To prevent the battery hitting zero, once it reaches 30%, the robot must stop deliveries and find the recharge station.

“This simple example illustrates why we use Markov Decision Processes: to create systems that maximize cumulative rewards through optimal policy selection.”

Rewards: The Feedback System for AI Learning

This brings us to the fourth component: Rewards.

Rewards are numerical feedback signals that guide the agent’s learning by indicating desirable or undesirable outcomes. These can be positive (passing with honors +100, passing +50) or negative (failing -100).

In our robot case, it earns 100 points for making a delivery but loses 1 point per move to maximize efficiency and prevent wandering. It also loses points for hitting walls, falling down stairs, or running out of battery.

We’re essentially punishing bad behavior and incentivizing good behavior through these reward signals.

Discount Factor: Balancing Immediate vs Future Rewards

Lastly, we have the discount factor, a value between 0 and 1 that determines how much your agent values future rewards versus immediate ones. (gamma) γ=0 means the agent only cares about immediate rewards. (gamma) γ=1 means future rewards equal current rewards in value.

Even though Markov Decision Processes are memoryless regarding the past, they can consider the future many steps ahead through what we call value functions. These functions estimate how much future reward an agent can expect from any state, allowing the system to be “locally myopic but globally optimal” – each transition only considers the immediate next state, but the value functions capture all downstream consequences. Value functions capture the long-term consequences of being in each state, making the agent forward-thinking despite the memoryless property.

Stationary vs Non-Stationary MDP Environments

Another consideration is our environment. In stationary worlds, probabilities are relatively fixed by external factors – this is particularly true for planning models dealing with traffic, weather, or infrastructure.

In non-stationary worlds, probabilities can change based on your actions and learning. You have control over improving underlying success rates through strategic decisions.

For example, in our study model, the student might discover that professors A and B have randomized schedules Monday through Thursday, while professor C only works Fridays. By timing paper submission for Friday, you shift probabilities in your favor – literally transforming your world.

The fascinating aspect of Markov Decision Processes is that in continuous or episodic systems, the agent simultaneously learns optimal policies while improving probabilities in its favor.

Through strategic actions, it updates its world knowledge in real-time, discovering both optimal paths and favorable probability shifts as it navigates the environment. This creates a powerful feedback loop: better decisions lead to better understanding, which leads to even better decisions.

The Philosophy of Machine Reasoning and Decision Making

Personally, I find this subject mind bending. Machine reasoning sits at the strangest intersection I know: where engineering meets existentialism.

Because as you get into the subject of machine reasoning, you’re not just in the world of engineering any longer. Essentially, you’re philosophizing using one of the most honest languages possible: code.

The deeper paradox: as we teach machines to reason, we’re forced to examine our own reasoning processes. I dare you to sit down with a pencil and paper and start mapping some of your own decision logic out. If the process doesn’t rattle you a little bit, I’m going to kindly ask that you unsubscribe to our channel. But seriously, I think you’ll find the process unbelievably fascinating.

Building artificial cognition becomes a recursive journey into the nature of thought itself—thinking about thinking about thinking.

“Building artificial cognition becomes a recursive journey into the nature of thought itself—thinking about thinking about thinking.”

Start Building Advanced AI Systems Today

If this all interests you and if you want to learn how to build out complex AI algorithms or applications without having to know how to code, be sure to head over to Nebulum today to browse through our training programs.

So that’s all I have for you. I hope you found this valuable. Again, don’t forget to like and subscribe.