Mastering MDPs: Why Your AI Needs the Markov Property to Succeed
Tobiloba OdejinmiBy Tobiloba Odejinmi
Education
May 30, 2026 • 7:40 PM
8m8 min read
Verified
Source: Unsplash
The Core Insight
This guide explores the transition from simple multi-armed bandit problems to the robust framework of Markov Decision Processes (MDPs). It defines the Markov property, the assumption that the future depends only on the present state, and explains why state representation is the most critical design choice in RL. The article also touches on the limitations of this property, introducing the concept of Partially Observable Markov Decision Processes (POMDPs) for scenarios where the full state is hidden.
T
Education Specialist & Editor
Tobiloba Odejinmi
Tobiloba Odejinmi is an education specialist dedicated to helping students and lifelong learners discover the best scholarship opportunities, study techniques, and career pathways.
The Kodawire Editorial Team consists of experienced journalists and subject matter experts dedicated to delivering accurate, well-researched, and engaging content.
States Matter: Unlike simple multi-armed bandits, real-world AI must account for context, as future outcomes depend on current conditions.
The Markov Property: A state is "Markov" if it contains all the information needed to predict the future, rendering past history irrelevant.
Modeling is Key: Markovian-ness is a design choice. If your model needs "memory," your state representation is likely insufficient.
Enrich, Don't Memorize: Instead of adding complex memory layers to your agent, focus on engineering a richer state representation that captures the necessary dynamics.
In the early stages of reinforcement learning, we often start with the multi-armed bandit, a stateless problem where an agent pulls levers to maximize rewards. It is a clean, isolated environment. But the real world is rarely that simple. Whether you are training an agent to play chess, navigate a vehicle through traffic, or manage a complex dialogue, the "best" action is dependent on the current situation. The action you take now alters the environment you face in the next moment. When architecting long-term memory for agents, it is easy to overlook the foundational state design.
To move beyond simple decision-making, we need a formal vocabulary to describe how states, transitions, and rewards interact. This is where the Markov Decision Process (MDP) becomes the backbone of almost every serious reinforcement learning architecture. Much like context engineering, the way you define your input space dictates the ceiling of your model's performance.
The Markov Property: The Foundation of Tractability
Before we can build an MDP, we must address the assumption that makes the math work: the Markov property. Informally, a state is Markov if the future depends on the past only through the present. Once you have the current state, the entire history of how you arrived there becomes irrelevant for predicting what happens next.
Mathematically, we define this by saying the distribution of the next state, $S_{t+1}$, conditioned on the entire history, reduces to a distribution conditioned only on the current state, $S_t$, and the action taken, $A_t$. Formally: P(S_{t+1} | S_t, A_t) = P(S_{t+1} | History). For those interested in the broader implications of model evaluation, traditional testing often fails to capture these nuances.
Behind the Scenes
This analysis synthesizes foundational RL principles, specifically the transition from stateless bandit problems to state-dependent MDPs. I have cross-referenced the mathematical definitions of the Markov property against standard control theory literature to clarify the distinction between "hidden states" and "Markov states." My goal is to strip away academic jargon and focus on the practical engineering decisions developers face when designing state representations.
Visualizing state transitions is critical for effective RL design. (Credit: Jeswin Thomas via Unsplash)
The Art of State Representation: A Case Study in Breakout
One of the most common pitfalls for practitioners is assuming that a "state" is a fixed, physical reality. It is a modeling choice. Consider the classic Atari game Breakout. If you feed a single screenshot into your agent, is that state Markov? No. From a single frame, you cannot determine the velocity or direction of the ball. The agent is blind to the dynamics of the game.
However, if you stack the last four frames together, you suddenly have a representation that captures the ball's trajectory. The state is now "approximately Markov." This illustrates a critical point: Markovian-ness is a design choice, not a physical constant. The art of reinforcement learning is often the art of designing a state representation that makes the Markov property hold well enough for your agent to learn. If you are struggling with performance, consider how benchmarking your model can reveal these state-based deficiencies.
The Hands-On Experience
When building an RL environment, I look for specific indicators that my state representation is failing. If I find myself needing to implement recurrent neural networks (RNNs) or long-short-term memory (LSTM) cells just to "remember" what happened three steps ago, I know I have failed at the state design level. It is almost always more efficient to enrich the input features, adding velocity, acceleration, or recent history, than to force the agent to learn memory-based heuristics.
Refining your state space is more effective than adding complex memory layers. (Credit: Daniil Komov via Unsplash)
When the Markov Property Fails: Understanding POMDPs
Sometimes, the Markov property simply cannot hold. This happens when the agent only sees partial observations of a hidden state. This is known as a Partially Observable Markov Decision Process (POMDP), a concept introduced by Karl Johan Åström in 1965. In a POMDP, the agent must maintain a "belief state", a probability distribution over what the true, hidden state might be. It is vital to recognize that many real-world problems are inherently partially observable.
The Contrarian's Corner
Many developers today are obsessed with "memory-heavy" architectures, believing that if an agent is smart enough, it can infer the state from a long sequence of past observations. I disagree. Relying on memory tricks to compensate for a poor state representation is a recipe for slow convergence and brittle models. If your state is insufficient, no amount of "memory" will make the training process stable.
Monitoring training stability is essential when iterating on state representations. (Credit: Veronica via Unsplash)
Interactive Decision-Making Tool
If you are struggling to define your state, ask yourself these three questions:
Can I predict the next state using only the current input? If yes, you are likely Markovian.
Is there missing information (like velocity or intent) that I am forcing the agent to "guess"? If yes, add that information to the state.
Am I using an RNN/LSTM to fix a lack of data? If yes, stop and redesign your input features.
My Personal Toolkit
Gymnasium: The industry standard for defining custom environments and state spaces.
Stable Baselines3: My go-to for reliable, well-tested implementations of standard RL algorithms.
Weights & Biases: Essential for tracking how changes in state representation affect training stability over time.
Engagement Conclusion
Have you ever spent hours debugging an RL agent only to realize your state representation was missing a key variable? I’m curious to hear about your experiences with state design versus memory-based architectures. I will be replying to every comment in the next 24 hours.
The Markov property states that the future of a system depends only on the current state, not on the history of how that state was reached.
State representation is a design choice because developers must decide which variables (like velocity or recent history) to include to ensure the environment behaves in a Markovian way for the agent.
A Partially Observable Markov Decision Process (POMDP) occurs when an agent cannot see the full state of the environment, requiring it to maintain a 'belief state' based on partial observations.
Active Engagement
Was this information helpful?
Join Discussions
0 Thoughts
Editorial Team • Question of the Day
"Do you believe that "memory-less" Markov states are sufficient for the future of AGI, or will we eventually need to move toward architectures that inherently handle long-term history?"
