What are the main challenges and limitations of Markov decision processes in data science applications?

1 What are MDPs?

MDPs are mathematical models that describe how an agent interacts with an environment over time. An MDP consists of four components: a set of states, a set of actions, a transition function, and a reward function. The agent chooses an action in each state, and the environment responds by moving to a new state and giving a reward. The goal of the agent is to maximize the expected cumulative reward over a horizon or indefinitely.

2 Why are MDPs useful?

MDPs are useful because they can capture the dynamics and uncertainties of complex systems and provide a principled way of finding optimal or near-optimal policies. A policy is a function that maps each state to an action. An optimal policy is one that maximizes the expected value of the objective function, which can be the total reward, the discounted reward, or the average reward. MDPs can also handle partial observability, stochasticity, and multiple objectives, by using extensions such as partially observable MDPs (POMDPs), Markov games, and multi-objective MDPs.

3 What are the challenges of MDPs?

MDPs come with their own set of challenges, such as the curse of dimensionality, which is the exponential growth of the MDP as the number of states and actions increases. This can be addressed with approximation techniques like function approximation, value iteration networks, or deep reinforcement learning. Additionally, data scientists must specify the transition and reward functions to use MDPs, which may not be known or easy to obtain in real-world problems. Model-free methods like Q-learning or policy gradient can be used in this case, or the model can be learned from data with Bayesian networks or neural networks. Lastly, agents need to balance exploration and exploitation when finding the optimal policy, which can be difficult when rewards are sparse, delayed, or noisy. Exploration strategies like epsilon-greedy, softmax, or upper confidence bound can be used to solve this issue.

5 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?