What Is Markov Decision Process?
This is a stochastic decision-making process that uses a mathematical framework. It evaluates which actions the decision-maker should take based on the current state and environment of the system. MDP is used in various fields such as operations research, computer science, economics and artificial intelligence. A Russian mathematician, Andrey Markov, shaped this process and has been in use since the 1950s.
MDPs are used in artificial intelligence to simulate probabilistic dynamics in sequential decision-making settings. They are employed in the design of intelligent devices or agents that must continue to operate in a setting where decisions may have unpredictable outcomes.
MDP is used in two sub-areas of AI: Probabilistic planning and reinforcement learning (RL). The field of probabilistic planning uses established models to achieve the goals and objectives of an agent. On the other hand, applications can learn to use reinforcement learning by using the input that agents receive from their surroundings.
Components of Markov decision process
An MDP has five components that define its working. These components of MDP are mentioned below:
States (S)
A finite set of states that the system can be in. The MDP process transitions between states based on the actions of the decision maker and the speculative character of the surroundings.
Actions (A)
A finite set of actions available to the decision maker. A state transition is the result of an action decision made in one state.
Transition model (P)
The probability that the system may change states in response to a certain action. P(s′∣s,a) represents the probability of moving from state s to state ′s′ after taking action a.
Reward function (R)
This is a function that gives a real number to each state-action pair (s,a). This represents the rewards that have been received after taking action a in state s. It may show both gain and loss to guide the decision-makers towards positive results.
Policy (π)
A policy is a plan that outlines the course of action for each state. A policy can be stochastic, in which a probability distribution across actions is defined for each state, or deterministic, in which a particular action is selected for each state.
Discount factor (γ)
Discount factor refers a number in the range of 0 to 1 that expresses the present value of benefits to come. The agent is deemed “short-sighted” if the discount factor is near 0, and “far-sighted” if it is near 1.
How does the Markov decision process work?
The MDP model works on key elements such as agent, states, actions, rewards and policies. The Markov Property, which asserts that only the current state, which contains all the relevant information from the past, can be used to predict the future, is employed by the MDP model. This equation can be used to evaluate the Markov Property:
P[St+1|St] = P[St+1 |S1,S2,S3……St]
Here P[St+1] is the probability of the next stage, (St) is the present state and (S1,S2,S3……St) are all the previous stages. This suggests that MDP evaluates the next actions only based on the current state, without relying on any states or acts from the past.
Importance of Markov decision process
MDP is an extremely important tool in the field of artificial intelligence. It has distinct capabilities and applications, transforming the decision-making processes and system automation.
Artificial intelligence
In the field of artificial intelligence, MDP is an important tool for modelling and solving sequential decision-making issues under uncertainty. It is the key component of AI algorithms and applications because of its ability to capture a board range of real-world events.
Application and industry relevance
MDP is important because of its extensive applications available across industries. Its influence on a variety of industries is still growing, ranging from enabling autonomous navigation in robotics to streamline resource allocation in business operations.
Methods of solving a Markov decision process
There are various methods of solving a Markov decision process. Some of them include:
Value iteration
It is an iterative algorithm that updates the value of each state. It updates the value of each state until the values converge to a stable set.
Policy iteration
It is an iterative algorithm that rotates between policy evaluation and policy improvement. This policy is repeated until it converges to the optimal policy.
Q-learning
This is a reinforcement learning technique that roughly calculates the value of each state-action pair.
Monte Carlo methods
This method uses sampling techniques to value function and/or policy.
Temporal difference learning
In this method, the aspects of Monte Carlo methods and dynamic programming are combined to calculate the value functions.
Pros and cons of MDP
It is important to understand the pros and cons of the Markov decision process so that its abilities can be used fully in AI applications in the right way. Given below are the pros and cons:
Pros
- It is flexible as it models a wide range of decision-making scenarios.
- It provides a framework for deriving optimal policies that maximise cumulative rewards over time.
Cons
- The computational and memory requirements of MDP algorithms become more difficult as the state and action spaces expand.
- The full observability that MDP expects may not always match with real-world settings. This could result in inaccurate decisions.
Examples of the Markov decision process
MDP has contributed in various domains such as computer science, electrical engineering, manufacturing, operations research, finance and economics, etc. These are some examples of the use of MDP:
Routing problems
MDP is used to solve routing problems such as those revealed in the travelling salesman problem (TSP). Its components are:
Salesman = agent
Routes available = the actions that the agent can take while in the present state
Rewards = the expense done in taking the specific routes
Goal = the policy that decreases the overall expense for the full duration of the tip
Managing dynamic systems
Due to actions in different environments, dynamic systems like cars and buses get worse. In this case, repairing tasks or replacing the key components of the vehicle is required. The system can select solutions that reduce the vehicle’s lifetime maintenance costs by framing this challenge under MDP.
Designing games
MDP is used widely to design a level-wise quiz game. Every level has a question with a monetary reward if the answer is accurate. The questions become harder and carry greater rewards as the level increases. In these games, a participant can decide, after winning some levels, if they want to continue playing or quit. The objective is to understand the pros and cons of continuing or giving up while optimising the gains.
At traffic intersection
Markov decision process helps to decide the time duration of the traffic lights. Here, the goal is to maximise the number of cars that can cross traffic crossings while monitoring their wait times. It is supposed that the traffic systems have data on the number of vehicles at the intersection. Depending on the number of cars at the intersection and how long they are expected to wait, you can use MDPs to determine whether to adjust the traffic lights.
The Markov decision process is a stochastic decision-making tool. It is based on the Markov principle. It offers a structured approach to navigating complex and uncertain environments. Furthermore, it provides strength to the decision-making in the AI landscape. This tool has great transformative potential and is applicable across many industries. Time and probability are important factors of the process. Its key properties are a fully observable environment, the future is dependent on the present and the next state depends only on the current state. Several industries are using MDP regularly to carry out their day-to-day tasks.
