Sequential decision problems occur when an agent must make a series of decisions in an environment, with each decision affecting not only the immediate outcome but also the future states of the environment. These decisions are interdependent, meaning that the optimal decision at any point depends on the decisions made previously and the potential decisions that will be made in the future.
- A classic example is the process of playing chess, where each move influences the subsequent moves and the overall outcome of the game. The challenge in such problems is to devise a strategy that optimizes a certain objective, such as maximizing the total reward or minimizing the total cost, over the entire sequence of decisions.
Five Key Components of Sequential Decision Problems
- States: The state represents the current situation of the environment. It encapsulates all the necessary information to make a decision. For example, in a game of chess, the state would include the positions of all the pieces on the board.
- Actions: Actions are the choices available to the agent at any given state. Each action leads to a transition from one state to another. In the chess example, an action would be moving a piece from one square to another.
- Transitions: The transition model describes how the state changes in response to an action. This is often probabilistic in nature, especially in environments where uncertainty plays a role.
- Rewards: The reward function assigns a numerical value to each state or state-action pair, representing the immediate benefit of being in that state or taking that action. The objective is typically to maximize the cumulative reward over time.
- Policies: A policy is a strategy that defines the action the agent will take in each state. An optimal policy maximizes the expected cumulative reward over time.
Types of Sequential Decision Problems
1. MDPs (Markov Decision Processes)
MDPs are a fundamental framework for modelling sequential decision problems where the environment is fully observable, and the transitions between states are probabilistic. The decision-making process relies on the Markov property, where the future state depends only on the current state and action, not on the history of past states.
2. POMDPs (Partially Observable Markov Decision Processes)
In many real-world scenarios, the agent does not have complete information about the current state of the environment. POMDPs extend MDPs by introducing hidden states and an observation model, making the decision-making process more complex.
3. Multi-armed bandits
This is a simpler form of sequential decision problem where the agent must choose between multiple actions (or arms), each with an unknown probability distribution of rewards. The challenge is to balance exploration (trying out different actions) and exploitation (choosing the action with the highest known reward).
4. Reinforcement learning
Reinforcement learning (RL) is a popular approach for solving sequential decision problems where the agent learns an optimal policy through trial and error, receiving rewards or penalties for its actions. RL is widely used in AI for tasks such as game playing, robotic control, and resource management.
Applications of Sequential Decision Problems
- Robotics
- Finance
- Healthcare
- Autonomous Systems
Challenges in solving SDPs
- Complexity in computation
- Uncertainty and exploration
- Scalability