What are the best practices for selecting and representing the state space for a POMDP?

1 What is a POMDP?

A POMDP is a generalization of a Markov decision process (MDP), which is a mathematical framework for modeling sequential decision making under uncertainty. In an MDP, the agent knows the exact state of the environment at each time step, and the state transition and reward functions are Markovian, meaning that they depend only on the current state and action. In a POMDP, however, the agent does not observe the state directly, but only receives some partial or noisy observation that depends on the state and the action. Therefore, the agent has to maintain a belief state, which is a probability distribution over the possible states, and update it based on the observation and the action.

2 Why is state representation important?

The state representation is the way the agent encodes the information about the environment into a vector or a tensor that can be used for learning and decision making. The state representation affects the performance and the complexity of the RL algorithm, as it determines how well the agent can generalize, learn, and explore. A good state representation should capture the essential features of the environment, be compact and informative, and be consistent and stable over time. However, finding a good state representation is not trivial, especially for POMDPs, where the agent has to deal with partial and noisy observations.

3 How to select and represent the state space for a POMDP?

When selecting and representing the state space for a POMDP, there are various approaches to consider. The simplest method is using the observation as the state, which does not require any prior knowledge or processing. Alternatively, a handcrafted feature extractor can be used to reduce the dimensionality and noise of the observation, and enhance interpretability. A learned feature extractor, such as a neural network, can automatically discover and adapt to important aspects of the environment. Additionally, a recurrent neural network (RNN) can capture temporal dependencies and dynamics of the environment and handle partial and noisy observations.

4 What are the advantages and disadvantages of each method?

When choosing a method for an agent, the scenario and goal must be taken into account. Factors such as computational complexity, data efficiency, robustness, and interpretability should be considered. For instance, using the observation as the state or a handcrafted feature extractor may be faster and simpler than using a learned feature extractor or an RNN, but they may also require more memory and data. Furthermore, a learned feature extractor or an RNN may be more data efficient than using the observation as the state or a handcrafted feature extractor, as they can exploit the structure and regularities of the environment. Additionally, an RNN may be more robust than a learned feature extractor, which may be more robust than a handcrafted feature extractor. Finally, a handcrafted feature extractor may be more interpretable than a learned feature extractor, which may be more interpretable than an RNN.

5 How to evaluate and compare different methods?

The evaluation and comparison of different methods for selecting and representing the state space for a POMDP is dependent on the criteria and metrics that are pertinent to the problem and agent. Performance, sample complexity, computational efficiency, and interpretability are common metrics that can be used to measure the agent's success. Performance is evaluated across different environments, tasks, or scenarios and compared using statistical tests or confidence intervals. Sample complexity can be estimated using learning curves or asymptotic analysis and compared using logarithmic or normalized scales. Computational efficiency can be measured using benchmarks, profiling, or simulation tools with absolute or relative values. Interpretability is assessed using qualitative or quantitative methods such as visualization, inspection, attribution, or evaluation with subjective or objective scores.