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Automatic basis function construction
Automatic basis function construction (or basis discovery) is the method of looking for a set of task-independent basis functions that map the state space to a lower-dimensional embedding, while still representing the value function accurately. Automatic basis construction is independent of prior knowledge of the domain, which allows it to perform well where expert-constructed basis functions are difficult or impossible to create.
==Motivation==
In reinforcement learning (RL), most real-world Markov Decision Process (MDP) problems have large or continuous state spaces, which typically require some sort of approximation to be represented efficiently.
Linear function approximators〔Keller,Philipp;Mannor,Shie;Precup,Doina. (2006) Automatic Basis Function Construction for Approximate Dynamic Programming and Reinforcement Learning. Proceedings of the 23rd International Conference on Machine Learning, Pittsburgh, PA.〕(LFAs) are widely adopted for their low theoretical complexity. Two subproblems needs to be solved for better approximation: weight optimization and basis construction. To solve the second problem, one way is to design special basis functions. Those basis functions work well in specific tasks but are significantly restricted to domains. Thus constructing basis construction functions automatically is preferred for broader applications.
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