Abstract
A construct that has been receiving attention recently in reinforcement learning is stochastic factorization (SF), a particular case of non-negative factorization (NMF) in which the matrices involved are stochastic. The idea is to use SF to approximate the transition matrices of a Markov decision process (MDP). This is useful for two reasons. First, learning the factors of the SF instead of the transition matrices can reduce significantly the number of parameters to be estimated. Second, it has been shown that SF can be used to reduce the number of operations needed to compute an MDP's value function. Recently, an algorithm called expectation-maximization SF (EMSF) has been proposed to compute a SF directly from transitions sampled from an MDP. In this paper we take a closer look at EMSF. First, by exploiting the assumptions underlying the algorithm, we show that it is possible to reduce it to simple multiplicative update rules similar to the ones that helped popularize NMF. Second, we analyze the optimization process underlying EMSF and find that it minimizes a modified version of the Kullback-Leibler divergence that is particularly well-suited for learning a SF from data sampled from an arbitrary distribution. Third, we build on this improved understanding of EMSF to draw an interesting connection with NMF and probabilistic latent semantic analysis. We also exploit the simplified update rules to introduce a new version of EMSF that generalizes and significantly improves its precursor. This new algorithm provides a practical mechanism to control the trade-off between memory usage and computing time, essentially freeing the space complexity of EMSF from its dependency on the number of sample transitions. The algorithm can also compute its approximation incrementally, which makes it possible to use it concomitantly with the collection of data. This feature makes the new version of EMSF particularly suitable for online reinforcement learning. Empirical results support the utility of the proposed algorithm.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Proceedings of the AAAI Conference on Artificial Intelligence
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.