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By combining with sparse kernel methods, least-squares temporal difference (LSTD) algorithms can construct the feature dictionary automatically and obtain a better generalization ability. However, the previous kernel-based LSTD algorithms do not consider regularization and their sparsification processes are batch or offline, which hinder their widespread applications in online learning problems. In this paper, we combine the following five techniques and propose two novel kernel recursive LSTD algorithms: (i) online sparsification, which can cope with unknown state regions and be used for online learning, (ii) L2 and L1 regularization, which can avoid overfitting and eliminate the influence of noise, (iii) recursive least squares, which can eliminate matrix-inversion operations and reduce computational complexity, (iv) a sliding-window approach, which can avoid caching all history samples and reduce the computational cost, and (v) the fixed-point subiteration and online pruning, which can make L1 regularization easy to implement. Finally, simulation results on two 50-state chain problems demonstrate the effectiveness of our algorithms.

Kernel Recursive Least-Squares Temporal Difference Algorithms with Sparsification and Regularization