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On-line decision making for a class of loss functions via Lempel-Ziv parsing

Prefetching in computer memory architectures is formalized as a sequential decision problem in which the instantaneous losses depend not only on the current action-observation pair, as in the traditional formulation, but also on past pairs. Motivated by the prefetching application, we study a class of loss functions that admit an efficient on-line decision algorithm. The algorithm uses the LZ78 parsing rule to dynamically build a tree, different from the classical LZ78 tree, and makes decisions based on the current node in a traversal path, determined by the sequence of observations. The asymptotic performance is essentially as good as that of the best finite-state strategy determined in hindsight, with full knowledge of the given sequence of observations. The related notion of delayed FS predictability is introduced, and its properties are studied.