The shortest path problem under partial monitoring
COLT'06 Proceedings of the 19th annual conference on Learning Theory
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Zero-delay lossy source coding schemes are considered for individual sequences.Performance is measured by the distortion redundancy, defined asthe difference between the normalized cumulative mean squared distortion ofthe scheme and the normalized cumulative distortion of the best scalar quantizerof the same rate which is matched to the entire sequence to be encoded.Recently, Weissman and Merhav constructed a randomized scheme which, forany bounded individual sequence of length n, achieves a distortion redundancyO(n-1/3log n). However, this scheme has prohibitive complexity (both spaceand time) which makes practical implementation infeasible. In this paper, wepresent an efficiently computable algorithm based on a "follow the perturbedleader"-type prediction method by Kalai and Vempala. Our algorithm achievesdistortion redundancy O(n-1/4 log n), which is somewhat worse than that of thescheme by Merhav and Weissman, but it has computational complexity that islinear in the sequence length n, and requires O(n1/4) storage capacity.