Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 58, Issue 3, Pages 1922-1927Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2009.2037062
Keywords
Prediction; quantization; randomized; sequential decisions; switching; universal
Categories
Funding
- TUBITAK [108E195]
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In this paper, we consider a competitive approach to sequential decision problems, suitable for a variety of signal processing applications where at each of a succession of times, a selection must be made from among a fixed set of strategies (or outcomes). For each such decision and outcome pair, loss is incurred, and it is the time-accumulation of these losses that is sought to be minimized. Rather than using a statistical performance measure, our goal in this pursuit is to sequentially accumulate loss that is no larger than that of the best loss that could be obtained through a partitioning of the sequence of observations into an arbitrary fixed number of segments and independently selecting a different strategy for each segment. For this purpose, we introduce a randomized sequential algorithm built upon that of Kozat and Singer that asymptotically achieves the performance of a noncausal algorithm that would be able to choose the number of segments and the best algorithm for each segment, based on observing the whole observation process a priori. In addition to improving upon the bounds of Kozat and Singer as well as Gyorgy et al., the results we provide hold for more general loss functions than the square-error loss studied therein.
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