Online Learning and Resource-Bounded Dimension: Winnow Yields New Lower Bounds for Hard Sets

Authors:
John M. Hitchcock
Affiliations:
-
Venue:
SIAM Journal on Computing
Year:
2007

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Abstract

We establish a relationship between the online mistake-bound model of learning and resource-bounded dimension. This connection is combined with the Winnow algorithm to obtain new results about the density of hard sets under adaptive reductions. This improves previous work of Fu [SIAM J. Comput., 24 (1995), pp. 1082-1090] and Lutz and Zhao [SIAM J. Comput., 30 (2000), pp. 1197-1210], and solves one of Lutz and Mayordomo’s “twelve problems in resource-bounded measure” [Bull. Eur. Assoc. Theor. Comput. Sci. EATSC, 68 (1999), pp. 64-80].