Abstract
The “no-free lunch theorems“ essentially say that for any two algorithms A and B, there are “as many“ targets (or priors over targets) for which A has lower expected loss than B as vice-versa. This can be made precise for certain loss functions [WM97]. This note concerns itself with cases where seemingly harder matrix versions of the algorithms have the same on-line loss bounds as the corresponding vector versions. So it seems that you get a free “matrix lunch“ (Our title is however not meant to imply that we have a technical refutation of the no-free lunch theorems).
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Warmuth, M.K. (2007). When Is There a Free Matrix Lunch?. In: Bshouty, N.H., Gentile, C. (eds) Learning Theory. COLT 2007. Lecture Notes in Computer Science(), vol 4539. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72927-3_48
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DOI: https://doi.org/10.1007/978-3-540-72927-3_48
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