Robustly Minimax Codes for Universal Data Compression

We introduce a notion of ‘relative redundancy’ for universal data compression and propose a universal code which asymptotically achieves the minimax value of the relative redundancy. The relative redundancy is a hybrid of redundancy and coding regret (pointwise redundancy), where a class of information sources and a class of codes are assumed. The minimax code for relative redundancy is an extension of the modified Jeffreys mixture, which was introduced by Takeuchi and Barron and is minimax for regret. Keywords— universal coding, redundancy, regret, Bayes mixture, Jeffreys prior, robust learning