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- W2895839692 abstract "We develop a new theoretical framework, the emph{envelope complexity}, to analyze the minimax regret with logarithmic loss functions and derive a Bayesian predictor that adaptively achieves the minimax regret over high-dimensional $ell_1$-balls within a factor of two. The prior is newly derived for achieving the minimax regret and called the emph{spike-and-tails~(ST) prior} as it looks like. The resulting regret bound is so simple that it is completely determined with the smoothness of the loss function and the radius of the balls except with logarithmic factors, and it has a generalized form of existing regret/risk bounds. In the preliminary experiment, we confirm that the ST prior outperforms the conventional minimax-regret prior under non-high-dimensional asymptotics." @default.
- W2895839692 created "2018-10-26" @default.
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- W2895839692 date "2018-10-09" @default.
- W2895839692 modified "2023-09-24" @default.
- W2895839692 title "Adaptive Minimax Regret against Smooth Logarithmic Losses over High-Dimensional $ell_1$-Balls via Envelope Complexity" @default.
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- W2895839692 doi "https://doi.org/10.48550/arxiv.1810.03825" @default.
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