This work provides test error bounds for iterative fixed point methods on
linear predictors -- specifically, stochastic and batch mirror descent (MD),
and stochastic temporal difference learning (TD) -- with two core
contributions: (a) a single proof technique which gives high probability
guarantees despite the absence of projections, regularization, or any
equivalents, even when optima have large or infinite norm, for
quadratically-bounded losses (e.g., providing unified treatment of squared and
logistic losses); (b) locally-adapted rates which depend not on global problem
structure (such as condition numbers and maximum margins), but rather on
properties of low norm predictors which may suffer some small excess test
error. The proof technique is an elementary and versatile coupling argument,
and is demonstrated here in the following settings: stochastic MD under
realizability; stochastic MD for general Markov data; batch MD for general IID
data; stochastic MD on heavy-tailed data (still without projections);
stochastic TD on Markov chains (all prior stochastic TD bounds are in
expectation).

本文针对线性预测器的迭代定点方法（特别是随机和批量镜像下降法及随机时间差分学习），提供了测试误差界限。主要贡献包括：通过单一证明技巧对收敛和非收敛状态下具有高概率保证的拟合损失进行统一处理，以无需投影、正则化或任何等效手段，适用于具有二次界限的损失（如平方和逻辑损失），并基于低范数预测器的特性提供局部自适应率。证明技巧采用基本且多功能的耦合论证法，在多种设置中进行了演示。