提出高效算法,在对抗标签下实现最优统计性能。
Oracle-efficient Hybrid Learning with Constrained Adversaries
- 约束对手标签函数类,结合ERM预言机设计新算法
- 后悔界依赖于假设类与对手类的Rademacher复杂度
- 适用于高维动作集的随机零和博弈均衡计算
混合在线学习问题中,特征独立同分布于未知分布,而标签由对抗者生成,处于统计学习与全对抗学习之间。以往工作存在两难:统计最优但计算不可行(Wu et al., 2023),或计算高效但统计次优(Wu et al., 2024)。本文在对手标签受限于固定、表达性强的函数类 $R$ 的设定下,提出新算法,仅需一个ERM预言机即可高效运行,并实现与从 $H$ 和 $R$ 导出类的Rademacher复杂度相关的后悔界。作为关键推论,该方法可高效求解高维动作集下具有低维结构的随机零和博弈均衡。技术上,提出带截断熵正则项的新Frank-Wolfe约简及一种针对“混合”鞅差序列的新型尾界。
原文摘要 · Abstract (English)
The Hybrid Online Learning Problem, where features are drawn i.i.d. from an unknown distribution but labels are generated adversarially, is a well-motivated setting positioned between statistical and fully-adversarial online learning. Prior work has presented a dichotomy: algorithms that are statistically-optimal, but computationally intractable (Wu et al., 2023), and algorithms that are computationally-efficient (given an ERM oracle), but statistically-suboptimal (Wu et al., 2024). This paper takes a significant step towards achieving statistical optimality and computational efficiency simultaneously in the Hybrid Learning setting. To do so, we consider a structured setting, where the Adversary is constrained to pick labels from an expressive, but fixed, class of functions $R$. Our main result is a new learning algorithm, which runs efficiently given an ERM oracle and obtains regret scaling with the Rademacher complexity of a class derived from the Learner's hypothesis class $H$ and the Adversary's label class $R$. As a key corollary, we give an oracle-efficient algorithm for computing equilibria in stochastic zero-sum games when action sets may be high-dimensional but the payoff function exhibits a type of low-dimensional structure. Technically, we develop a number of tools for the design and analysis of our learning algorithm, including a novel Frank-Wolfe reduction with "truncated entropy regularizer" and a new tail bound for sums of "hybrid" martingale difference sequences.
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