Model selection in supervised learning provides costless guarantees as if the model that best balances bias and variance was known a priori. We study the feasibility of similar guarantees for cumulative regret minimization in the stochastic contextual bandit setting. Recent work [Marinov and Zimmert, 2021] identifies instances where no algorithm can guarantee costless regret bounds. Nevertheless, we identify benign conditions where costless model selection is feasible: gradually increasing class complexity, and diminishing marginal returns for best-in-class policy value with increasing class complexity. Our algorithm is based on a novel misspecification test, and our analysis demonstrates the benefits of using model selection for reward estimation. Unlike prior work on model selection in contextual bandits, our algorithm carefully adapts to the evolving bias-variance trade-off as more data is collected. In particular, our algorithm and analysis go beyond adapting to the complexity of the simplest realizable class and instead adapt to the complexity of the simplest class whose estimation variance dominates the bias. For short horizons, this provides improved regret guarantees that depend on the complexity of simpler classes.

翻译：监督学习中的模型选择提供了无成本的保证，仿佛预先知道最佳平衡偏差与方差的模型。我们研究了在随机上下文Bandit设置中，针对累积遗憾最小化实现类似保证的可行性。近期工作[Marinov and Zimmert, 2021]指出，在某些实例中，任何算法都无法保证无成本遗憾界。尽管如此，我们识别出无成本模型选择可行的良性条件：类复杂度的逐步增加，以及随着类复杂度增加的最佳类策略值边际收益递减。我们的算法基于一种新颖的误设定检验，且分析展示了利用模型选择进行奖励估计的优势。与上下文Bandit中模型选择的先前工作不同，我们的算法会随着数据收集仔细适应不断演进的偏差-方差权衡。特别地，我们的算法与分析不仅适应最简单可实现类的复杂度，而是适应其估计方差主导偏差的最简单类的复杂度。对于短时间范围，这提供了依赖于更简单类复杂度的改进遗憾保证。