We consider adaptive decision-making problems where an agent optimizes a cumulative performance objective by repeatedly choosing among a finite set of options. Compared to the classical prediction-with-expert-advice set-up, we consider situations where losses are constrained and derive algorithms that exploit the additional structure in optimal and computationally efficient ways. Our algorithm and our analysis is instance dependent, that is, suboptimal choices of the environment are exploited and reflected in our regret bounds. The constraints handle general dependencies between losses (even across time), and are flexible enough to also account for a loss budget, which the environment is not allowed to exceed. The performance of the resulting algorithms is highlighted in two numerical examples, which include a nonlinear and online system identification task.

本文探讨了自适应决策问题，提出一种可在有限的选项中选择以优化累积表现目标的算法，并考虑了损失受限的情况，得出了构建最优和高效算法的结论，涉及非线性和在线系统识别等具体应用。

具有约束和相关损失的自适应决策：性能保证及其在在线和非线性识别中的应用