This paper investigates the robustness of causal bandits (CBs) in the face of temporal model fluctuations. This setting deviates from the existing literature's widely-adopted assumption of constant causal models. The focus is on causal systems with linear structural equation models (SEMs). The SEMs and the time-varying pre- and post-interventional statistical models are all unknown and subject to variations over time. The goal is to design a sequence of interventions that incur the smallest cumulative regret compared to an oracle aware of the entire causal model and its fluctuations. A robust CB algorithm is proposed, and its cumulative regret is analyzed by establishing both upper and lower bounds on the regret. It is shown that in a graph with maximum in-degree $d$, length of the largest causal path $L$, and an aggregate model deviation $C$, the regret is upper bounded by $\tilde{\mathcal{O}}(d^{L-\frac{1}{2}}(\sqrt{T} + C))$ and lower bounded by $\Omega(d^{\frac{L}{2}-2}\max\{\sqrt{T}\; ,\; d^2C\})$. The proposed algorithm achieves nearly optimal $\tilde{\mathcal{O}}(\sqrt{T})$ regret when $C$ is $o(\sqrt{T})$, maintaining sub-linear regret for a broad range of $C$.

翻译：本文研究了因果强盗（CBs）在时间模型波动下的鲁棒性。该设定偏离了现有文献广泛采用的恒定因果模型假设。研究聚焦于具有线性结构方程模型（SEMs）的因果系统。SEMs以及随时间变化的前后干预统计模型均为未知，且会随时间变化。目标是设计一组干预序列，使其相较于知晓整个因果模型及其波动的理想情况，产生的累积遗憾最小。本文提出了一种鲁棒CB算法，并通过建立遗憾的上界和下界分析了其累积遗憾。证明表明，在最大入度为$d$、最长因果路径长度为$L$、模型总偏差为$C$的图中，遗憾的上界为$\tilde{\mathcal{O}}(d^{L-\frac{1}{2}}(\sqrt{T} + C))$，下界为$\Omega(d^{\frac{L}{2}-2}\max\{\sqrt{T}\; ,\; d^2C\})$。当$C$为$o(\sqrt{T})$时，所提算法实现了近乎最优的$\tilde{\mathcal{O}}(\sqrt{T})$遗憾，并在广泛的$C$范围内保持次线性遗憾。