In combinatorial causal bandits (CCB), the learning agent chooses a subset of variables in each round to intervene and collects feedback from the observed variables to minimize expected regret or sample complexity. Previous works study this problem in both general causal models and binary generalized linear models (BGLMs). However, all of them require prior knowledge of causal graph structure. This paper studies the CCB problem without the graph structure on binary general causal models and BGLMs. We first provide an exponential lower bound of cumulative regrets for the CCB problem on general causal models. To overcome the exponentially large space of parameters, we then consider the CCB problem on BGLMs. We design a regret minimization algorithm for BGLMs even without the graph skeleton and show that it still achieves $O(\sqrt{T}\ln T)$ expected regret. This asymptotic regret is the same as the state-of-art algorithms relying on the graph structure. Moreover, we sacrifice the regret to $O(T^{\frac{2}{3}}\ln T)$ to remove the weight gap covered by the asymptotic notation. At last, we give some discussions and algorithms for pure exploration of the CCB problem without the graph structure.

翻译：在组合因果强盗（CCB）问题中，学习代理每轮选择干预的变量子集，并从观测变量处收集反馈以最小化期望遗憾或样本复杂度。以往研究在一般因果模型和二元广义线性模型（BGLM）中探讨了此问题，然而所有工作均需预先知道因果图结构。本文研究无需图结构的二元一般因果模型及BGLM上的CCB问题。首先，我们给出一般因果模型下CCB问题累积遗憾的指数级下界。为克服参数空间的指数爆炸，进一步考虑BGLM上的CCB问题。即使缺乏图骨架，我们为BGLM设计了一个遗憾最小化算法，并证明其仍能达到$O(\sqrt{T}\ln T)$的期望遗憾。该渐近遗憾值与依赖图结构的最优算法一致。此外，我们牺牲遗憾至$O(T^{\frac{2}{3}}\ln T)$以消除渐近记号掩盖的权重间隙。最后，针对无图结构的CCB问题纯探索，我们给出相关讨论与算法。