Feng Shi

Shi Feng, Wei Chen

In combinatorial causal bandits (CCB), the learning agent chooses at most $K$ variables in each round to intervene, collects feedback from the observed variables, with the goal of minimizing expected regret on the target variable $Y$. We study under the context of binary generalized linear models (BGLMs) with a succinct parametric representation of the causal models. We present the algorithm BGLM-OFU for Markovian BGLMs (i.e. no hidden variables) based on the maximum likelihood estimation method, and show that it achieves $O(\sqrt{T}\log T)$ regret, where $T$ is the time horizon. For the special case of linear models with hidden variables, we apply causal inference techniques such as the do-calculus to convert the original model into a Markovian model, and then show that our BGLM-OFU algorithm and another algorithm based on the linear regression both solve such linear models with hidden variables. Our novelty includes (a) considering the combinatorial intervention action space and the general causal models including ones with hidden variables, (b) integrating and adapting techniques from diverse studies such as generalized linear bandits and online influence maximization, and (c) avoiding unrealistic assumptions (such as knowing the joint distribution of the parents of $Y$ under all interventions) and regret factors exponential to causal graph size in prior studies.

Shi Feng, Nuoya Xiong, Wei Chen

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 or unrealistic assumptions. 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, as long as the causal graph satisfies a weight gap assumption. This asymptotic regret is the same as the state-of-art algorithms relying on the graph structure. Moreover, we propose another algorithm with $O(T^{\frac{2}{3}}\ln T)$ regret to remove the weight gap assumption.

Yiling Chen, Shi Feng, Sadie Zhao

We study repeated contextual procurement auctions in which the platform must learn context-dependent product values from bandit feedback. We give an exactly truthful explore-then-commit mechanism with $\widetilde O((ng)^{1/3}T^{2/3})$ regret. We also give a frozen-payment UCB mechanism with a regret-incentive tradeoff: the near-UCB tuning attains \(\widetilde O(\sqrt{ngT})\) welfare regret, while for fixed \(n,g\) its total incentive error is \(\widetilde O(T^{3/4})\); the balanced tuning gives \(\widetilde O(T^{2/3})\) on both scales. Regret is measured as welfare loss relative to the full-information efficient allocation. We prove a matching lower bound for the frozen-payment regret-incentive tradeoff.