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 give regret analysis for it. 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 graph structures 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.

Peer prediction refers to a collection of mechanisms for eliciting information from human agents when direct verification of the obtained information is unavailable. They are designed to have a game-theoretic equilibrium where everyone reveals their private information truthfully. This result holds under the assumption that agents are Bayesian and they each adopt a fixed strategy across all tasks. Human agents however are observed in many domains to exhibit learning behavior in sequential settings. In this paper, we explore the dynamics of sequential peer prediction mechanisms when participants are learning agents. We first show that the notion of no regret alone for the agents’ learning algorithms cannot guarantee convergence to the truthful strategy. We then focus on a family of learning algorithms where strategy updates only depend on agents’ cumulative rewards and prove that agents' strategies in the popular Correlated Agreement (CA) mechanism converge to truthful reporting when they use algorithms from this family. This family of algorithms is not necessarily no-regret, but includes several familiar no-regret learning algorithms (e.g multiplicative weight update and Follow the Perturbed Leader) as special cases. Simulation of several algorithms in this family as well as the $\epsilon$-greedy algorithm, which is outside of this family, shows convergence to the truthful strategy in the CA mechanism.