Incentivizing Exploration with Linear Contexts and Combinatorial Actions
This addresses the challenge of designing incentive-compatible algorithms for exploration in multi-armed bandits with linear contexts, which is incremental but relevant for applications like recommendation systems.
The paper tackles the problem of incentivized exploration in linear bandits by showing that Thompson sampling becomes incentive compatible under a convexity condition, enabling efficient exploration in high-dimensional spaces, and improves sample complexity for initial data collection in the semibandit model.
We advance the study of incentivized bandit exploration, in which arm choices are viewed as recommendations and are required to be Bayesian incentive compatible. Recent work has shown under certain independence assumptions that after collecting enough initial samples, the popular Thompson sampling algorithm becomes incentive compatible. We give an analog of this result for linear bandits, where the independence of the prior is replaced by a natural convexity condition. This opens up the possibility of efficient and regret-optimal incentivized exploration in high-dimensional action spaces. In the semibandit model, we also improve the sample complexity for the pre-Thompson sampling phase of initial data collection.