Information Directed Sampling for Linear Partial Monitoring
This provides a unified solution for a broad class of bandit problems including linear, combinatorial, and dueling bandits, with applications extended to contextual and kernelized settings.
The authors tackled the problem of sequential decision making under uncertainty in partial monitoring games by introducing information directed sampling (IDS) for stochastic partial monitoring with linear structure, achieving adaptive worst-case regret rates that match optimal rates up to logarithmic factors across all finite games without hyper-parameter tuning.
Partial monitoring is a rich framework for sequential decision making under uncertainty that generalizes many well known bandit models, including linear, combinatorial and dueling bandits. We introduce information directed sampling (IDS) for stochastic partial monitoring with a linear reward and observation structure. IDS achieves adaptive worst-case regret rates that depend on precise observability conditions of the game. Moreover, we prove lower bounds that classify the minimax regret of all finite games into four possible regimes. IDS achieves the optimal rate in all cases up to logarithmic factors, without tuning any hyper-parameters. We further extend our results to the contextual and the kernelized setting, which significantly increases the range of possible applications.