Stochastic Multi-Armed Bandits with Control Variates
This work addresses a problem in applications like queuing and wireless networks where prior knowledge of exogenous variables can enhance decision-making, representing an incremental improvement by adapting existing methods to a new variant.
The paper tackles the stochastic multi-armed bandits problem by incorporating auxiliary information as control variates to reduce variance in reward estimates, resulting in tighter confidence bounds and improved regret bounds characterized by correlation with control variates, validated through experiments on synthetic instances.
This paper studies a new variant of the stochastic multi-armed bandits problem where auxiliary information about the arm rewards is available in the form of control variates. In many applications like queuing and wireless networks, the arm rewards are functions of some exogenous variables. The mean values of these variables are known a priori from historical data and can be used as control variates. Leveraging the theory of control variates, we obtain mean estimates with smaller variance and tighter confidence bounds. We develop an upper confidence bound based algorithm named UCB-CV and characterize the regret bounds in terms of the correlation between rewards and control variates when they follow a multivariate normal distribution. We also extend UCB-CV to other distributions using resampling methods like Jackknifing and Splitting. Experiments on synthetic problem instances validate performance guarantees of the proposed algorithms.