Linear Bandit algorithms using the Bootstrap
This provides a new alternative for solving linear bandit problems, particularly useful when noise distribution is unknown, but it appears incremental as it builds on existing bootstrap methods.
The study tackled linear stochastic bandit problems by introducing two new algorithms, X-Random and X-Fixed bootstrap bandits, which use bootstrapping to create confidence bounds without assumptions about noise distribution. The X-Random bootstrap performed better than baselines like OFUL, LinUCB, and Thompson Sampling in terms of cumulative regret, with regret less than half of the best baseline in some settings.
This study presents two new algorithms for solving linear stochastic bandit problems. The proposed methods use an approach from non-parametric statistics called bootstrapping to create confidence bounds. This is achieved without making any assumptions about the distribution of noise in the underlying system. We present the X-Random and X-Fixed bootstrap bandits which correspond to the two well-known approaches for conducting bootstraps on models, in the literature. The proposed methods are compared to other popular solutions for linear stochastic bandit problems, namely, OFUL, LinUCB and Thompson Sampling. The comparisons are carried out using a simulation study on a hierarchical probability meta-model, built from published data of experiments, which are run on real systems. The model representing the response surfaces is conceptualized as a Bayesian Network which is presented with varying degrees of noise for the simulations. One of the proposed methods, X-Random bootstrap, performs better than the baselines in-terms of cumulative regret across various degrees of noise and different number of trials. In certain settings the cumulative regret of this method is less than half of the best baseline. The X-Fixed bootstrap performs comparably in most situations and particularly well when the number of trials is low. The study concludes that these algorithms could be a preferred alternative for solving linear bandit problems, especially when the distribution of the noise in the system is unknown.