Multi-Armed Bandits: Combinatorial/Submodular/Gaussian:

Combinatorial Bandits:

Exploiting structure in the data across multiple dimensions can lead to efficient techniques for efficient sampling and fingerprinting. The figure alongside shows different network service attributes dependence on time, spatial locations and data service quality measurements thus motivating tensor structure. Further, the map shows the received signal strength in indoor has spatial dependence and the signals from different APs are correlated and thus adaptive sampling can reduce fingerprints needed for localization.

Gaussian Process Bandits:

Bayesian optimization is a framework for global search via maximum a posteriori updates rather than simulated annealing, and has gained prominence for decision-making under uncertainty. In this work, we cast Bayesian optimization as a multi-armed bandit problem, where the payoff function is sampled from a Gaussian process (GP). Further, we focus on action selections via upper confidence bound (UCB) or expected improvement (EI) due to their prevalent use in practice. We derive sublinear regret bounds of GP bandit algorithms up to factors depending on the compression parameter for both discrete and continuous action sets. Experimentally, we observe state of the art accuracy and complexity tradeoffs for GP bandit algorithms applied to global optimization, suggesting the merits of compressed GPs in bandit settings.