They can work in conjunction - In the domain of website optimization, where visitor attributes are often greater predictors of value than website content, a system driven by search space optimization can more easily take into account changes in those variables - eg; time of day, traffic source, device type - and incorporate those inputs to climb multiple 'hills' simultaneously.
The allocation of traffic based on the evolving optimal search space (blue button for visitors from Facebook) can then be driven through an MAB or something similar.
The allocation of traffic based on the evolving optimal search space (blue button for visitors from Facebook) can then be driven through an MAB or something similar.