Stochastic Process Bandits: Upper Confidence Bounds Algorithms via Generic Chaining
This work addresses optimization challenges in continuous domains for machine learning and statistics, offering a novel algorithmic approach with theoretical guarantees.
The paper tackles the problem of global optimization in stochastic process bandits by introducing a UCB algorithm that uses generic chaining to operate over continuous domains, deriving generic regret bounds and proving lower bounds for Gaussian processes to assess optimality.
The paper considers the problem of global optimization in the setup of stochastic process bandits. We introduce an UCB algorithm which builds a cascade of discretization trees based on generic chaining in order to render possible his operability over a continuous domain. The theoretical framework applies to functions under weak probabilistic smoothness assumptions and also extends significantly the spectrum of application of UCB strategies. Moreover generic regret bounds are derived which are then specialized to Gaussian processes indexed on infinite-dimensional spaces as well as to quadratic forms of Gaussian processes. Lower bounds are also proved in the case of Gaussian processes to assess the optimality of the proposed algorithm.