Solving large-scale optimization problems has become feasible through distributed implementations.

Bayesian optimization has been successful at global optimization of expensive-to-evaluate multimodal objective functions.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

The dueling bandit is a learning framework wherein the feedback information in the learning process is restricted to a noisy comparison between a pair of actions. In this research, we address a dueling bandit problem based on a cost function over a continuous space. We propose a stochastic mirror descent algorithm and show that the algorithm achieves an O ( T log T) -regret bound under strong convexity and smoothness assumptions for the cost function. Subsequently, we clarify the equivalence between regret minimization in dueling bandit and convex optimization for the cost function. Moreover, when considering a lower bound in convex optimization, our algorithm is shown to achieve the optimal convergence rate in convex optimization and the optimal regret in dueling bandit except for a logarithmic factor.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

In order to improve the learning process, we follow a multi-batch approach in which the batch changes at each iteration.

Neural Information Processing Systems http://nips.cc/

This ambiguity in the optimization process can be removed by interpreting the space of weight vectors as a Riemannian manifold on which all the scaled versions of a weight vector correspond to a single point on the manifold.