A framework based on iterative coordinate minimization (CM) is developed for stochastic convex optimization. Given that exact coordinate minimization is impossible due to the unknown stochastic nature of the objective function, the crux of the proposed optimization algorithm is an optimal control of the minimization precision in each iteration. We establish the optimal precision control and the resulting order-optimal regret performance for strongly convex and separably nonsmooth functions. An interesting finding is that the optimal progression of precision across iterations is independent of the low-dimensional CM routine employed, suggesting a general framework for extending low-dimensional optimization routines to high-dimensional problems. The proposed algorithm is amenable to online implementation and inherits the scalability and parallelizability properties of CM for large-scale optimization. Requiring only a sublinear order of message exchanges, it also lends itself well to distributed computing as compared with the alternative approach of coordinate gradient descent.

We investigate crowdsourcing algorithms for finding the top-quality item within a large collection of objects with unknown intrinsic quality values. This is an important problem with many relevant applications, for example in networked recommendation systems. The core of the algorithms is that objects are distributed to crowd workers, who return a noisy and biased evaluation. All received evaluations are then combined, to identify the top-quality object. We first present a simple probabilistic model for the system under investigation. Then, we devise and study a class of efficient adaptive algorithms to assign in an effective way objects to workers. We compare the performance of several algorithms, which correspond to different choices of the design parameters/metrics. In the simulations we show that some of the algorithms achieve near optimal performance for a suitable setting of the system parameters.