Fast Algorithms for Online Stochastic Convex Programming
This work addresses a broad class of stochastic online optimization problems, including packing and matching, with incremental improvements in algorithm efficiency and simplicity.
The authors tackled the online stochastic Convex Programming problem, a general framework for stochastic online problems with concave objectives and convex constraints, and presented fast algorithms achieving near-optimal regret guarantees in i.i.d. and random permutation models, with applications like online packing yielding simpler, faster primal-dual algorithms with optimal competitive ratios.
We introduce the online stochastic Convex Programming (CP) problem, a very general version of stochastic online problems which allows arbitrary concave objectives and convex feasibility constraints. Many well-studied problems like online stochastic packing and covering, online stochastic matching with concave returns, etc. form a special case of online stochastic CP. We present fast algorithms for these problems, which achieve near-optimal regret guarantees for both the i.i.d. and the random permutation models of stochastic inputs. When applied to the special case online packing, our ideas yield a simpler and faster primal-dual algorithm for this well studied problem, which achieves the optimal competitive ratio. Our techniques make explicit the connection of primal-dual paradigm and online learning to online stochastic CP.