Conservative Stochastic Optimization With Expectation Constraints

This paper considers stochastic convex optimization problems where the objective and constraint functions involve expectations with respect to data indices or environmental variables, in addition deterministic constraints on domain of variables. Since underlying distribution is unknown a priori, closed-form solution generally not available, classical paradigms are applicable. State-of-the-art approaches, such as those using saddle point framework, able ensure that optimality gap well violation decay O (T -1/2 ) T number gradients. In this work, we propose novel conservative algorithm (CSOA) achieves zero average gap. Further, also consider scenario carrying out projection step onto at every iteration viable. Traditionally, operation can be avoided by considering conditional gradient Frank-Wolfe (FW) variant algorithm. The state-of-the-art FW variants achieve an xmlns:xlink="http://www.w3.org/1999/xlink">-1/3 after iterations, though these algorithms have been applied functional expectation constraints. FW-CSOA only projection-free but xmlns:xlink="http://www.w3.org/1999/xlink">-1/4 efficacy proposed tested two relevant problems: fair classification structured matrix completion.