A stochastic feasible level-set method maintains a high-probability feasible solution path for convex optimization with expectation constraints, with iteration complexity comparable to stochastic subgradient methods.
Linear Convergence of Stochastic Frank Wolfe Variants
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abstract
In this paper, we show that the Away-step Stochastic Frank-Wolfe Algorithm (ASFW) and Pairwise Stochastic Frank-Wolfe algorithm (PSFW) converge linearly in expectation. We also show that if an algorithm convergences linearly in expectation then it converges linearly almost surely. In order to prove these results, we develop a novel proof technique based on concepts of empirical processes and concentration inequalities. Such a technique has rarely been used to derive the convergence rates of stochastic optimization algorithms. In large-scale numerical experiments, ASFW and PSFW perform as well as or better than their stochastic competitors in actual CPU time.
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A Data Efficient and Feasible Level Set Method for Stochastic Convex Optimization with Expectation Constraints
A stochastic feasible level-set method maintains a high-probability feasible solution path for convex optimization with expectation constraints, with iteration complexity comparable to stochastic subgradient methods.