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• W2912995476 abstract "We consider the problem of stochastic optimization with nonlinear constraints, where the decision variable is not vector-valued but instead a function belonging to a reproducing Kernel Hilbert Space (RKHS). Currently, there exist solutions to only special cases of this problem. To solve this constrained problem with kernels, we first generalize the Representer Theorem to a class of saddle-point problems defined over RKHS. Furthermore, we develop a primal-dual method which executes alternating projected primal/dual stochastic descent/ascent on the dual-augmented Lagrangian of this problem. The primal projection sets are low-dimensional subspaces of the ambient function space which are greedily constructed using matching pursuit. By tuning the projection-induced error to the algorithm step-size, we are able to establish mean convergence both in primal objective sub-optimality and constraint violation, respectively to the $mathcal{O}(sqrt{T})$ and $mathcal{O}(T^{3/4})$ neighborhoods, where $T$ is the total number of iterations. We evaluate the proposed method through numerical tests for the application of risk-aware supervised learning." @default.
• W2912995476 created "2019-02-21" @default.
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• W2912995476 date "2018-12-01" @default.
• W2912995476 modified "2023-10-01" @default.
• W2912995476 title "Projected Stochastic Primal-Dual Method for Constrained Online Learning with Kernels" @default.
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• W2912995476 doi "https://doi.org/10.1109/cdc.2018.8619068" @default.
• W2912995476 hasPublicationYear "2018" @default.
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