Projected Stochastic Primal-Dual Method for Constrained Online Learning With Kernels

You are here

Top Reasons to Join SPS Today!

1. IEEE Signal Processing Magazine
2. Signal Processing Digital Library*
3. Inside Signal Processing Newsletter
4. SPS Resource Center
5. Career advancement & recognition
6. Discounts on conferences and publications
7. Professional networking
8. Communities for students, young professionals, and women
9. Volunteer opportunities
10. Coming soon! PDH/CEU credits
Click here to learn more.

Projected Stochastic Primal-Dual Method for Constrained Online Learning With Kernels

By: 
Alec Koppel; Kaiqing Zhang; Hao Zhu; Tamer Başar

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. Then, we develop a primal-dual method which that executes alternating projected primal/dual stochastic gradient descent/ascent on the dual-augmented Lagrangian of the 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 in both primal objective sub-optimality and constraint violation, to respective O(T)  and O(T3/4 )  neighborhoods. Here, T is the final iteration index and the constant step-size is chosen as 1/T √  with 1/T approximation budget. Finally, we demonstrate experimentally the effectiveness of the proposed method for risk-aware supervised learning.

Table of Contents:

TSP Featured Articles

SPS on Facebook

SPS on Twitter

SPS Videos


Signal Processing in Home Assistants

 


Multimedia Forensics


Careers in Signal Processing             

 


Under the Radar