Regularized quasi-monotone method for stochastic optimization

We adapt the quasi-monotone method, an algorithm characterized by uniquely having convergence quality guarantees for last iterate, composite convex minimization in stochastic setting. For proposed numerical scheme we derive optimal rate of $$\text{ O }\left( \frac{1}{\sqrt{k+1}}\right)$$ terms rather than on average as it is standard subgradient methods. The theoretical guarantee individual regularized method confirmed experiments $$\ell _1$$ -regularized robust linear regression.