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A new approach in stochastic optimization via the use of stochastic gradientLangevin dynamics (SGLD) algorithms, which is a variant of stochastic gradientdecent (SGD) methods, allows us to efficiently approximate global minimizers ofpossibly complicated, high-dimensional landscapes. With this in mind, we extendhere the non-asymptotic analysis of SGLD to the case of discontinuousstochastic gradients. We are thus able to provide theoretical guarantees forthe algorithm's convergence in (standard) Wasserstein distances for both convexand non-convex objective functions. We also provide explicit upper estimates ofthe expected excess risk associated with the approximation of global minimizersof these objective functions. All these findings allow us to devise and presenta fully data-driven approach for the optimal allocation of weights for theminimization of CVaR of portfolio of assets with complete theoreticalguarantees for its performance. Numerical results illustrate our main findings.

A fully data-driven approach to minimizing CVaR for portfolio of assets via SGLD with discontinuous updating