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

arXiv: https://arxiv.org/abs/2007.01672 · HTML: https://mlsanity.com/paper/2007.01672/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2020.

## Built on by (most cited first, 4 of 4)

- [Non-asymptotic estimates for TUSLA algorithm for non-convex learning with applications to neural networks with ReLU activation function](https://mlsanity.com/paper/2107.08649/) (2021)
- [Langevin dynamics based algorithm e-THvarepsilonO POULA for stochastic optimization problems with discontinuous stochastic gradient](https://mlsanity.com/paper/2210.13193/) (2022)
- [kTULA: A Langevin sampling algorithm with improved KL bounds under super-linear log-gradients](https://mlsanity.com/paper/2506.04878/) (2025)
- [The Tamed Subgradient Unadjusted Langevin Algorithm beyond Convexity](https://mlsanity.com/paper/2608.06283/) (2026)

## Abstract (arXiv)

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