# Accelerating Convergence in Global Non-Convex Optimization with Reversible Diffusion

arXiv: https://arxiv.org/abs/2305.11493 · HTML: https://mlsanity.com/paper/2305.11493/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 33 references that are in the map.
- First posted on arXiv 19 May 2023.

## Builds on (most cited first, 14 of 14)

- [Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis](https://mlsanity.com/paper/1702.03849/) (2017)
- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [A Complete Recipe for Stochastic Gradient MCMC](https://mlsanity.com/paper/1506.04696/) (2015)
- [Global Convergence of Langevin Dynamics Based Algorithms for Nonconvex Optimization](https://mlsanity.com/paper/1707.06618/) (2017)
- [Wasserstein Control of Mirror Langevin Monte Carlo](https://mlsanity.com/paper/2002.04363/) (2020)
- [Global Non-convex Optimization with Discretized Diffusions](https://mlsanity.com/paper/1810.12361/) (2018)
- [Convergence of the Riemannian Langevin Algorithm](https://mlsanity.com/paper/2204.10818/) (2022)
- [State-Dependent Temperature Control for Langevin Diffusions](https://mlsanity.com/paper/2011.07456/) (2020)
- [Fast Convergence of Langevin Dynamics on Manifold: Geodesics meet Log-Sobolev](https://mlsanity.com/paper/2010.05263/) (2020)
- [Improved Convergence Rate of Stochastic Gradient Langevin Dynamics with Variance Reduction and its Application to Optimization](https://mlsanity.com/paper/2203.16217/) (2022)
- [Langevin Dynamics with Continuous Tempering for Training Deep Neural Networks](https://mlsanity.com/paper/1703.04379/) (2017)
- [Adaptive State-Dependent Diffusion for Derivative-Free Optimization](https://mlsanity.com/paper/2302.04370/) (2023)
- [An Algebraically Converging Stochastic Gradient Descent Algorithm for Global Optimization](https://mlsanity.com/paper/2204.05923/) (2022)
- [Improved Langevin Monte Carlo for stochastic optimization via landscape modification](https://mlsanity.com/paper/2302.03973/) (2023)

## Abstract (arXiv)

Langevin Dynamics has been extensively employed in global non-convex optimization due to the concentration of its stationary distribution around the global minimum of the potential function at low temperatures. In this paper, we propose to utilize a more comprehensive class of stochastic processes, known as reversible diffusion, and apply the Euler-Maruyama discretization for global non-convex optimization. We design the diffusion coefficient to be larger when distant from the optimum and smaller when near, thus enabling accelerated convergence while regulating discretization error, a strategy inspired by landscape modifications. Our proposed method can also be seen as a time change of Langevin Dynamics, and we prove convergence with respect to KL divergence, investigating the trade-off between convergence speed and discretization error. The efficacy of our proposed method is demonstrated through numerical experiments.