# Ito Diffusion Approximation of Universal Ito Chains for Sampling, Optimization and Boosting

arXiv: https://arxiv.org/abs/2310.06081 · HTML: https://mlsanity.com/paper/2310.06081/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 61 references that are in the map.
- First posted on arXiv 9 Oct 2023.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis](https://mlsanity.com/paper/1702.03849/) (2017)
- [A Tail-Index Analysis of Stochastic Gradient Noise in Deep Neural Networks](https://mlsanity.com/paper/1901.06053/) (2019)
- [Theoretical guarantees for approximate sampling from smooth and log-concave densities](https://mlsanity.com/paper/1412.7392/) (2014)
- [Optimal rates for zero-order convex optimization: the power of two function evaluations](https://mlsanity.com/paper/1312.2139/) (2013)
- [High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1605.01559/) (2016)
- [A Variational Inequality Perspective on Generative Adversarial Networks](https://mlsanity.com/paper/1802.10551/) (2018)
- [Analysis of Langevin Monte Carlo via convex optimization](https://mlsanity.com/paper/1802.09188/) (2018)
- [Implicit regularization for deep neural networks driven by an Ornstein-Uhlenbeck like process](https://mlsanity.com/paper/1904.09080/) (2019)
- [User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient](https://mlsanity.com/paper/1710.00095/) (2017)
- [Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundations](https://mlsanity.com/paper/1811.01558/) (2018)
- [Sharp convergence rates for Langevin dynamics in the nonconvex setting](https://mlsanity.com/paper/1805.01648/) (2018)
- [Sampling Can Be Faster Than Optimization](https://mlsanity.com/paper/1811.08413/) (2018)
- [Global Non-convex Optimization with Discretized Diffusions](https://mlsanity.com/paper/1810.12361/) (2018)
- [Stochastic Runge-Kutta Accelerates Langevin Monte Carlo and Beyond](https://mlsanity.com/paper/1906.07868/) (2019)
- [Efficient Regret Minimization in Non-Convex Games](https://mlsanity.com/paper/1708.00075/) (2017)
- [Langevin Monte Carlo without smoothness](https://mlsanity.com/paper/1905.13285/) (2019)
- [Continuous-time Models for Stochastic Optimization Algorithms](https://mlsanity.com/paper/1810.02565/) (2018)
- [Uniform-in-Time Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximation](https://mlsanity.com/paper/1902.00635/) (2019)
- [SGLB: Stochastic Gradient Langevin Boosting](https://mlsanity.com/paper/2001.07248/) (2020)
- [Stochastic Gradient Langevin Dynamics Algorithms with Adaptive Drifts](https://mlsanity.com/paper/2009.09535/) (2020)
- [Dimension-free convergence rates for gradient Langevin dynamics in RKHS](https://mlsanity.com/paper/2003.00306/) (2020)
- [Adaptively Preconditioned Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/1906.04324/) (2019)

## Abstract (arXiv)

In this work, we consider rather general and broad class of Markov chains, Ito chains, that look like Euler-Maryama discretization of some Stochastic Differential Equation. The chain we study is a unified framework for theoretical analysis. It comes with almost arbitrary isotropic and state-dependent noise instead of normal and state-independent one as in most related papers. Moreover, in our chain the drift and diffusion coefficient can be inexact in order to cover wide range of applications as Stochastic Gradient Langevin Dynamics, sampling, Stochastic Gradient Descent or Stochastic Gradient Boosting. We prove the bound in W2-distance between the laws of our Ito chain and corresponding differential equation. These results improve or cover most of the known estimates. And for some particular cases, our analysis is the first.