# Stochastic Multiple Target Sampling Gradient Descent

arXiv: https://arxiv.org/abs/2206.01934 · HTML: https://mlsanity.com/paper/2206.01934/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 42 references that are in the map.
- First posted on arXiv 4 Jun 2022.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Pareto Multi-Task Learning](https://mlsanity.com/paper/1912.12854/) (2019)
- [Learning the Pareto Front with Hypernetworks](https://mlsanity.com/paper/2010.04104/) (2020)
- [Pareto Self-Supervised Training for Few-Shot Learning](https://mlsanity.com/paper/2104.07841/) (2021)
- [Multi-Objective Meta Learning](https://mlsanity.com/paper/2102.07121/) (2021)
- [A Modest Pareto Optimisation Analysis of Dependency Parsers in 2021](https://mlsanity.com/paper/2106.04216/) (2021)
- [Adaptive Distillation: Aggregating Knowledge from Multiple Paths for Efficient Distillation](https://mlsanity.com/paper/2110.09674/) (2021)

## Built on by (most cited first, 14 of 14)

- [Beyond Losses Reweighting: Empowering Multi-Task Learning via the Generalization Perspective](https://mlsanity.com/paper/2211.13723/) (2022)
- [Flat Seeking Bayesian Neural Networks](https://mlsanity.com/paper/2302.02713/) (2023)
- [Controllable Prompt Tuning For Balancing Group Distributional Robustness](https://mlsanity.com/paper/2403.02695/) (2024)
- [Diffusion Models For Multi-Modal Generative Modeling](https://mlsanity.com/paper/2407.17571/) (2024)
- [FERERO: A Flexible Framework for Preference-Guided Multi-Objective Learning](https://mlsanity.com/paper/2412.01773/) (2024)
- [Enhancing Domain Adaptation through Prompt Gradient Alignment](https://mlsanity.com/paper/2406.09353/) (2024)
- [Optimal Transport Model Distributional Robustness](https://mlsanity.com/paper/2306.04178/) (2023)
- [Beyond Reasoning Gains: Mitigating General-Capability Forgetting in Large Reasoning Models](https://mlsanity.com/paper/2510.21978/) (2025)
- [Improving Pareto Set Learning for Expensive Multi-objective Optimization via Stein Variational Hypernetworks](https://mlsanity.com/paper/2412.17312/) (2024)
- [Sharpness-Guided Group Relative Policy Optimization via Probability Shaping](https://mlsanity.com/paper/2511.00066/) (2025)
- [Multiple Wasserstein Gradient Descent Algorithm for Multi-Objective Distributional Optimization](https://mlsanity.com/paper/2505.18765/) (2025)
- [Agnostic Sharpness-Aware Minimization](https://mlsanity.com/paper/2406.07107/) (2024)
- [Multi-objective Differentiable Neural Architecture Search](https://mlsanity.com/paper/2402.18213/) (2024)
- [Accelerated Multiple Wasserstein Gradient Flows for Multi-objective Distributional Optimization](https://mlsanity.com/paper/2601.19220/) (2026)

## Abstract (arXiv)

Sampling from an unnormalized target distribution is an essential problem with many applications in probabilistic inference. Stein Variational Gradient Descent (SVGD) has been shown to be a powerful method that iteratively updates a set of particles to approximate the distribution of interest. Furthermore, when analysing its asymptotic properties, SVGD reduces exactly to a single-objective optimization problem and can be viewed as a probabilistic version of this single-objective optimization problem. A natural question then arises: "Can we derive a probabilistic version of the multi-objective optimization?". To answer this question, we propose Stochastic Multiple Target Sampling Gradient Descent (MT-SGD), enabling us to sample from multiple unnormalized target distributions. Specifically, our MT-SGD conducts a flow of intermediate distributions gradually orienting to multiple target distributions, which allows the sampled particles to move to the joint high-likelihood region of the target distributions. Interestingly, the asymptotic analysis shows that our approach reduces exactly to the multiple-gradient descent algorithm for multi-objective optimization, as expected. Finally, we conduct comprehensive experiments to demonstrate the merit of our approach to multi-task learning.