# Two-Timescale Stochastic Approximation for Bilevel Optimisation Problems in Continuous-Time Models

arXiv: https://arxiv.org/abs/2206.06995 · HTML: https://mlsanity.com/paper/2206.06995/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 45 references that are in the map.
- First posted on arXiv 14 Jun 2022.

## Builds on (most cited first, 22 of 22)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [Meta-learning with differentiable closed-form solvers](https://mlsanity.com/paper/1805.08136/) (2018)
- [Approximation Methods for Bilevel Programming](https://mlsanity.com/paper/1802.02246/) (2018)
- [Truncated Back-propagation for Bilevel Optimization](https://mlsanity.com/paper/1810.10667/) (2018)
- [A Two-Timescale Framework for Bilevel Optimization: Complexity Analysis and Application to Actor-Critic](https://mlsanity.com/paper/2007.05170/) (2020)
- [A Finite Time Analysis of Two Time-Scale Actor Critic Methods](https://mlsanity.com/paper/2005.01350/) (2020)
- [Finite Time Analysis of Linear Two-timescale Stochastic Approximation with Markovian Noise](https://mlsanity.com/paper/2002.01268/) (2020)
- [Continuous-Time Model-Based Reinforcement Learning](https://mlsanity.com/paper/2102.04764/) (2021)
- [Finite-Time Performance Bounds and Adaptive Learning Rate Selection for Two Time-Scale Reinforcement Learning](https://mlsanity.com/paper/1907.06290/) (2019)
- [Nonlinear Two-Time-Scale Stochastic Approximation: Convergence and Finite-Time Performance](https://mlsanity.com/paper/2011.01868/) (2020)
- [Finite-Sample Analysis of Off-Policy Natural Actor-Critic Algorithm](https://mlsanity.com/paper/2102.09318/) (2021)
- [Multi-Level Stochastic Gradient Methods for Nested Composition Optimization](https://mlsanity.com/paper/1801.03600/) (2018)
- [Finite-Time Analysis and Restarting Scheme for Linear Two-Time-Scale Stochastic Approximation](https://mlsanity.com/paper/1912.10583/) (2019)
- [Stochastic Gradient Descent in Continuous Time](https://mlsanity.com/paper/1611.05545/) (2016)
- [Stochastic Gradient Descent in Continuous Time: A Central Limit Theorem](https://mlsanity.com/paper/1710.04273/) (2017)
- [Parameter Estimation for the McKean-Vlasov Stochastic Differential Equation](https://mlsanity.com/paper/2106.13751/) (2021)
- [Multimodal Meta-Learning for Time Series Regression](https://mlsanity.com/paper/2108.02842/) (2021)
- [Online Maximum Likelihood Estimation of the Parameters of Partially Observed Diffusion Processes](https://mlsanity.com/paper/1611.00170/) (2016)
- [Two-Timescale Stochastic Gradient Descent in Continuous Time with Applications to Joint Online Parameter Estimation and Optimal Sensor Placement](https://mlsanity.com/paper/2007.15998/) (2020)
- [On stochastic mirror descent with interacting particles: convergence properties and variance reduction](https://mlsanity.com/paper/2007.07704/) (2020)

## Built on by (most cited first, 2 of 2)

- [Recursive Maximum Likelihood Estimation for Interacting Particle Systems using Virtual Particles](https://mlsanity.com/paper/2605.00786/) (2026)
- [Distribution-Aware Robust Bilevel Optimization: Quantile-Guided Huber Updates in Two-Timescale Stochastic Approximation](https://mlsanity.com/paper/2606.22436/) (2026)

## Abstract (arXiv)

We analyse the asymptotic properties of a continuous-time, two-timescale stochastic approximation algorithm designed for stochastic bilevel optimisation problems in continuous-time models. We obtain the weak convergence rate of this algorithm in the form of a central limit theorem. We also demonstrate how this algorithm can be applied to several continuous-time bilevel optimisation problems.