• Corpus ID: 249642237

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

  title={Two-Timescale Stochastic Approximation for Bilevel Optimisation Problems in Continuous-Time Models},
  author={Louis Sharrock},
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. 

Parameter Estimation for the McKean-Vlasov Stochastic Differential Equation

We consider the problem of parameter estimation for a stochastic McKean-Vlasov equation, and the associated system of weakly interacting particles. We study two cases: one in which we observe



Convergence rate and averaging of nonlinear two-time-scale stochastic approximation algorithms

It is shown that both components of the averaged two-time-scale stochastic approximation algorithm simultaneously converge at the optimal rate $\sqrt{n}$.

On a continuous time stochastic approximation problem

The main effort is to derive the asymptotic properties of the algorithm, and it is shown that ast → ∞, a suitably normalized sequence of the estimation error,Τ√t(¯xtr−θ) is equivalent to a scaled sequences of the random noise process, namely, (1/ ∼t)∫0tr ξsds.

Nonlinear Two-Time-Scale Stochastic Approximation: Convergence and Finite-Time Performance

This paper studies the asymptotic convergence and finite-time analysis of the nonlinear two-time-scale stochastic approximation and shows that the method achieves a convergence in expectation at a rate $\mathcal{O}(1/k^{2/3})$, where $k$ is the number of iterations.

Continuous-time stochastic approximation: Convergence and asymptotic efficiency

A continuous-time stochastic approximation algorithm is proposed. It is shown that the estimate x y is strongly consistent and the averaged estimate is asymptotically efficient. The characteristics

Two-Timescale Stochastic Gradient Descent in Continuous Time with Applications to Joint Online Parameter Estimation and Optimal Sensor Placement

In this paper, we establish the almost sure convergence of two-timescale stochastic gradient descent algorithms in continuous time under general noise and stability conditions, extending well known

Stochastic Gradient Descent in Continuous Time: A Central Limit Theorem

The asymptotic convergence rate of the SGDCT algorithm is analyzed by proving a central limit theorem for strongly convex objective functions and, under slightly stronger conditions, for nonconvex objectives as well.

A Two-Timescale Framework for Bilevel Optimization: Complexity Analysis and Application to Actor-Critic

These are the first convergence rate results for using nonlinear TTSA algorithms on the concerned class of bilevel optimization problems and it is shown that a two-timescale actor-critic proximal policy optimization algorithm can be viewed as a special case of the framework.

Stochastic approximation with two time scales

On continuous-time stochastic approximation

The continuous-time RM and KW procedures are modified to suit the case when the measurement error is the process of dependent increment. By using a combined method connecting the probabilistic method

Asymptotic properties of two time-scale stochastic approximation algorithms with constant step sizes

  • V. TadićS. Meyn
  • Computer Science, Mathematics
    Proceedings of the 2003 American Control Conference, 2003.
  • 2003
Asymptotic properties of two time-scale stochastic approximation algorithms with constant step sizes are analyzed and the algorithms with additive noise and non-additive noise are considered.