• 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. 



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

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.

Approximation Methods for Bilevel Programming

An approximation algorithm is presented for solving a class of bilevel programming problem where the inner objective function is strongly convex and its finite-time convergence analysis under different convexity assumption on the outer objective function.

Finite Time Analysis of Linear Two-timescale Stochastic Approximation with Markovian Noise

The bounds show that there is no discrepancy in the convergence rate between Markovian and martingale noise, only the constants are affected by the mixing time of the Markov chain.