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

2022/06/14 by Louis Sharrock, Sharrock, Louis
Decision Sciences · Economics, Econometrics and Finance · #Economic theories and models #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2206.06995

openalex publication_date 2022/06/14 · openalex created_date 2022/06/17 · openalex updated_date 2026/07/28

Abstract

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.

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