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

This paper analyzes a two-timescale stochastic algorithm framework for bilevel optimization. Bilevel optimization is a class of problems which exhibits a two-level structure, and its goal is to minimize an outer objective function with variables which are constrained to be the optimal solution to an (inner) optimization problem. We consider the case when the inner problem is unconstrained and strongly convex, while the outer problem is constrained and has a smooth objective function. We propose a two-timescale stochastic approximation (TTSA) algorithm for tackling such a bilevel problem. In the algorithm, a stochastic gradient update with a larger step size is used for the inner problem, while a projected stochastic gradient update with a smaller step size is used for the outer problem. We analyze the convergence rates for the TTSA algorithm under various settings: when the outer problem is strongly convex (resp. weakly convex), the TTSA algorithm finds an-optimal (resp.-stationary) solution, where is the total iteration number. As an application, we show that a two-timescale natural actor-critic proximal policy optimization algorithm can be viewed as a special case of our TTSA framework. Importantly, the natural actor-critic algorithm is shown to converge at a rate of in terms of the gap in expected discounted reward compared to a global optimal policy.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON OPTIMIZATION; Vol.33 No.1 January-March 2023

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 147-180

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

BILEVEL OPTIMIZATION
TWO-TIMESCALE STOCHASTIC APPROXIMATION
ACTOR-CRITIC

Info Detail Spesifik

https://doi.org/10.1137/20M1387341

Pernyataan Tanggungjawab

Mingyi Hong, Hoi-To Wai, Zhaoran Wang, Zhuoran Yang

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