Efficiently Escaping Saddle Points for Policy Optimization

arXiv (Cornell University)

Abstract

Policy gradient (PG) is widely used in reinforcement learning due to its scalability and good performance. In recent years, several variance-reduced PG methods have been proposed with a theoretical guarantee of converging to an approximate first-order stationary point (FOSP) with the sample complexity of $O(ε^{-3})$. However, FOSPs could be bad local optima or saddle points. Moreover, these algorithms often use importance sampling (IS) weights which could impair the statistical effectiveness of variance reduction. In this paper, we propose a variance-reduced second-order method that uses second-order information in the form of Hessian vector products (HVP) and converges to an approximate second-order stationary point (SOSP) with sample complexity of $\tilde{O}(ε^{-3})$. This rate improves the best-known sample complexity for achieving approximate SOSPs by a factor of $O(ε^{-0.5})$. Moreover, the proposed variance reduction technique bypasses IS weights by using HVP terms. Our experimental results show that the proposed algorithm outperforms the state of the art and is more robust to changes in random seeds.

Authors 5

1. Sadegh Khorasani

   École Polytechnique Fédérale de Lausanne

   Affiliation as printed

   School of Computer and Communication Sciences , EPFL" Lausanne , Switzerland

2. Saber Salehkaleybar Aachen Leiden Institute of Advanced Computer Science

   Leiden University · University of Applied Sciences Leiden

   Affiliation as printed

   Leiden Institute of Advanced Computer Science (LIACS) , Leiden University , , Leiden , The Netherlands

3. Negar Kiyavash

   École Polytechnique Fédérale de Lausanne

   Affiliation as printed

   College of Management of Technology , EPFL , Lausanne , Switzerland

4. Niao He

   ETH Zurich

   Affiliation as printed

   Department of Computer Science ETH Zurich

5. Matthias Grossglauser

   École Polytechnique Fédérale de Lausanne

   Affiliation as printed

   School of Computer and Communication Sciences , EPFL" Lausanne , Switzerland