Global Convergence of Policy Gradient Primal-Dual Methods for Risk-Constrained LQRs

Feiran Zhao, Keyou You, Tamer Basar

Research output: Contribution to journalArticlepeer-review


While the techniques in optimal control theory are often model-based, the policy optimization (PO) approach directly optimizes the performance metric of interest. Even though it has been an essential approach for reinforcement learning problems, there is little theoretical understanding of its performance. In this article, we focus on the risk-constrained linear quadratic regulator problem via the PO approach, which requires addressing a challenging nonconvex constrained optimization problem. To solve it, we first build on our earlier result that an optimal policy has a time-invariant affine structure to show that the associated Lagrangian function is coercive, locally gradient dominated, and has a local Lipschitz continuous gradient, based on which we establish strong duality. Then, we design policy gradient primal-dual methods with global convergence guarantees in both model-based and sample-based settings. Finally, we use samples of system trajectories in simulations to validate our methods.

Original languageEnglish (US)
Pages (from-to)2934-2949
Number of pages16
JournalIEEE Transactions on Automatic Control
Issue number5
StatePublished - May 1 2023


  • Gradient descent
  • policy optimization (PO)
  • reinforcement learning
  • risk-constrained linear quadratic regulator (RC-LQR)
  • stochastic control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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