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Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator
Maryam Fazel · Rong Ge · Sham Kakade · Mehran Mesbahi

Fri Jul 13 07:00 AM -- 07:20 AM (PDT) @ A1

Direct policy gradient methods for reinforcement learning and continuous control problems are a popular approach for a variety of reasons: 1) they are easy to implement without explicit knowledge of the underlying model, 2) they are an ``end-to-end'' approach, directly optimizing the performance metric of interest, 3) they inherently allow for richly parameterized policies. A notable drawback is that even in the most basic continuous control problem (that of linear quadratic regulators), these methods must solve a non-convex optimization problem, where little is understood about their efficiency from both computational and statistical perspectives. In contrast, system identification and model based planning in optimal control theory have a much more solid theoretical footing, where much is known with regards to their computational and statistical properties. This work bridges this gap showing that (model free) policy gradient methods globally converge to the optimal solution and are efficient (polynomially so in relevant problem dependent quantities) with regards to their sample and computational complexities.

Author Information

Maryam Fazel (University of Washington)
Rong Ge (Duke University)
Sham Kakade (University of Washington)

Sham Kakade is a Gordon McKay Professor of Computer Science and Statistics at Harvard University and a co-director of the recently announced Kempner Institute. He works on the mathematical foundations of machine learning and AI. Sham's thesis helped in laying the statistical foundations of reinforcement learning. With his collaborators, his additional contributions include: one of the first provably efficient policy search methods, Conservative Policy Iteration, for reinforcement learning; developing the mathematical foundations for the widely used linear bandit models and the Gaussian process bandit models; the tensor and spectral methodologies for provable estimation of latent variable models; the first sharp analysis of the perturbed gradient descent algorithm, along with the design and analysis of numerous other convex and non-convex algorithms. He is the recipient of the ICML Test of Time Award (2020), the IBM Pat Goldberg best paper award (in 2007), INFORMS Revenue Management and Pricing Prize (2014). He has been program chair for COLT 2011. Sham was an undergraduate at Caltech, where he studied physics and worked under the guidance of John Preskill in quantum computing. He then completed his Ph.D. in computational neuroscience at the Gatsby Unit at University College London, under the supervision of Peter Dayan. He was a postdoc at the Dept. of Computer Science, University of Pennsylvania , where he broadened his studies to include computational game theory and economics from the guidance of Michael Kearns. Sham has been a Principal Research Scientist at Microsoft Research, New England, an associate professor at the Department of Statistics, Wharton, UPenn, and an assistant professor at the Toyota Technological Institute at Chicago.

Mehran Mesbahi

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