On the Global Convergence and Approximation Benefits of Policy Gradient Methods

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Shows that gradient descent on parameterized policies avoids suboptimal stationary points when two concrete conditions hold: the policy class is closed under policy improvement and each one‑step policy‑improvement subproblem has no bad stationary points. Proof rewrites the multi‑period loss via a weighted Bellman single‑period objective, assumes exact gradients and full‑support initial state weighting, and recovers prior LQR/global results. For state aggregation the limiting loss is within two times inherent error of optimal.

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1. 0:00Global Optimality Guarantee and Approximation Benefits of Policy Gradient Methods Daniel Russo Columbia Business School
2. 9:07So we've reduced DP to Nonconvex Optimiza For a simple two state example where the parameterized policy class contains the optimum, PG can get stuck in a bad local minimum.
3. 10:18Hope and Mystery What drives global convergence? What is special about LQ control?
4. 11:53Main Contribution of Bhandari & Russo, 2019 We identify general conditions ensuring the policy gradient loss function has no suboptimal stationary points.
5. 20:58Some related work Prior work • Thomas (2014) shows the policy gradient is never exactly zero for softmax policies with • Kakade and Langford (2002) CPI analysis lays groundwork for PG analysis
6. 23:36Approximation benefits of policy gradient met PG inherits nice structure to the problem that makes policy iteration tractable. But why are we using policy gradient? Benefits of directly optimizing

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