{"ID":2851431,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.19141","arxiv_id":"2510.19141","title":"Policy Gradient Method for LQG Control via Input-Output-History Representation: Convergence to $O(ε)$-Stationary Points","abstract":"We study the policy gradient method (PGM) for the linear quadratic Gaussian (LQG) dynamic output-feedback control problem using an input-output-history (IOH) representation of the closed-loop system. First, we show that any dynamic output-feedback controller is equivalent to a static partial-state feedback gain for a new system representation characterized by a finite-length IOH. Leveraging this equivalence, we reformulate the search for an optimal dynamic output feedback controller as an optimization problem over the corresponding partial-state feedback gain. Next, we introduce a relaxed version of the IOH-based LQG problem by incorporating a small process noise with covariance $εI$ into the new system to ensure coerciveness, a key condition for establishing gradient-based convergence guarantees. Consequently, we show that a vanilla PGM for the relaxed problem converges to an $\\mathcal{O}(ε)$-stationary point, i.e., $\\overline{K}$ satisfying $\\|\\nabla J(\\overline{K})\\|_F \\leq \\mathcal{O}(ε)$, where $J$ denotes the original LQG cost. Numerical experiments empirically indicate convergence to the vicinity of the globally optimal LQG controller.","short_abstract":"We study the policy gradient method (PGM) for the linear quadratic Gaussian (LQG) dynamic output-feedback control problem using an input-output-history (IOH) representation of the closed-loop system. First, we show that any dynamic output-feedback controller is equivalent to a static partial-state feedback gain for a n...","url_abs":"https://arxiv.org/abs/2510.19141","url_pdf":"https://arxiv.org/pdf/2510.19141v1","authors":"[\"Tomonori Sadamoto\",\"Takashi Tanaka\"]","published":"2025-10-22T00:19:53Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}