We study policy optimization for gain-scheduled linear quadratic regulation, where one schedule of gains, interpolated through fixed weighting functions, is optimized against a family of plants. The resulting cost can develop spurious local minima, and existing convergence certificates are either local or severely conservative. We establish an exact identity: when the gradient of the cost is evaluated with the minimizer's closed-loop covariances, the scheduled cost is star-convex about the minimizer. The identity holds on the entire feasible set, for any parametrization of the schedule. Convergence is governed by a single dimensionless ratio. Wherever the ratio satisfies a threshold condition, gradient descent converges linearly to the optimum on entire sublevel regions at an explicit rate; at every spurious stationary point the condition necessarily fails. Experiments that maximize the ratio directly show the threshold to be an active boundary of the landscape. This extended version contains the complete proofs and additional numerical studies omitted from the letter for space.
The Frank--Wolfe framework is extended to input design for system identification with unknown dynamics and adaptive online LQR, and an $\mathcal{O}(1/M)$ convergence rate is established for the objective value, while strong convexity yields an $\mathcal{O}(1/\sqrt{M})$ rate for the iterates.
Fethi Bencherki, Bruce D. Lee, Nikolai Matni et al.· 0 citations
This letter develops a time-parallel policy-gradient framework for discrete-time nonlinear control-affine systems and proves that, for any finite horizon T, the state solver recovers the exact trajectory from any initialization in at most T iterations.
A novel spectrum assignment method is proposed to obtain an initial stabilizer for PI in continuous-time indefinite stochastic linear quadratic control with the help of the Lyapunov-type operator's spectrum, which is gradually approximated from the stable auxiliary system by adjusting a cumulative factor, thereby obtai...
We study policy optimization for discrete-time robust $\mathcal{H}_\infty$ control with static output-feedback, and present the first feasibility-preserving algorithm with a deterministic, non-asymptotic complexity guarantee. This problem naturally leads to a nonsmooth and nonconvex optimization over the set of stabili...
This appears to be the first time that a stochastic model-free policy optimization method for LQR converges with high probability with $\tilde{O}(1)$ per-iteration computation and polylogarithmic dependence on the confidence level.
This work introduces Boundary-Seeking Policy Gradient (BSPG), a first-order method whose update combines a tangential component that improves reward while preserving cost to first order with a signed, residual-driven normal component that regulates the policy toward the active boundary from either side.
Chenhua Fan, Jiahui Zhu, Yuhang Zhang et al.· 0 citations
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