Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization
We introduce an autonomous system with closed-loop damping for first-order convex optimization. While, to this day, optimal rates of convergence are almost exclusively achieved by non-autonomous methods via open-loop damping (e.g., Nesterov's algorithm), we show that our system, featuring a closed-loop damping, exhibits a rate arbitrarily close to the optimal one. We do so by coupling the damping and the speed of convergence of the system via a well-chosen Lyapunov function. By discretizing our system we then derive an algorithm and present numerical experiments supporting our theoretical findings.
Code (1)
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
A closed loop gradient descent algorithm applied to Rosenbrock's function
We introduce a novel adaptive damping technique for an inertial gradient system which finds application as a gradient descent algorithm for unconstrained optimisation. In an example using the non-convex Rosenbrock's func…
Composite learning backstepping control with guaranteed exponential stability and robustness
Adaptive backstepping control provides a feasible solution to achieve asymptotic tracking for mismatched uncertain nonlinear systems. However, input-to-state stability depends on high-gain feedback generated by nonlinear…
parameter estimationNeural Lyapunov Control of Unknown Nonlinear Systems with Stability Guarantees
Learning for control of dynamical systems with formal guarantees remains a challenging task. This paper proposes a learning framework to simultaneously stabilize an unknown nonlinear system with a neural controller and l…
validStabilization with Closed-loop DOA Enlargement: An Interval Analysis Approach
In this paper, the stabilization problem with closed-loop domain of attraction (DOA) enlargement for discrete-time general nonlinear plants is solved. First, a sufficient condition for asymptotic stabilization and estima…
Model-free Nearly Optimal Control of Constrained-Input Nonlinear Systems Based on Synchronous Reinforcement Learning
In this paper a novel model-free algorithm is proposed. This algorithm can learn the nearly optimal control law of constrained-input systems from online data without requiring any a priori knowledge of system dynamics. B…
Reinforcement Learning (RL)