We consider two algorithms that have been shown to have accelerated performance, Polyak's heavy ball method and Nesterov's acceleration method. In the context of adaptive control, we show that both algorithms will present accelerated learning phenomenon under persistent excitation. Simulation results show that the two algorithms have very similar behavior and are both faster than normalized gradient descent.
This paper considers the problem of real-time control and learning in dynamic systems subjected to uncertainties. Adaptive approaches are proposed to address the problem, which are combined with methods and tools in Reinforcement Learning (RL) and Machine Learning (ML). Algorithms are proposed in continuous-time that combine adaptive approaches with RL leading to online control policies that guarantee stable behavior in the presence of parametric uncertainties that occur in real-time. Algorithms are proposed in discrete-time that combine adaptive approaches proposed for parameter and output estimation and ML approaches proposed for accelerated performance that guarantee stable estimation even in the presence of time-varying regressors, and for accelerated learning of the parameters with persistent excitation. Numerical validations of all algorithms are carried out using a quadrotor landing task on a moving platform and benchmark problems in ML. All results clearly point out the advantage of the proposed integrative approaches for real-time control and learning.
Recent methods in the machine learning literature have proposed a Gaussian noisebased exogenous signal to learn the parameters of a dynamic system. In this paper, we propose the use of a spectral lines-based deterministic exogenous signal to solve the same problem. Our theoretical analysis consists of a new toolkit which employs the theory of spectral lines, retains the stochastic setting, and leads to non-asymptotic bounds on the parameter estimation error. The results are shown to lead to a tunable parameter identification error. In particular, it is shown that the identification error can be minimized through an an optimal choice of the spectrum of the exogenous signal.Preprint. Under review.
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