2016/12/31 by Jan-Peter Calliess, Calliess, Jan-Peter · 5 citations
Computer Science · Engineering · #Artificial Intelligence (cs.AI) #Control Systems and Identification #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #G.1.2 #G.3 #Gaussian Processes and Bayesian Inference #I.2.6 #I.2.8 #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Systems and Control (eess.SY) #Target Tracking and Data Fusion in Sensor Networks #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1701.00178
openalex publication_date 2016/12/31 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
Techniques known as Nonlinear Set Membership prediction, Lipschitz\nInterpolation or Kinky Inference are approaches to machine learning that\nutilise presupposed Lipschitz properties to compute inferences over unobserved\nfunction values. Provided a bound on the true best Lipschitz constant of the\ntarget function is known a priori they offer convergence guarantees as well as\nbounds around the predictions. Considering a more general setting that builds\non Hoelder continuity relative to pseudo-metrics, we propose an online method\nfor estimating the Hoelder constant online from function value observations\nthat possibly are corrupted by bounded observational errors. Utilising this to\ncompute adaptive parameters within a kinky inference rule gives rise to a\nnonparametric machine learning method, for which we establish strong universal\napproximation guarantees. That is, we show that our prediction rule can learn\nany continuous function in the limit of increasingly dense data to within a\nworst-case error bound that depends on the level of observational uncertainty.\nWe apply our method in the context of nonparametric model-reference adaptive\ncontrol (MRAC). Across a range of simulated aircraft roll-dynamics and\nperformance metrics our approach outperforms recently proposed alternatives\nthat were based on Gaussian processes and RBF-neural networks. For\ndiscrete-time systems, we provide guarantees on the tracking success of our\nlearning-based controllers both for the batch and the online learning setting.\n