Learning to Satisfy Unknown Constraints in Iterative MPC

We propose a control design method for linear time-invariant systems that iteratively learns to satisfy unknown polyhedral state constraints. At each iteration of a repetitive task, the method constructs an estimate of the unknown environment constraints using collected closed-loop trajectory data. This estimated constraint set is improved iteratively upon collection of additional data. An MPC controller is then designed to robustly satisfy the estimated constraint set. This paper presents the details of the proposed approach, and provides robust and probabilistic guarantees of constraint satisfaction as a function of the number of executed task iterations. We demonstrate the safety of the proposed framework and explore the safety vs. performance trade-off in a detailed numerical example.Comment: Long version of the final paper for IEEE-CDC 2020. First two authors contributed equall

Convergence in Models with Bounded Expected Relative Hazard Rates

We provide a general framework to study stochastic sequences related to individual learning in economics, learning automata in computer sciences, social learning in marketing, and other applications. More precisely, we study the asymptotic properties of a class of stochastic sequences that take values in $[0,1]$ and satisfy a property called "bounded expected relative hazard rates." Sequences that satisfy this property and feature "small step-size" or "shrinking step-size" converge to 1 with high probability or almost surely, respectively. These convergence results yield conditions for the learning models in B\"orgers, Morales, and Sarin (2004), Erev and Roth (1998), and Schlag (1998) to choose expected payoff maximizing actions with probability one in the long run.Comment: After revision. Accepted for publication by Journal of Economic Theor

Development Of Learning Material Of Pakem-Plus For Mathematics Lesson At Elementary School

Active, creative, effective, and enjoy full learning (PAKEM) needs to be supported by good teachers’ understanding about both of content and choosing context. In Aceh Province having Islamic educational concept, it is rather difficult to find teachers who have both good knowledge and religious concept. To solve that problem, this research develops some learning material for PAKEM to grow optimally potential students, teachers, and culture (including the Islamic culture) and to improve the education quality, which is writer called PAKEM-Plus. Learning material developed consist of teacher’s guidebook, lesson plan, student’s worksheet, and classroom assessment for mathematics at grade 5 which satisfy validity and practicality criteria. This is a developmental research to develop a learning material. The result of this research is a learning material has satisfied validity and practicality criteria. Key word: Active, creative, effective, and enjoy full learning (PAKEM), Islamic cultur

Learning science and technology through cooperative education.

Cooperative education, a form of experiential or work‐integrated learning is common in tertiary educational institutions worldwide. However, in New Zealand few institutions provide work‐integrated learning programs in science or technology, and the management and process of work‐integrated learning programs is not that well understood. How well do such programs work? What infrastructure is needed to ensure learning actually occurs? Are graduates of work‐integrated learning programs able to satisfy employer needs? This chapter synthesizes decades of work around such issues, and details research initiatives that provide valuable insights into how students learn science on in the workplace, how their skill development matches that desired by employers, and best practice for management of work‐integrated learning in science and engineering (Asia‐Pacific Journal of Cooperative Education, 2007, 8(2), 131‐147)

Axiomatic Interpretability for Multiclass Additive Models

Generalized additive models (GAMs) are favored in many regression and binary classification problems because they are able to fit complex, nonlinear functions while still remaining interpretable. In the first part of this paper, we generalize a state-of-the-art GAM learning algorithm based on boosted trees to the multiclass setting, and show that this multiclass algorithm outperforms existing GAM learning algorithms and sometimes matches the performance of full complexity models such as gradient boosted trees. In the second part, we turn our attention to the interpretability of GAMs in the multiclass setting. Surprisingly, the natural interpretability of GAMs breaks down when there are more than two classes. Naive interpretation of multiclass GAMs can lead to false conclusions. Inspired by binary GAMs, we identify two axioms that any additive model must satisfy in order to not be visually misleading. We then develop a technique called Additive Post-Processing for Interpretability (API), that provably transforms a pre-trained additive model to satisfy the interpretability axioms without sacrificing accuracy. The technique works not just on models trained with our learning algorithm, but on any multiclass additive model, including multiclass linear and logistic regression. We demonstrate the effectiveness of API on a 12-class infant mortality dataset.Comment: KDD 201