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Repairing Learned Controllers with Convex Optimization: A Case Study

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 11494)


Despite the increasing popularity of Machine Learning methods, their usage in safety-critical applications is sometimes limited by the impossibility of providing formal guarantees on their behaviour. In this work we focus on one such application, where Kernel Ridge Regression with Random Fourier Features is used to learn controllers for a prosthetic hand. Due to the non-linearity of the activation function used, these controllers sometimes fail in correctly identifying users’ intention. Under specific circumstances muscular activation levels may be misinterpreted by the method, resulting in the prosthetic hand not behaving as intended. To alleviate this problem, we propose a novel method to verify the presence of this kind of intent detection mismatch and to repair controllers leveraging off-the-shelf LP technology without using additional data. We demonstrate the feasibility of our approach using datasets gathered from human participants.

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  1. 1.

    In practice, the value of \(t_a\) is upper bounded by operating range of EMG sensors.

  2. 2.

    We implemented our procedure using Python version 2.7. and the libraries sklearn and cvxopt for learning and optimization respectively. The default solver of cvxopt, i.e., conelp, was used – see [27] for more details. All the experiments are capped at 10 min of CPU time and 4 GBs of memory; experiments ran on a Ubuntu 18.04 machine equipped with a quad-core i5 Intel CPU running at 2.60 GHz.

  3. 3.

    Notice that for power-grasping \(a_{max}\) is equal to one.


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Correspondence to Dario Guidotti .

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Guidotti, D., Leofante, F., Castellini, C., Tacchella, A. (2019). Repairing Learned Controllers with Convex Optimization: A Case Study. In: Rousseau, LM., Stergiou, K. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2019. Lecture Notes in Computer Science(), vol 11494. Springer, Cham.

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