Estimation of Spectral Risk Measures

Authors

  • Ajay Kumar Pandey Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai, India
  • Prashanth L.A. Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai, India
  • Sanjay P. Bhat TCS Research, Hyderabad, India, and Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India

Keywords:

Stochastic Optimization

Abstract

We consider the problem of estimating a spectral risk measure (SRM) from i.i.d. samples, and propose a novel method that is based on numerical integration. We show that our SRM estimate concentrates exponentially, when the underlying distribution has bounded support. Further, we also consider the case when the underlying distribution satisfies an exponential moment bound, which includes sub-Gaussian and subexponential distributions. For these distributions, we derive a concentration bound for our estimation scheme. We validate the theoretical findings on a synthetic setup, and in a vehicular traffic routing application.

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Published

2021-05-18

How to Cite

Pandey, A. K., L.A., P., & Bhat, S. P. (2021). Estimation of Spectral Risk Measures. Proceedings of the AAAI Conference on Artificial Intelligence, 35(13), 12166-12173. Retrieved from https://ojs.aaai.org/index.php/AAAI/article/view/17444

Issue

Section

AAAI Technical Track on Reasoning under Uncertainty