mlsanityData to 14 Oct 2026

Online Estimation and Optimization of Utility-Based Shortfall Risk

arXiv 2111.08805 ↗First posted 16 Nov 2021stat.ML cs.LG q-fin.RMcited by 5

Not on the map. Why?

Abstract (arXiv)

Utility-Based Shortfall Risk (UBSR) is a risk metric that is increasingly popular in financial applications, owing to certain desirable properties that it enjoys. We consider the problem of estimating UBSR in a recursive setting, where samples from the underlying loss distribution are available one-at-a-time. We cast the UBSR estimation problem as a root finding problem, and propose stochastic approximation-based estimations schemes. We derive non-asymptotic bounds on the estimation error in the number of samples. We also consider the problem of UBSR optimization within a parameterized class of random variables. We propose a stochastic gradient descent based algorithm for UBSR optimization, and derive non-asymptotic bounds on its convergence.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 17 of its 67 references that are in the map. First posted on arXiv 16 Nov 2021.

Builds on

17 of 67 references.

References · 17

  1. 2016Optimization Methods for Large-Scale Machine Learningcited by 1,150
  2. 2013Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programmingcited by 724
  3. 2020Biased Stochastic First-Order Methods for Conditional Stochastic Optimization and Applications in Meta Learningcited by 47
  4. 2019Non-asymptotic Analysis of Biased Stochastic Approximation Schemecited by 45
  5. 2018Convergence and Concentration of Empirical Measures under Wasserstein Distance in Unbounded Functional Spacescited by 41
  6. 2018Zeroth-order Nonconvex Stochastic Optimization: Handling Constraints, High-Dimensionality and Saddle-Pointscited by 37
  7. 2015Cumulative Prospect Theory Meets Reinforcement Learning: Prediction and Controlcited by 34
  8. 2020Learning Bounds for Risk-sensitive Learningcited by 33
  9. 2019Distribution oblivious, risk-aware algorithms for multi-armed bandits with unbounded rewardscited by 19
  10. 2019A Wasserstein distance approach for concentration of empirical risk estimatescited by 18
  11. 2013Concentration bounds for temporal difference learning with linear function approximation: The case of batch data and uniform samplingcited by 13
  12. 2020PAC-Bayesian Bound for the Conditional Value at Riskcited by 13
5 more
  1. 2019Estimation of Spectral Risk Measurescited by 9
  2. 2017Computational aspects of robust optimized certainty equivalents and option pricingcited by 7
  3. 2020Non-asymptotic bounds for stochastic optimization with biased noisy gradient oraclescited by 6
  4. 2021Smoothed functional-based gradient algorithms for off-policy reinforcement learning: A non-asymptotic viewpointcited by 5
  5. 2014On perturbed proximal gradient algorithmscited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 2; 2025: 1; 2026: 1.

5 papers.

  1. 2024Multi-level Monte-Carlo Gradient Methods for Stochastic Optimization with Biased Oraclescited by 5
  2. 2023Optimization of utility-based shortfall risk: A non-asymptotic viewpointcited by 2
  3. 2024Concentration Bounds for Optimized Certainty Equivalent Risk Estimationcited by 2
  4. 2026Optimized Certainty Equivalent Risk Minimization Using Samples: Algorithms, Convergence Rates, and Applicationscited by 1
  5. 2025Optimizing Shortfall Risk Metric for Learning Regression Modelscited by 0