# Online Estimation and Optimization of Utility-Based Shortfall Risk

arXiv: https://arxiv.org/abs/2111.08805 · HTML: https://mlsanity.com/paper/2111.08805/

## 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 (most cited first, 17 of 17)

- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Biased Stochastic First-Order Methods for Conditional Stochastic Optimization and Applications in Meta Learning](https://mlsanity.com/paper/2002.10790/) (2020)
- [Non-asymptotic Analysis of Biased Stochastic Approximation Scheme](https://mlsanity.com/paper/1902.00629/) (2019)
- [Convergence and Concentration of Empirical Measures under Wasserstein Distance in Unbounded Functional Spaces](https://mlsanity.com/paper/1804.10556/) (2018)
- [Zeroth-order Nonconvex Stochastic Optimization: Handling Constraints, High-Dimensionality and Saddle-Points](https://mlsanity.com/paper/1809.06474/) (2018)
- [Cumulative Prospect Theory Meets Reinforcement Learning: Prediction and Control](https://mlsanity.com/paper/1506.02632/) (2015)
- [Learning Bounds for Risk-sensitive Learning](https://mlsanity.com/paper/2006.08138/) (2020)
- [Distribution oblivious, risk-aware algorithms for multi-armed bandits with unbounded rewards](https://mlsanity.com/paper/1906.00569/) (2019)
- [A Wasserstein distance approach for concentration of empirical risk estimates](https://mlsanity.com/paper/1902.10709/) (2019)
- [Concentration bounds for temporal difference learning with linear function approximation: The case of batch data and uniform sampling](https://mlsanity.com/paper/1306.2557/) (2013)
- [PAC-Bayesian Bound for the Conditional Value at Risk](https://mlsanity.com/paper/2006.14763/) (2020)
- [Estimation of Spectral Risk Measures](https://mlsanity.com/paper/1912.10398/) (2019)
- [Computational aspects of robust optimized certainty equivalents and option pricing](https://mlsanity.com/paper/1706.10186/) (2017)
- [Non-asymptotic bounds for stochastic optimization with biased noisy gradient oracles](https://mlsanity.com/paper/2002.11440/) (2020)
- [Smoothed functional-based gradient algorithms for off-policy reinforcement learning: A non-asymptotic viewpoint](https://mlsanity.com/paper/2101.02137/) (2021)
- [On perturbed proximal gradient algorithms](https://mlsanity.com/paper/1402.2365/) (2014)

## Built on by (most cited first, 5 of 5)

- [Multi-level Monte-Carlo Gradient Methods for Stochastic Optimization with Biased Oracles](https://mlsanity.com/paper/2408.11084/) (2024)
- [Optimization of utility-based shortfall risk: A non-asymptotic viewpoint](https://mlsanity.com/paper/2310.18743/) (2023)
- [Concentration Bounds for Optimized Certainty Equivalent Risk Estimation](https://mlsanity.com/paper/2405.20933/) (2024)
- [Optimized Certainty Equivalent Risk Minimization Using Samples: Algorithms, Convergence Rates, and Applications](https://mlsanity.com/paper/2608.07113/) (2026)
- [Optimizing Shortfall Risk Metric for Learning Regression Models](https://mlsanity.com/paper/2505.17777/) (2025)

## 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.