# Risk-averse Learning with Non-Stationary Distributions

arXiv: https://arxiv.org/abs/2404.02988 · HTML: https://mlsanity.com/paper/2404.02988/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 35 references that are in the map.
- First posted on arXiv 3 Apr 2024.

## Builds on (most cited first, 18 of 18)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Non-stationary Stochastic Optimization](https://mlsanity.com/paper/1307.5449/) (2013)
- [Outside the Echo Chamber: Optimizing the Performative Risk](https://mlsanity.com/paper/2102.08570/) (2021)
- [Risk-Averse Offline Reinforcement Learning](https://mlsanity.com/paper/2102.05371/) (2021)
- [An Online Convex Optimization Approach to Dynamic Network Resource Allocation](https://mlsanity.com/paper/1701.03974/) (2017)
- [Bandit Convex Optimization in Non-stationary Environments](https://mlsanity.com/paper/1907.12340/) (2019)
- [Decision-Dependent Risk Minimization in Geometrically Decaying Dynamic Environments](https://mlsanity.com/paper/2204.08281/) (2022)
- [Online Stochastic Optimization with Wasserstein Based Non-stationarity](https://mlsanity.com/paper/2012.06961/) (2020)
- [Statistical Learning with Conditional Value at Risk](https://mlsanity.com/paper/2002.05826/) (2020)
- [No-Regret Learning in Unknown Games with Correlated Payoffs](https://mlsanity.com/paper/1909.08540/) (2019)
- [A Risk-Sensitive Finite-Time Reachability Approach for Safety of Stochastic Dynamic Systems](https://mlsanity.com/paper/1902.11277/) (2019)
- [Risk-Averse Stochastic Convex Bandit](https://mlsanity.com/paper/1810.00737/) (2018)
- [Risk-Averse No-Regret Learning in Online Convex Games](https://mlsanity.com/paper/2203.08957/) (2022)
- [Toward a Scalable Upper Bound for a CVaR-LQ Problem](https://mlsanity.com/paper/2103.02136/) (2021)
- [A Zeroth-Order Momentum Method for Risk-Averse Online Convex Games](https://mlsanity.com/paper/2209.02838/) (2022)
- [Online Stochastic Convex Optimization: Wasserstein Distance Variation](https://mlsanity.com/paper/2006.01397/) (2020)

## Built on by (most cited first, 2 of 2)

- [Risk-Averse Certification of Bayesian Neural Networks](https://mlsanity.com/paper/2411.19729/) (2024)
- [Risk-Averse Learning with Varying Risk Levels](https://mlsanity.com/paper/2512.22986/) (2025)

## Abstract (arXiv)

Considering non-stationary environments in online optimization enables decision-maker to effectively adapt to changes and improve its performance over time. In such cases, it is favorable to adopt a strategy that minimizes the negative impact of change to avoid potentially risky situations. In this paper, we investigate risk-averse online optimization where the distribution of the random cost changes over time. We minimize risk-averse objective function using the Conditional Value at Risk (CVaR) as risk measure. Due to the difficulty in obtaining the exact CVaR gradient, we employ a zeroth-order optimization approach that queries the cost function values multiple times at each iteration and estimates the CVaR gradient using the sampled values. To facilitate the regret analysis, we use a variation metric based on Wasserstein distance to capture time-varying distributions. Given that the distribution variation is sub-linear in the total number of episodes, we show that our designed learning algorithm achieves sub-linear dynamic regret with high probability for both convex and strongly convex functions. Moreover, theoretical results suggest that increasing the number of samples leads to a reduction in the dynamic regret bounds until the sampling number reaches a specific limit. Finally, we provide numerical experiments of dynamic pricing in a parking lot to illustrate the efficacy of the designed algorithm.