# Optimal Thompson Sampling strategies for support-aware CVaR bandits

arXiv: https://arxiv.org/abs/2012.05754 · HTML: https://mlsanity.com/paper/2012.05754/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2020.

## Built on by (most cited first, 26 of 26)

- [Top Two Algorithms Revisited](https://mlsanity.com/paper/2206.05979/) (2022)
- [The Fragility of Optimized Bandit Algorithms](https://mlsanity.com/paper/2109.13595/) (2021)
- [Almost Optimal Variance-Constrained Best Arm Identification](https://mlsanity.com/paper/2201.10142/) (2022)
- [Bayesian Fixed-Budget Best-Arm Identification](https://mlsanity.com/paper/2211.08572/) (2022)
- [Optimistic Posterior Sampling for Reinforcement Learning with Few Samples and Tight Guarantees](https://mlsanity.com/paper/2209.14414/) (2022)
- [Accelerating Approximate Thompson Sampling with Underdamped Langevin Monte Carlo](https://mlsanity.com/paper/2401.11665/) (2024)
- [A Unifying Theory of Thompson Sampling for Continuous Risk-Averse Bandits](https://mlsanity.com/paper/2108.11345/) (2021)
- [A Survey of Risk-Aware Multi-Armed Bandits](https://mlsanity.com/paper/2205.05843/) (2022)
- [From Optimality to Robustness: Dirichlet Sampling Strategies in Stochastic Bandits](https://mlsanity.com/paper/2111.09724/) (2021)
- [A Simple and Optimal Policy Design with Safety against Heavy-Tailed Risk for Stochastic Bandits](https://mlsanity.com/paper/2206.02969/) (2022)
- [Optimality of Thompson Sampling with Noninformative Priors for Pareto Bandits](https://mlsanity.com/paper/2302.01544/) (2023)
- [Risk-sensitive Bandits: Arm Mixture Optimality and Regret-efficient Algorithms](https://mlsanity.com/paper/2503.08896/) (2025)
- [Conditionally Risk-Averse Contextual Bandits](https://mlsanity.com/paper/2210.13573/) (2022)
- [A Distribution Optimization Framework for Confidence Bounds of Risk Measures](https://mlsanity.com/paper/2306.07059/) (2023)
- [Conformal Risk-Averse Decision Making with Action Conditional Guarantee](https://mlsanity.com/paper/2606.05551/) (2026)
- [Risk averse non-stationary multi-armed bandits](https://mlsanity.com/paper/2109.13977/) (2021)
- [Risk-averse Contextual Multi-armed Bandit Problem with Linear Payoffs](https://mlsanity.com/paper/2206.12463/) (2022)
- [Risk-aware linear bandits with convex loss](https://mlsanity.com/paper/2209.07154/) (2022)
- [Order Optimal Regret Bounds for Sharpe Ratio Optimization under Thompson Sampling](https://mlsanity.com/paper/2508.13749/) (2025)
- [Learning to Decide with AI Assistance under Human-Alignment](https://mlsanity.com/paper/2605.12646/) (2026)
- [Towards an efficient and risk aware strategy for guiding farmers in identifying best crop management](https://mlsanity.com/paper/2210.04537/) (2022)
- [Towards Fully Automated Decision-Making Systems for Greenhouse Control: Challenges and Opportunities](https://mlsanity.com/paper/2503.21640/) (2025)
- [Non-Linear Model-Based Sequential Decision-Making in Agriculture](https://mlsanity.com/paper/2509.01924/) (2025)
- [EVaR-Optimal Arm Identification in Bandits](https://mlsanity.com/paper/2510.04728/) (2025)
- [Instantiating Bayesian CVaR lower bounds in Interactive Decision Making Problems](https://mlsanity.com/paper/2604.12519/) (2026)
- [Asymptotic Optimality of Thompson Sampling for Risk-Averse Bandits with Sub-Gaussian Rewards](https://mlsanity.com/paper/2606.09191/) (2026)

## Abstract (arXiv)

In this paper we study a multi-arm bandit problem in which the quality of each arm is measured by the Conditional Value at Risk (CVaR) at some level alpha of the reward distribution. While existing works in this setting mainly focus on Upper Confidence Bound algorithms, we introduce a new Thompson Sampling approach for CVaR bandits on bounded rewards that is flexible enough to solve a variety of problems grounded on physical resources. Building on a recent work by Riou & Honda (2020), we introduce B-CVTS for continuous bounded rewards and M-CVTS for multinomial distributions. On the theoretical side, we provide a non-trivial extension of their analysis that enables to theoretically bound their CVaR regret minimization performance. Strikingly, our results show that these strategies are the first to provably achieve asymptotic optimality in CVaR bandits, matching the corresponding asymptotic lower bounds for this setting. Further, we illustrate empirically the benefit of Thompson Sampling approaches both in a realistic environment simulating a use-case in agriculture and on various synthetic examples.