# A Unifying Theory of Thompson Sampling for Continuous Risk-Averse Bandits

arXiv: https://arxiv.org/abs/2108.11345 · HTML: https://mlsanity.com/paper/2108.11345/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 36 references that are in the map.
- First posted on arXiv 25 Aug 2021.

## Builds on (most cited first, 9 of 9)

- [Explore First, Exploit Next: The True Shape of Regret in Bandit Problems](https://mlsanity.com/paper/1602.07182/) (2016)
- [Learning Bounds for Risk-sensitive Learning](https://mlsanity.com/paper/2006.08138/) (2020)
- [Off-Policy Risk Assessment in Contextual Bandits](https://mlsanity.com/paper/2104.08977/) (2021)
- [Thompson Sampling Algorithms for Mean-Variance Bandits](https://mlsanity.com/paper/2002.00232/) (2020)
- [Exploration vs Exploitation vs Safety: Risk-averse Multi-Armed Bandits](https://mlsanity.com/paper/1401.1123/) (2014)
- [Optimal Thompson Sampling strategies for support-aware CVaR bandits](https://mlsanity.com/paper/2012.05754/) (2020)
- [Optimal Best-Arm Identification Methods for Tail-Risk Measures](https://mlsanity.com/paper/2008.07606/) (2020)
- [Risk-Constrained Thompson Sampling for CVaR Bandits](https://mlsanity.com/paper/2011.08046/) (2020)
- [Continuous Mean-Covariance Bandits](https://mlsanity.com/paper/2102.12090/) (2021)

## Built on by (most cited first, 9 of 9)

- [Almost Optimal Variance-Constrained Best Arm Identification](https://mlsanity.com/paper/2201.10142/) (2022)
- [A Survey of Risk-Aware Multi-Armed Bandits](https://mlsanity.com/paper/2205.05843/) (2022)
- [Risk-sensitive Bandits: Arm Mixture Optimality and Regret-efficient Algorithms](https://mlsanity.com/paper/2503.08896/) (2025)
- [Probably Anytime-Safe Stochastic Combinatorial Semi-Bandits](https://mlsanity.com/paper/2301.13393/) (2023)
- [Variance-Optimal Arm Selection: Misallocation Minimization and Best Arm Identification](https://mlsanity.com/paper/2505.11985/) (2025)
- [Balancing Risk and Reward: An Automated Phased Release Strategy](https://mlsanity.com/paper/2305.09626/) (2023)
- [Conformal bandits: bringing statistical validity and reward efficiency under weak arm separability](https://mlsanity.com/paper/2512.09850/) (2025)
- [Fast Online Learning with Gaussian Prior-Driven Hierarchical Unimodal Thompson Sampling](https://mlsanity.com/paper/2602.15972/) (2026)
- [Asymptotic Optimality of Thompson Sampling for Risk-Averse Bandits with Sub-Gaussian Rewards](https://mlsanity.com/paper/2606.09191/) (2026)

## Abstract (arXiv)

This paper unifies the design and the analysis of risk-averse Thompson sampling algorithms for the multi-armed bandit problem for a class of risk functionals ρ that are continuous and dominant. We prove generalised concentration bounds for these continuous and dominant risk functionals and show that a wide class of popular risk functionals belong to this class. Using our newly developed analytical toolkits, we analyse the algorithm ρ-MTS (for multinomial distributions) and prove that they admit asymptotically optimal regret bounds of risk-averse algorithms under CVaR, proportional hazard, and other ubiquitous risk measures. More generally, we prove the asymptotic optimality of ρ-MTS for Bernoulli distributions for a class of risk measures known as empirical distribution performance measures (EDPMs); this includes the well-known mean-variance. Numerical simulations show that the regret bounds incurred by our algorithms are reasonably tight vis-`a-vis algorithm-independent lower bounds.