# Continuous Mean-Covariance Bandits

arXiv: https://arxiv.org/abs/2102.12090 · HTML: https://mlsanity.com/paper/2102.12090/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 41 references that are in the map.
- First posted on arXiv 24 Feb 2021.

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

- [Multi-armed Bandit Models for the Optimal Design of Clinical Trials: Benefits and Challenges](https://mlsanity.com/paper/1507.08025/) (2015)
- [An optimal algorithm for the Thresholding Bandit Problem](https://mlsanity.com/paper/1605.08671/) (2016)
- [Conservative Contextual Linear Bandits](https://mlsanity.com/paper/1611.06426/) (2016)
- [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)
- [Combinatorial semi-bandit with known covariance](https://mlsanity.com/paper/1612.01859/) (2016)
- [Risk-Averse Multi-Armed Bandit Problems under Mean-Variance Measure](https://mlsanity.com/paper/1604.05257/) (2016)
- [Distribution oblivious, risk-aware algorithms for multi-armed bandits with unbounded rewards](https://mlsanity.com/paper/1906.00569/) (2019)
- [Phased Exploration with Greedy Exploitation in Stochastic Combinatorial Partial Monitoring Games](https://mlsanity.com/paper/1608.06403/) (2016)

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

- [A Unifying Theory of Thompson Sampling for Continuous Risk-Averse Bandits](https://mlsanity.com/paper/2108.11345/) (2021)
- [Risk-Averse Best Arm Set Identification with Fixed Budget and Fixed Confidence](https://mlsanity.com/paper/2506.22253/) (2025)

## Abstract (arXiv)

Existing risk-aware multi-armed bandit models typically focus on risk measures of individual options such as variance. As a result, they cannot be directly applied to important real-world online decision making problems with correlated options. In this paper, we propose a novel Continuous Mean-Covariance Bandit (CMCB) model to explicitly take into account option correlation. Specifically, in CMCB, there is a learner who sequentially chooses weight vectors on given options and observes random feedback according to the decisions. The agent's objective is to achieve the best trade-off between reward and risk, measured with option covariance. To capture different reward observation scenarios in practice, we consider three feedback settings, i.e., full-information, semi-bandit and full-bandit feedback. We propose novel algorithms with optimal regrets (within logarithmic factors), and provide matching lower bounds to validate their optimalities. The experimental results also demonstrate the superiority of our algorithms. To the best of our knowledge, this is the first work that considers option correlation in risk-aware bandits and explicitly quantifies how arbitrary covariance structures impact the learning performance. The novel analytical techniques we developed for exploiting the estimated covariance to build concentration and bounding the risk of selected actions based on sampling strategy properties can likely find applications in other bandit analysis and be of independent interests.