Continuous Mean-Covariance Bandits

TL;DR

This paper introduces the Continuous Mean-Covariance Bandit model that accounts for option correlations in risk-aware online decision making, proposing optimal algorithms and analyzing their theoretical performance.

Contribution

It is the first to explicitly incorporate option correlation in risk-aware bandits and develop algorithms with provably optimal regret bounds across various feedback settings.

Findings

Proposed algorithms achieve near-optimal regret bounds.

Validated the algorithms' superiority through experiments.

Analyzed the impact of covariance structures on learning performance.

Abstract

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.