Risk-Averse Multi-Armed Bandit Problems under Mean-Variance Measure
This addresses risk management for decision-making in economics and finance, but is incremental as it adapts existing policies to a new risk measure.
The paper tackles risk in multi-armed bandit problems by using the mean-variance measure, showing that regret lower bounds are Ω(log T) for model-specific and Ω(T^{2/3}) for model-independent cases, and that variations of UCB and DSEE policies achieve these bounds.
The multi-armed bandit problems have been studied mainly under the measure of expected total reward accrued over a horizon of length $T$. In this paper, we address the issue of risk in multi-armed bandit problems and develop parallel results under the measure of mean-variance, a commonly adopted risk measure in economics and mathematical finance. We show that the model-specific regret and the model-independent regret in terms of the mean-variance of the reward process are lower bounded by $Ω(\log T)$ and $Ω(T^{2/3})$, respectively. We then show that variations of the UCB policy and the DSEE policy developed for the classic risk-neutral MAB achieve these lower bounds.