- Typically, expected performance under observation noise is used for evaluation because the decision-maker is interested in the true objective function and the noise is assumed to be noise (misleading, not representative). In the formulation in this paper, the decision maker does care about the noise; rather the objective function of interest is the stochastic noisy function. It would be good to make this distinction clearer upfront. - The RF experiment is not super compelling. It is not nearly as interesting as the FEL problem, and the risk aversion does not make a significant difference in average performance. Overall the empirical evaluation is fairly limited. - It is unclear why the mean-variance model is the best metric to use for evaluating performance - Why not also evaluate performance in terms of the VaR or CVaR? - The MV objective is nice for the proposed UCB-style algorithm and theoretical work, but for evaluation VaR and CVaR also are important considerations
Writing: - Very high quality and easy to follow writing - Grammar: - L164: “that that” - Figure 5 caption: “Simple regret fat the reprted”
Questions: - Figure 2: “RAHBO not only leads to strong results in terms of MV, but also in terms of mean objective”? Why is it better than GP-UCB on this metric? Is this an artifact of the specific toy problem?
Limitations are discussed and potential future directions are interesting. “We are not aware of any societal impacts of our work” – this (as with an optimization algorithm) could be used for nefarious endeavors and could be discussed.
- Typically, expected performance under observation noise is used for evaluation because the decision-maker is interested in the true objective function and the noise is assumed to be noise (misleading, not representative). In the formulation in this paper, the decision maker does care about the noise; rather the objective function of interest is the stochastic noisy function. It would be good to make this distinction clearer upfront.