Risk-averse learning with delayed feedback
<|reference_start|>Risk-averse learning with delayed feedback: In real-world scenarios, the impacts of decisions may not manifest immediately. Taking these delays into account facilitates accurate assessment and management of risk in real-world environments, thereby ensuring the efficacy of strategies. In this paper, we investigate risk-averse learning using Conditional Value at Risk (CVaR) as risk measure, while incorporating delayed feedback with unknown but bounded delays. We develop two risk-averse learning algorithms that rely on one-point and two-point zeroth-order optimization approaches, respectively. The regret achieved by the algorithms is analyzed in terms of the cumulative delay and the number of total samplings. The results suggest that the two-point risk-averse learning achieves a smaller regret bound than the one-point algorithm. Furthermore, the one-point risk-averse learning algorithm attains sublinear regret under certain delay conditions, and the two-point risk-averse learning algorithm achieves sublinear regret with minimal restrictions on the delay. We provide numerical experiments on a dynamic pricing problem to demonstrate the performance of the proposed algorithms.<|reference_end|>
@article{wang2024risk-averse,
    title={Risk-averse learning with delayed feedback},
    author={Siyi Wang, Zifan Wang, Karl Henrik Johansson and Sandra Hirche},
    journal={arXiv preprint arXiv:2409.16866},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.16866},
    primaryClass={cs.LG math.OC}
}