Risk-Averse Learning with Varying Risk Levels
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917173322055680 |
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| author | Wang, Siyi Wang, Zifan Johansson, Karl H. |
| author_facet | Wang, Siyi Wang, Zifan Johansson, Karl H. |
| contents | In safety-critical decision-making, the environment may evolve over time, and the learner adjusts its risk level accordingly. This work investigates risk-averse online optimization in dynamic environments with varying risk levels, employing Conditional Value-at-Risk (CVaR) as the risk measure. To capture the dynamics of the environment and risk levels, we employ the function variation metric and introduce a novel risk-level variation metric. Two information settings are considered: a first-order scenario, where the learner observes both function values and their gradients; and a zeroth-order scenario, where only function evaluations are available. For both cases, we develop risk-averse learning algorithms with a limited sampling budget and analyze their dynamic regret bounds in terms of function variation, risk-level variation, and the total number of samples. The regret analysis demonstrates the adaptability of the algorithms in non-stationary and risk-sensitive settings. Finally, numerical experiments are presented to demonstrate the efficacy of the methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22986 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Risk-Averse Learning with Varying Risk Levels Wang, Siyi Wang, Zifan Johansson, Karl H. Optimization and Control Machine Learning In safety-critical decision-making, the environment may evolve over time, and the learner adjusts its risk level accordingly. This work investigates risk-averse online optimization in dynamic environments with varying risk levels, employing Conditional Value-at-Risk (CVaR) as the risk measure. To capture the dynamics of the environment and risk levels, we employ the function variation metric and introduce a novel risk-level variation metric. Two information settings are considered: a first-order scenario, where the learner observes both function values and their gradients; and a zeroth-order scenario, where only function evaluations are available. For both cases, we develop risk-averse learning algorithms with a limited sampling budget and analyze their dynamic regret bounds in terms of function variation, risk-level variation, and the total number of samples. The regret analysis demonstrates the adaptability of the algorithms in non-stationary and risk-sensitive settings. Finally, numerical experiments are presented to demonstrate the efficacy of the methods. |
| title | Risk-Averse Learning with Varying Risk Levels |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2512.22986 |