{"ID":2824665,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.22986","arxiv_id":"2512.22986","title":"Risk-Averse Learning with Varying Risk Levels","abstract":"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.","short_abstract":"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 o...","url_abs":"https://arxiv.org/abs/2512.22986","url_pdf":"https://arxiv.org/pdf/2512.22986v1","authors":"[\"Siyi Wang\",\"Zifan Wang\",\"Karl H. Johansson\"]","published":"2025-12-28T16:09:29Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.LG\"]","methods":"[]","has_code":false}