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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…

Optimization and Control · Mathematics 2025-12-30 Siyi Wang , Zifan Wang , Karl H. Johansson

We consider an online stochastic game with risk-averse agents whose goal is to learn optimal decisions that minimize the risk of incurring significantly high costs. Specifically, we use the Conditional Value at Risk (CVaR) as a risk measure…

Machine Learning · Computer Science 2022-06-17 Zifan Wang , Yi Shen , Michael M. Zavlanos

In real-world scenarios, risk-averse learning is valuable for mitigating potential adverse outcomes. However, the delayed feedback makes it challenging to assess and manage risk effectively. In this paper, we investigate risk-averse…

Machine Learning · Computer Science 2025-08-06 Siyi Wang , Zifan Wang , Karl Henrik Johansson , Sandra Hirche

In this work, we consider a sequence of stochastic optimization problems following a time-varying distribution via the lens of online optimization. Assuming that the loss function satisfies the Polyak-{\L}ojasiewicz condition, we apply…

Optimization and Control · Mathematics 2023-09-19 Yuen-Man Pun , Farhad Farokhi , Iman Shames

We propose a risk-averse statistical learning framework wherein the performance of a learning algorithm is evaluated by the conditional value-at-risk (CVaR) of losses rather than the expected loss. We devise algorithms based on stochastic…

Machine Learning · Computer Science 2020-02-17 Tasuku Soma , Yuichi Yoshida

In high-stakes machine learning applications, it is crucial to not only perform well on average, but also when restricted to difficult examples. To address this, we consider the problem of training models in a risk-averse manner. We propose…

Machine Learning · Computer Science 2020-11-09 Sebastian Curi , Kfir. Y. Levy , Stefanie Jegelka , Andreas Krause

In this paper, we study risk-sensitive Reinforcement Learning (RL), focusing on the objective of Conditional Value at Risk (CVaR) with risk tolerance $\tau$. Starting with multi-arm bandits (MABs), we show the minimax CVaR regret rate is…

Machine Learning · Computer Science 2023-05-26 Kaiwen Wang , Nathan Kallus , Wen Sun

We consider risk-averse learning in repeated unknown games where the goal of the agents is to minimize their individual risk of incurring significantly high cost. Specifically, the agents use the conditional value at risk (CVaR) as a risk…

Machine Learning · Computer Science 2022-09-08 Zifan Wang , Yi Shen , Zachary I. Bell , Scott Nivison , Michael M. Zavlanos , Karl H. Johansson

Distributional reinforcement learning (RL) -- in which agents learn about all the possible long-term consequences of their actions, and not just the expected value -- is of great recent interest. One of the most important affordances of a…

Artificial Intelligence · Computer Science 2021-11-15 Chris Gagne , Peter Dayan

We study a first-order primal-dual subgradient method to optimize risk-constrained risk-penalized optimization problems, where risk is modeled via the popular conditional value at risk (CVaR) measure. The algorithm processes independent and…

Optimization and Control · Mathematics 2021-09-03 Avinash N. Madavan , Subhonmesh Bose

Online learning has traditionally focused on the expected rewards. In this paper, a risk-averse online learning problem under the performance measure of the mean-variance of the rewards is studied. Both the bandit and full information…

Machine Learning · Statistics 2019-03-15 Sattar Vakili , Alexis Boukouvalas , Qing Zhao

Mainstream approximate action-value iteration reinforcement learning (RL) algorithms suffer from overestimation bias, leading to suboptimal policies in high-variance stochastic environments. Quantile-based action-value iteration methods…

Machine Learning · Computer Science 2025-12-09 Clinton Enwerem , Aniruddh G. Puranic , John S. Baras , Calin Belta

Training Reinforcement Learning (RL) agents in high-stakes applications might be too prohibitive due to the risk associated to exploration. Thus, the agent can only use data previously collected by safe policies. While previous work…

Machine Learning · Computer Science 2021-02-11 Núria Armengol Urpí , Sebastian Curi , Andreas Krause

In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in costs in addition to minimizing a standard criterion. Conditional value-at-risk (CVaR) is a relatively new risk measure that…

Artificial Intelligence · Computer Science 2014-07-14 Yinlam Chow , Mohammad Ghavamzadeh

We study the problem of online learning and online regret minimization when samples are drawn from a general unknown non-stationary process. We introduce the concept of a dynamic changing process with cost $K$, where the conditional…

Machine Learning · Computer Science 2023-11-14 Changlong Wu , Ananth Grama , Wojciech Szpankowski

Optimizing risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) of a general loss distribution is usually difficult, because 1) the loss function might lack structural properties such as convexity or…

Optimization and Control · Mathematics 2016-08-03 Helin Zhu , Joshua Hale , Enlu Zhou

We present a polynomial-time online algorithm for maximizing the conditional value at risk (CVaR) of a monotone stochastic submodular function. Given $T$ i.i.d. samples from an underlying distribution arriving online, our algorithm produces…

Data Structures and Algorithms · Computer Science 2021-05-21 Tasuku Soma , Yuichi Yoshida

In this paper, we consider the problem of distributed online convex optimization, where a group of agents collaborate to track the global minimizers of a sum of time-varying objective functions in an online manner. Specifically, we propose…

Optimization and Control · Mathematics 2020-10-14 Yan Zhang , Robert J. Ravier , Vahid Tarokh , Michael M. Zavlanos

Non-stationary online learning has drawn much attention in recent years. In particular, dynamic regret and adaptive regret are proposed as two principled performance measures for online convex optimization in non-stationary environments. To…

Machine Learning · Computer Science 2025-09-10 Peng Zhao , Yan-Feng Xie , Lijun Zhang , Zhi-Hua Zhou

We investigate online convex optimization in non-stationary environments and choose dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible…

Machine Learning · Computer Science 2024-04-09 Peng Zhao , Yu-Jie Zhang , Lijun Zhang , Zhi-Hua Zhou
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