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Safety in reinforcement learning (RL) is a key property in both training and execution in many domains such as autonomous driving or finance. In this paper, we formalize it with a constrained RL formulation in the distributional RL setting.…

Machine Learning · Computer Science 2021-03-01 Jianyi Zhang , Paul Weng

We consider regularly varying random vectors. Our goal is to estimate in a non-parametric way some characteristics related to conditioning on an extreme event, like the tail dependence coefficient. We introduce a quasi-spectral…

Methodology · Statistics 2015-02-26 Rafał Kulik , Zhigang Tong

Many novel notions of "risk" (e.g., CVaR, tilted risk, DRO risk) have been proposed and studied, but these risks are all at least as sensitive as the mean to loss tails on the upside, and tend to ignore deviations on the downside. We study…

Machine Learning · Statistics 2023-02-17 Matthew J. Holland

This paper proposes a safety analysis method that facilitates a tunable balance between the worst-case and risk-neutral perspectives. First, we define a risk-sensitive safe set to specify the degree of safety attained by a stochastic…

Systems and Control · Electrical Eng. & Systems 2020-07-28 Margaret P. Chapman , Jonathan P. Lacotte , Kevin M. Smith , Insoon Yang , Yuxi Han , Marco Pavone , Claire J. Tomlin

In this paper, we develop a theoretical framework for bounding the CVaR of a random variable $X$ using another related random variable $Y$, under assumptions on their cumulative and density functions. Our results yield practical tools for…

Statistics Theory · Mathematics 2025-07-31 Yaacov Pariente , Vadim Indelman

Considering non-stationary environments in online optimization enables decision-maker to effectively adapt to changes and improve its performance over time. In such cases, it is favorable to adopt a strategy that minimizes the negative…

Systems and Control · Electrical Eng. & Systems 2024-04-05 Siyi Wang , Zifan Wang , Xinlei Yi , Michael M. Zavlanos , Karl H. Johansson , Sandra Hirche

Imitation learning algorithms learn viable policies by imitating an expert's behavior when reward signals are not available. Generative Adversarial Imitation Learning (GAIL) is a state-of-the-art algorithm for learning policies when the…

Conditional value-at-risk (CoVaR) is one of the most important measures of systemic risk. It is defined as the high quantile conditional on a related variable being extreme, widely used in the field of quantitative risk management. In this…

Methodology · Statistics 2026-02-12 Zhaowen Wang , Yutao Liu , Deyuan Li

Cross-validation (CV) is one of the main tools for performance estimation and parameter tuning in machine learning. The general recipe for computing CV estimate is to run a learning algorithm separately for each CV fold, a computationally…

Machine Learning · Statistics 2015-07-02 Pooria Joulani , András György , Csaba Szepesvári

This paper develops a safety analysis method for stochastic systems that is sensitive to the possibility and severity of rare harmful outcomes. We define risk-sensitive safe sets as sub-level sets of the solution to a non-standard optimal…

Systems and Control · Electrical Eng. & Systems 2022-06-28 Margaret P. Chapman , Riccardo Bonalli , Kevin M. Smith , Insoon Yang , Marco Pavone , Claire J. Tomlin

Conditional Value-at-Risk (CoVaR) quantifies systemic financial risk by measuring the loss quantile of one asset, conditional on another asset experiencing distress. We develop a Transformer-based methodology that integrates financial news…

Econometrics · Economics 2026-02-16 Junyu Chen , Tom Boot , Lingwei Kong , Weining Wang

Continual learning, an important aspect of artificial intelligence and machine learning research, focuses on developing models that learn and adapt to new tasks while retaining previously acquired knowledge. Existing continual learning…

Machine Learning · Computer Science 2024-04-04 Liwei Kang , Wee Sun Lee

We study scalable alternatives to robust gradient descent (RGD) techniques that can be used when the losses and/or gradients can be heavy-tailed, though this will be unknown to the learner. The core technique is simple: instead of trying to…

Machine Learning · Statistics 2020-12-15 Matthew J. Holland

Machine learning (ML) models used in prediction and classification tasks may display performance disparities across population groups determined by sensitive attributes (e.g., race, sex, age). We consider the problem of evaluating the…

Machine Learning · Computer Science 2024-05-28 Lucas Monteiro Paes , Ananda Theertha Suresh , Alex Beutel , Flavio P. Calmon , Ahmad Beirami

The global financial crisis of 2007-2009 highlighted the crucial role systemic risk plays in ensuring stability of financial markets. Accurate assessment of systemic risk would enable regulators to introduce suitable policies to mitigate…

Statistics Theory · Mathematics 2022-03-03 Natalia Nolde , Chen Zhou , Menglin Zhou

The popularity of Conditional Value-at-Risk (CVaR), a risk functional from finance, has been growing in the control systems community due to its intuitive interpretation and axiomatic foundation. We consider a nonstandard optimal control…

Systems and Control · Electrical Eng. & Systems 2022-06-22 Margaret P. Chapman , Michael Fauss , Kevin M. Smith

Fine-tuning pre-trained diffusion and flow models to optimize downstream utilities is central to real-world deployment. Existing entropy-regularized methods primarily maximize expected reward, providing no mechanism to shape tail behavior.…

Machine Learning · Computer Science 2026-02-20 Zifan Wang , Riccardo De Santi , Xiaoyu Mo , Michael M. Zavlanos , Andreas Krause , Karl H. Johansson

We derive PAC-Bayesian learning guarantees for heavy-tailed losses, and obtain a novel optimal Gibbs posterior which enjoys finite-sample excess risk bounds at logarithmic confidence. Our core technique itself makes use of PAC-Bayesian…

Machine Learning · Statistics 2019-12-19 Matthew J. Holland

The multi-armed bandit (MAB) problem is a ubiquitous decision-making problem that exemplifies the exploration-exploitation tradeoff. Standard formulations exclude risk in decision making. Risk notably complicates the basic reward-maximising…

Machine Learning · Computer Science 2021-02-05 Joel Q. L. Chang , Qiuyu Zhu , Vincent Y. F. Tan

In safety-critical applications of reinforcement learning such as healthcare and robotics, it is often desirable to optimize risk-sensitive objectives that account for tail outcomes rather than expected reward. We prove the first regret…

Machine Learning · Computer Science 2022-10-12 O. Bastani , Y. J. Ma , E. Shen , W. Xu