风险建模

Constrained optimization provides a common framework for dealing with conflicting objectives in reinforcement learning (RL). In most of these settings, the objectives (and constraints) are expressed though the expected accumulated reward. However, this formulation neglects risky or even possibly catastrophic events at the tails of the reward distribution, and is often insufficient for high-stakes applications in which the risk involved in outliers is critical. In this work, we propose a framework for risk-aware constrained RL, which exhibits per-stage robustness properties jointly in reward values and time using optimized certainty equivalents (OCEs). Our framework ensures an exact equivalent to the original constrained problem within a parameterized strong Lagrangian duality framework under appropriate constraint qualifications, and yields a simple algorithmic recipe which can be wrapped around standard RL solvers, such as PPO. Lastly, we establish the convergence of the proposed algorithm and verify the risk-aware properties of our approach through several numerical experiments.

Calibrating blackbox machine learning models to achieve risk control is crucial to ensure reliable decision-making. A rich line of literature has been studying how to calibrate a model so that its predictions satisfy explicit finite-sample statistical guarantees under a _fixed_, _static_, and unknown data-generating distribution. However, prediction-supported decisions may influence the outcome they aim to predict, a phenomenon named _performativity_ of predictions, which is commonly seen in social science and economics. In this paper, we introduce _Performative Risk Control_, a framework to calibrate models to achieve risk control under performativity with provable theoretical guarantees. Specifically, we provide an iteratively refined calibration process, where we ensure the predictions are improved and risk-controlled throughout the process. We also study different types of risk measures and choices of tail bounds. Lastly, we demonstrate the effectiveness of our framework by numerical experiments on the task of predicting credit default risk. To the best of our knowledge, this work is the first one to study statistically rigorous risk control under performativity, which will serve as an important safeguard against a wide range of strategic manipulation in decision-making processes.

This paper addresses the problem of multi-risk measure agnostic multi-armed bandits in heavy-tailed reward settings. We propose a framework that leverages novel deviation inequalities for the $1$-Wasserstein distance to construct confidence intervals for Lipschitz risk measures. The distributional LCB (DistLCB) algorithm is introduced, which achieves asymptotic optimality by deriving the first lower bounds for risk measure aware bandits with explicit sub-optimality gap dependencies. The DistLCB is further extended to multi-risk objectives, which enables Pareto-optimal solutions that consider multiple aspects of reward distributions. Additionally, we provide a regret analysis that includes both gap-dependent and gap-independent bounds for multi-risk settings. Experiments validate the effectiveness of the proposed methods in synthetic and real-world applications.

Human safety awareness gaps often prevent the timely recognition of everyday risks. In solving this problem, a proactive safety artificial intelligence (AI) system would work better than a reactive one. Instead of just reacting to users' questions, it would actively watch people’s behavior and their environment to detect potential dangers in advance. Our Proactive Safety Bench (PaSBench) evaluates this capability through 416 multimodal scenarios (128 image sequences, 288 text logs) spanning 5 safety-critical domains. Evaluation of 36 advanced models reveals fundamental limitations: Top performers like Gemini-2.5-pro achieve 71\% image and 64\% text accuracy, but miss 45-55\% risks in repeated trials. Through failure analysis, we identify unstable proactive reasoning rather than knowledge deficits as the primary limitation. This work establishes (1) a proactive safety benchmark, (2) systematic evidence of model limitations, and (3) critical directions for developing reliable protective AI. We believe our dataset and findings can promote the development of safer AI assistants that actively prevent harm rather than merely respond to requests.

Risk-averse modeling is critical in safety-sensitive and high-stakes applications. Conditional Value-at-Risk (CVaR) quantifies such risk by measuring the expected loss in the tail of the loss distribution, and minimizing it provides a principled framework for training robust models. However, direct CVaR minimization remains challenging due to the difficulty of accurately estimating rare, high-loss events—particularly at extreme quantiles. In this work, we propose a novel training framework that synthesizes informative samples for CVaR optimization using score-based generative models. Specifically, we guide a diffusion-based generative model to sample from a reweighted distribution that emphasizes inputs likely to incur high loss under a pretrained reference model. These samples are then incorporated via a loss-weighted importance sampling scheme to reduce noise in stochastic optimization. We establish convergence guarantees and show that the synthesized, high-loss-emphasized dataset substantially contributes to the noise reduction. Empirically, we validate the effectiveness of our approach across multiple settings, including a real-world wireless channel compression task, where our method achieves significant improvements over standard risk minimization strategies.

This work examines risk bounds for nonparametric distributional regression estimators. For convex-constrained distributional regression, general upper bounds are established for the continuous ranked probability score (CRPS) and the worst-case mean squared error (MSE) across the domain. These theoretical results are applied to isotonic and trend filtering distributional regression, yielding convergence rates consistent with those for mean estimation. Furthermore, a general upper bound is derived for distributional regression under non-convex constraints, with a specific application to neural network-based estimators. Comprehensive experiments on both simulated and real data validate the theoretical contributions, demonstrating their practical effectiveness.

Ensemble learning is a popular technique to improve the accuracy of machine learning models. It traditionally hinges on the rationale that aggregating multiple weak models can lead to better models with lower variance and hence higher stability, especially for discontinuous base learners. In this paper, we provide a new perspective on ensembling. By selecting the most frequently generated model from the base learner when repeatedly applied to subsamples, we can attain exponentially decaying tails for the excess risk, even if the base learner suffers from slow (i.e., polynomial) decay rates. This tail enhancement power of ensembling applies to base learners that have reasonable predictive power to begin with and is stronger than variance reduction in the sense of exhibiting rate improvement. We demonstrate how our ensemble methods can substantially improve out-of-sample performances in a range of numerical examples involving heavy-tailed data or intrinsically slow rates.

Risk-averse total-reward Markov Decision Processes (MDPs) offer a promising framework for modeling and solving undiscounted infinite-horizon objectives. Existing model-based algorithms for risk measures like the entropic risk measure (ERM) and entropic value-at-risk (EVaR) are effective in small problems, but require full access to transition probabilities. We propose a Q-learning algorithm to compute the optimal stationary policy for total-reward ERM and EVaR objectives with strong convergence and performance guarantees. The algorithm and its optimality are made possible by ERM's dynamic consistency and elicitability. Our numerical results on tabular domains demonstrate quick and reliable convergence of the proposed Q-learning algorithm to the optimal risk-averse value function.

Surrogate regret bounds, also known as excess risk bounds, bridge the gap between the convergence rates of surrogate and target losses. The regret transfer is lossless if the surrogate regret bound is linear. While convex smooth surrogate losses are appealing in particular due to the efficient estimation and optimization, the existence of a trade-off between the loss smoothness and linear regret bound has been believed in the community. Under this scenario, the better optimization and estimation properties of convex smooth surrogate losses may inevitably deteriorate after undergoing the regret transfer onto a target loss. We overcome this dilemma for arbitrary discrete target losses by constructing a convex smooth surrogate loss, which entails a linear surrogate regret bound composed with a tailored prediction link. The construction is based on Fenchel--Young losses generated by the *convolutional negentropy*, which are equivalent to the infimal convolution of a generalized negentropy and the target Bayes risk. Consequently, the infimal convolution enables us to derive a smooth loss while maintaining the surrogate regret bound linear. We additionally benefit from the infimal convolution to have a consistent estimator of the underlying class probability. Our results are overall a novel demonstration of how convex analysis penetrates into optimization and statistical efficiency in risk minimization.