In this paper, we aim to tackle flexible cost requirements for long-tail datasets, where we need to construct a (a) cost-sensitive and (b) class-distribution robust learning framework. The misclassification cost and the area under the ROC curve (AUC) are popular metrics for (a) and (b), respectively. However, limited by their formulations, models trained with AUC cannot be applied to cost-sensitive decision problems, and models trained with fixed costs are sensitive to the class distribution shift. To address this issue, we present a new setting where costs are treated like a dataset to deal with arbitrarily unknown cost distributions. Moreover, we propose a novel weighted version of AUC where the cost distribution can be integrated into its calculation through decision thresholds. To formulate this setting, we propose a novel bilevel paradigm to bridge weighted AUC (WAUC) and cost. The inner-level problem approximates the optimal threshold from sampling costs, and the outer-level problem minimizes the WAUC loss over the optimal threshold distribution. To optimize this bilevel paradigm, we employ a stochastic optimization algorithm (SACCL) to optimize it. Finally, experiment results show that our algorithm performs better than existing cost-sensitive learning methods and two-stage AUC decisions approach.

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 reduce this bias by learning a distribution of the expected cost-to-go using quantile regression. However, ensuring that the learned policy satisfies safety constraints remains a challenge when these constraints are not explicitly integrated into the RL framework. Existing methods often require complex neural architectures or manual tradeoffs due to combined cost functions. To address this, we propose a risk-regularized quantile-based algorithm integrating Conditional Value-at-Risk (CVaR) to enforce safety without complex architectures. We also provide theoretical guarantees on the contraction properties of the risk-sensitive distributional Bellman operator in Wasserstein space, ensuring convergence to a unique cost distribution. Simulations of a mobile robot in a dynamic reach-avoid task show that our approach leads to more goal successes, fewer collisions, and better safety-performance trade-offs than risk-neutral methods.

Database research and development often require a large number of SQL queries for benchmarking purposes. However, acquiring real-world SQL queries is challenging due to privacy concerns, and existing SQL generation methods are limited in customization and in satisfying realistic constraints. To address this issue, we present SQLBarber, a system based on Large Language Models (LLMs) to generate customized and realistic SQL workloads. SQLBarber (i) eliminates the need for users to manually craft SQL templates in advance, while providing the flexibility to accept natural language specifications to constrain SQL templates, (ii) scales efficiently to generate large volumes of queries matching any user-defined cost distribution (e.g., cardinality and execution plan cost), and (iii) uses execution statistics from Amazon Redshift and Snowflake to derive SQL template specifications and query cost distributions that reflect real-world query characteristics. SQLBarber introduces (i) a declarative interface for users to effortlessly generate customized SQL templates, (ii) an LLM-powered pipeline augmented with a self-correction module that profiles, refines, and prunes SQL templates based on query costs, and (iii) a Bayesian Optimizer to efficiently explore different predicate values and identify a set of queries that satisfy the target cost distribution. We construct and open-source ten benchmarks of varying difficulty levels and target query cost distributions based on real-world statistics from Snowflake and Amazon Redshift. Extensive experiments on these benchmarks show that SQLBarber is the only system that can generate customized SQL templates. It reduces query generation time by one to three orders of magnitude, and significantly improves alignment with the target cost distribution, compared with existing methods.

When these weighting functions output constant, we can infer that the cost function is a linear transformation of AUC. W AUC. The idea of weighting thresholds in AUC is first described by [ Bilevel optimization is a classical algorithm for operations research. B.1 Main Idea of Experiments Our experiments mainly explore the following three problems: Traditional AUC is inconsistent with the cost-related metrics and cannot be used in cost-sensitive learning scenarios. From the experimental results in our paper, we can see that most AUC optimization methods do not minimize the misclassification cost. Ultimately, the misclassification cost of the decision is not acceptable.

Receiver Operating Characteristics (ROC) is a popular tool to describe the trade-off between the True Positive Rate (TPR) and False Positive Rate (FPR) of a scoring function.

Vision-language-action models (VLAs) have shown great potential as generalist robot policies. However, these models pose urgent safety challenges during deployment, including the risk of physical harm to the environment, the robot itself, and humans. How can safety be explicitly incorporated into VLAs? In this work, we propose SafeVLA, a novel algorithm designed to integrate safety into VLAs, ensuring the protection of the environment, robot hardware and humans in real-world settings. SafeVLA effectively balances safety and task performance by employing large-scale constrained learning within simulated environments. We demonstrate that SafeVLA outperforms the current state-of-the-art method in both safety and task performance, achieving average improvements of 83.58% and 3.85%, respectively, in simulation. By prioritizing safety, our approach eliminates high-risk behaviors and reduces the upper bound of unsafe behaviors to 1/35 of that in the current state-of-the-art, thereby significantly mitigating long-tail risks. Furthermore, the learned safety constraints generalize to diverse, unseen scenarios, including multiple out-of-distribution perturbations and tasks. Our data, models and newly proposed benchmark environment are available at https://sites.google.com/view/pku-safevla.