This paper studies the problem of safe meta-reinforcement learning (safe metaRL), where an agent efficiently adapts to unseen tasks while satisfying safety constraints at all times during adaptation. We propose a framework consisting of two complementary modules: safe policy adaptation and safe meta-policy training. The first module introduces a novel one-step safe policy adaptation method that admits a closed-form solution, ensuring monotonic improvement, constraint satisfaction at every step, and high computational efficiency. The second module develops a Hessian-free meta-training algorithm that incorporates safety constraints on the meta-policy and leverages the analytical form of the adapted policy to enable scalable optimization. Together, these modules yield three key advantages over existing safe meta-RL methods: (i) superior optimality, (ii) anytime safety guarantee, and (iii) high computational efficiency. Beyond existing safe meta-RL analyses, we prove the anytime safety guarantee of policy adaptation and provide a lower bound of the expected total reward of the adapted policies compared with the optimal policies, which shows that the adapted policies are nearly optimal. Empirically, our algorithm achieves superior optimality, strict safety compliance, and substantial computational gains--up to 70% faster training and 50% faster testing--across diverse locomotion and navigation benchmarks.

The constrained version of the standard online convex optimization (OCO) framework, called COCO is considered, where on every round, a convex cost function and a convex constraint function are revealed to the learner after it chooses the action for that round. The objective is to simultaneously minimize the static regret and cumulative constraint violation (CCV). An algorithm is proposed that guarantees a static regret of O( T) and a CCV of min{V,O( Tlog T)}, where V depends on the distance between the consecutively revealed constraint sets, the shape of constraint sets, dimension of action space and the diameter of the action space. When constraint sets have additional structure, V = O(1). Compared to the state of the art results, static regret of O( T) and CCV of O( T log T), that were universal, the new result on CCV is instance dependent, which is derived by exploiting the geometric properties of the constraint sets.

Efficiently solving constrained optimization problems is crucial for numerous realworld applications, yet traditional solvers are often computationally prohibitive for real-time use. Machine learning-based approaches have emerged as a promising alternative to provide approximate solutions at faster speeds, but they struggle to strictly enforce constraints, leading to infeasible solutions in practice. To address this, we propose the Feasibility-Seeking Neural Network (FSNet), which integrates a feasibility-seeking step directly into its solution procedure to ensure constraint satisfaction. This feasibility-seeking step solves an unconstrained optimization problem that minimizes constraint violations in a differentiable manner, enabling end-to-end training and providing guarantees on feasibility and convergence. Our experiments across a range of different optimization problems, including both smooth/nonsmooth and convex/nonconvex problems, demonstrate that FSNet can provide feasible solutions with solution quality comparable to (or in some cases better than) traditional solvers, at significantly faster speeds.1

We introduce BikeBench, an engineering design benchmark for evaluating generative models on problems with multiple real-world objectives and constraints. As generative AI's reach continues to grow, evaluating its capability to understand physical laws, human guidelines, and hard constraints grows increasingly important. Engineering product design lies at the intersection of these difficult tasks, providing new challenges for AI capabilities. BikeBench evaluates AI models' capabilities to generate bicycle designs that not only resemble the dataset, but meet specific performance objectives and constraints. To do so, BikeBench quantifies a variety of human-centered and multiphysics performance characteristics, such as aerodynamics, ergonomics, structural mechanics, human-rated usability, and similarity to subjective text or image prompts. Supporting the benchmark are several datasets of simulation results, a dataset of 10,000 human-rated bicycle assessments, and a synthetically generated dataset of 1.6M designs, each with a parametric, CAD/XML, SVG, and PNG representation. BikeBench is uniquely configured to evaluate tabular generative models, large language models (LLMs), design optimization, and hybrid algorithms side-by-side. Our experiments indicate that LLMs and tabular generative models fall short of hybrid GenAI+optimization algorithms in design quality, constraint satisfaction, and similarity scores, suggesting significant room for improvement. We hope that BikeBench, a first-of-its-kind benchmark, will help catalyze progress in generative AI for constrained multi-objective engineering design problems.

In constrained MDPs (CMDPs) with adversarial rewards and constraints, a known impossibility result prevents any algorithm from attaining sublinear regret and constraint violation, when competing against a best-in-hindsight policy that satisfies the constraints on average. In this paper, we show how to ease such a negative result, by considering settings that generalize both stochastic CMDPs and adversarial ones. We provide algorithms whose performances smoothly degrade as the level of environment adverseness increases. Specifically, they attain eO( T +C) regret and positive constraint violation under bandit feedback, where C measures the adverseness of rewards and constraints. This is C = Θ(T) in the worst case, coherently with the impossibility result for adversarial CMDPs. First, we design an algorithm with the desired guarantees when C is known. Then, in the case C is unknown, we obtain the same results by embedding multiple instances of such an algorithm in a general meta-procedure, which suitably selects them so as to balance the trade-off between regret and constraint violation.

Performative prediction is a recently proposed framework where predictions guide decision-making and hence influence future data distributions. Such performative phenomena are ubiquitous in various areas, such as transportation, finance, public policy, and recommendation systems. To date, work on performative prediction has only focused on unconstrained scenarios, neglecting the fact that many realworld learning problems are subject to constraints.

Integrating logical constraints into object detection models for autonomous driving (AD) is a promising way to enhance their compliance with rules and thereby increase the safety of the system. T-norms have been utilized to calculate the constrained loss, i.e., the violations of logical constraints as losses. While prior works have statically selected a few t-norms, we conduct an extensive experimental study to identify the most effective choices, as suboptimal t-norms can lead to undesired model behavior. To this end, we present MOD-ECL, a neurosymbolic framework that implements a wide range of t-norms and applies them in an adaptive manner. It includes an algorithm that selects well-performing t-norms during training and a scheduler that regulates the impact of the constrained loss. We evaluate its effectiveness on the ROAD-R and ROAD-Waymo-R datasets for object detection in AD, using attached common-sense constraints. Our results show that careful selection of parameters is crucial for effective constrained loss behavior. Moreover, our framework not only reduces constraint violations but also, in some cases, improves detection performance. Additionally, our methods offer fine-grained control over the trade-off between accuracy and constraint violation.

In constrained MDPs (CMDPs) with adversarial rewards and constraints, a known impossibility result prevents any algorithm from attaining sublinear regret and constraint violation, when competing against a best-in-hindsight policy that satisfies the constraints on average. In this paper, we show how to ease such a negative result, by considering settings that generalize both stochastic CMDPs and adversarial ones. We provide algorithms whose performances smoothly degrade as the level of environment adverseness increases. In this paper, we show that this negative result can be eased in CMDPs with non-stationary rewards and constraints, by providing algorithms whose performances smoothly degrade as non-stationarity increases. Specifically, they attain $\widetilde{\mathcal{O}} (\sqrt{T} + C)$ regret and positive constraint violation under bandit feedback, where $C$ measures the adverseness of rewards and constraints. This is $C = \Theta(T)$ in the worst case, coherently with the impossibility result for adversarial CMDPs. First, we design an algorithm with the desired guarantees when $C$ is known. Then, in the case $C$ is unknown, we obtain the same results by embedding multiple instances of such an algorithm in a general meta-procedure, which suitably selects them so as to balance the trade-off between regret and constraint violation.

Bandits, Reinforcement Learning

In contrast to the advances in characterizing the sample complexity for solving Markov decision processes (MDPs), the optimal statistical complexity for solving constrained MDPs (CMDPs) remains unknown. We resolve this question by providing minimax upper and lower bounds on the sample complexity for learning near-optimal policies in a discounted CMDP with access to a generative model (simulator). In particular, we design a model-based algorithm that addresses two settings: (i) relaxed feasibility, where small constraint violations are allowed, and (ii) strict feasibility, where the output policy is required to satisfy the constraint.