Despite the popularity of these algorithms, it is well understood that the Sum-of-Squares (SOS) hierarchy based on semidefinite programming (SDP) can provide superior guarantees.

We study convex resource allocation problems with m hard constraints under (\varepsilon,\delta) -joint differential privacy (Joint-DP or JDP) in an offline setting. To approximately solve the problem, we propose a generic algorithm called Noisy Dual Mirror Descent. The algorithm applies noisy Mirror Descent to a dual problem from relaxing the hard constraints for private shadow prices, and then uses the shadow prices to coordinate allocations in the primal problem. When strong duality holds, both preceding results can be improved to \widetilde{\mathcal{O}}(\frac{\sqrt{\ln(1/\delta)}}{\varepsilon}) by better utilizing the geometric structure of the dual space, which is neglected by existing works. To complement our results under strong duality, we derive a minimax lower bound \Omega(\frac{m}{\varepsilon}) for any JDP algorithm outputting feasible allocations.

Humans can observe a single, imperfect demonstration and immediately generalize to very different problem settings. Robots, in contrast, often require hundreds of examples and still struggle to generalize beyond the training conditions. We argue that this limitation arises from the inability to recover the latent explanations that underpin intelligent behavior, and that these explanations can take the form of structured programs consisting of high-level goals, sub-task decomposition, and execution constraints. In this work, we introduce Rational Inverse Reasoning (RIR), a framework for inferring these latent programs through a hierarchical generative model of behavior. RIR frames few-shot imitation as Bayesian program induction: a vision-language model iteratively proposes structured symbolic task hypotheses, while a planner-in-the-loop inference scheme scores each by the likelihood of the observed demonstration under that hypothesis. This loop yields a posterior over concise, executable programs. We evaluate RIR on a suite of continuous manipulation tasks designed to test one-shot and few-shot generalization across variations in object pose, count, geometry, and layout. With as little as one demonstration, RIR infers the intended task structure and generalizes to novel settings, outperforming state-of-the-art vision-language model baselines.

Constraint modelling languages like MiniZinc and Essence rely on unrolling loops (in the form of quantified expressions and comprehensions) during compilation. Standard approaches generate all combinations of induction variables and use partial evaluation to discard those that simplify to identity elements of associative-commutative operators (e.g. true for conjunction, 0 for summation). This can be inefficient for problems where most combinations are ultimately irrelevant. We present a method that avoids full enumeration by using a solver to compute only the combinations required to generate the final set of constraints. The resulting model is identical to that produced by conventional flattening, but compilation can be significantly faster. This improves the efficiency of translating high-level user models into solver-ready form, particularly when induction variables range over large domains with selective preconditions.

Articulated vehicles such as tractor-trailers, yard trucks, and similar platforms must often reverse and maneuver in cluttered spaces where pedestrians are present. We present how Barrier-Rate guided Model Predictive Path Integral (BR-MPPI) control can solve navigation in such challenging environments. BR-MPPI embeds Control Barrier Function (CBF) constraints directly into the path-integral update. By steering the importance-sampling distribution toward collision-free, dynamically feasible trajectories, BR-MPPI enhances the exploration strength of MPPI and improves robustness of resulting trajectories. The method is evaluated in the high-fidelity CarMaker simulator on a 12 [m] tractor-trailer tasked with reverse and forward parking in a parking lot. BR-MPPI computes control inputs in above 100 [Hz] on a single GPU (for scenarios with eight obstacles) and maintains better parking clearance than a standard MPPI baseline and an MPPI with collision cost baseline.

RL-based medical questionnaire systems have shown great potential in medical scenarios. However, their safety and robustness remain unresolved. This study performs a comprehensive evaluation on adversarial attack methods to identify and analyze their potential vulnerabilities. We formulate the diagnosis process as a Markov Decision Process (MDP), where the state is the patient responses and unasked questions, and the action is either to ask a question or to make a diagnosis. We implemented six prevailing major attack methods, including the Fast Gradient Signed Method (FGSM), Projected Gradient Descent (PGD), Carlini & Wagner Attack (C&W) attack, Basic Iterative Method (BIM), DeepFool, and AutoAttack, with seven epsilon values each. To ensure the generated adversarial examples remain clinically plausible, we developed a comprehensive medical validation framework consisting of 247 medical constraints, including physiological bounds, symptom correlations, and conditional medical constraints. We achieved a 97.6% success rate in generating clinically plausible adversarial samples. We performed our experiment on the National Health Interview Survey (NHIS) dataset (https://www.cdc.gov/nchs/nhis/), which consists of 182,630 samples, to predict the participant's 4-year mortality rate. We evaluated our attacks on the AdaptiveFS framework proposed in arXiv:2004.00994. Our results show that adversarial attacks could significantly impact the diagnostic accuracy, with attack success rates ranging from 33.08% (FGSM) to 64.70% (AutoAttack). Our work has demonstrated that even under strict medical constraints on the input, such RL-based medical questionnaire systems still show significant vulnerabilities.

Digital advertising platforms operate millisecond-level auctions through Real-Time Bidding (RTB) systems, where advertisers compete for ad impressions through algorithmic bids. This dynamic mechanism enables precise audience targeting but introduces profound operational complexity due to advertiser heterogeneity: budgets and ROI targets span orders of magnitude across advertisers, from individual merchants to multinational brands. This diversity creates a demanding adaptation landscape for Multi-Constraint Bidding (MCB). Traditional auto-bidding solutions fail in this environment due to two critical flaws: 1) severe sample inefficiency, where failed explorations under specific constraints yield no transferable knowledge for new budget-ROI combinations, and 2) limited generalization under constraint shifts, as they ignore physical relationships between constraints and bidding coefficients. To address this, we propose HALO: Hindsight-Augmented Learning for Online Auto-Bidding. HALO introduces a theoretically grounded hindsight mechanism that re-purposes all explorations into training data for arbitrary constraint configuration via trajectory reorientation. Further, it employs B-spline functional representation, enabling continuous, derivative-aware bid mapping across constraint spaces. HALO ensures robust adaptation even when budget/ROI requirements differ drastically from training scenarios. Industrial dataset evaluations demonstrate the superiority of HALO in handling multi-scale constraints, reducing constraint violations while improving GMV .

Biclustering, also known as co-clustering or two-way clustering, simultaneously partitions the rows and columns of a data matrix to reveal submatrices with coherent patterns. Incorporating background knowledge into clustering to enhance solution quality and interpretability has attracted growing interest in mathematical optimization and machine learning research. Extending this paradigm to biclustering enables prior information to guide the joint grouping of rows and columns. We study constrained biclustering with pairwise constraints, namely must-link and cannot-link constraints, which specify whether objects should belong to the same or different biclusters. As a model problem, we address the constrained version of the k-densest disjoint biclique problem, which aims to identify k disjoint complete bipartite subgraphs (called bicliques) in a weighted complete bipartite graph, maximizing the total density while satisfying pairwise constraints. We propose both exact and heuristic algorithms. The exact approach is a tailored branch-and-cut algorithm based on a low-dimensional semidefinite programming (SDP) relaxation, strengthened with valid inequalities and solved in a cutting-plane fashion. Exploiting integer programming tools, a rounding scheme converts SDP solutions into feasible biclusterings at each node. For large-scale instances, we introduce an efficient heuristic based on the low-rank factorization of the SDP. The resulting nonlinear optimization problem is tackled with an augmented Lagrangian method, where the subproblem is solved by decomposition through a block-coordinate projected gradient algorithm. Extensive experiments on synthetic and real-world datasets show that the exact method significantly outperforms general-purpose solvers, while the heuristic achieves high-quality solutions efficiently on large instances.