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.

Functional object arrangement (FORM) is the task of arranging objects to fulfill a function, e.g., "set up a dining table for two". One key challenge here is that the instructions for FORM are often under-specified and do not explicitly specify the desired object goal poses. This paper presents SetItUp, a neuro-symbolic framework that learns to specify the goal poses of objects from a few training examples and a structured natural-language task specification. SetItUp uses a grounding graph, which is composed of abstract spatial relations among objects (e.g., left-of), as its intermediate representation. This decomposes the FORM problem into two stages: (i) predicting this graph among objects and (ii) predicting object poses given the grounding graph. For (i), SetItUp leverages large language models (LLMs) to induce Python programs from a task specification and a few training examples. This program can be executed to generate grounding graphs in novel scenarios. For (ii), SetItUp pre-trains a collection of diffusion models to capture primitive spatial relations and online composes these models to predict object poses based on the grounding graph. We evaluated SetItUp on a dataset spanning three distinct task families: arranging tableware on a dining table, organizing items on a bookshelf, and laying out furniture in a bedroom. Experiments show that SetItUp outperforms existing models in generating functional, physically feasible, and aesthetically pleasing object arrangements. This article extends our conference paper published at Robotics: Science and Systems (RSS) 2024.

Circuit Satisfiability (CSAT) plays a pivotal role in Electronic Design Automation. The standard workflow for solving CSAT problems converts circuits into Conjunctive Normal Form (CNF) and employs generic SAT solvers powered by Conflict-Driven Clause Learning (CDCL). However, this process inherently discards rich structural and functional information, leading to suboptimal solver performance. To address this limitation, we introduce CASCAD, a novel circuit-aware SAT solving framework that directly leverages circuit-level conditional probabilities computed via Graph Neural Networks (GNNs). By explicitly modeling gate-level conditional probabilities, CASCAD dynamically guides two critical CDCL heuristics -- variable phase selection and clause managementto significantly enhance solver efficiency. Extensive evaluations on challenging real-world Logical Equivalence Checking (LEC) benchmarks demonstrate that CASCAD reduces solving times by up to 10x compared to state-of-the-art CNF-based approaches, achieving an additional 23.5% runtime reduction via our probability-guided clause filtering strategy. Our results underscore the importance of preserving circuit-level structural insights within SAT solvers, providing a robust foundation for future improvements in SAT-solving efficiency and EDA tool design.

Understanding and adhering to soft constraints is essential for safe and socially compliant autonomous driving. However, such constraints are often implicit, context-dependent, and difficult to specify explicitly. In this work, we present DRIVE, a novel framework for Dynamic Rule Inference and Verified Evaluation that models and evaluates human-like driving constraints from expert demonstrations. DRIVE leverages exponential-family likelihood modeling to estimate the feasibility of state transitions, constructing a probabilistic representation of soft behavioral rules that vary across driving contexts. These learned rule distributions are then embedded into a convex optimization-based planning module, enabling the generation of trajectories that are not only dynamically feasible but also compliant with inferred human preferences. Unlike prior approaches that rely on fixed constraint forms or purely reward-based modeling, DRIVE offers a unified framework that tightly couples rule inference with trajectory-level decision-making. It supports both data-driven constraint generalization and principled feasibility verification. We validate DRIVE on large-scale naturalistic driving datasets, including inD, highD, and RoundD, and benchmark it against representative inverse constraint learning and planning baselines. Experimental results show that DRIVE achieves 0.0% soft constraint violation rates, smoother trajectories, and stronger generalization across diverse driving scenarios. Verified evaluations further demonstrate the efficiency, explanability, and robustness of the framework for real-world deployment.

We adapt alignment techniques from reasoning LLMs to the task of generating engineering sketch constraints found in computer-aided design (CAD) models. Engineering sketches consist of geometric primitives (e.g. points, lines) connected by constraints (e.g. perpendicular, tangent) that define the relationships between them. For a design to be easily editable, the constraints must effectively capture design intent, ensuring the geometry updates predictably when parameters change. Although current approaches can generate CAD designs, an open challenge remains to align model outputs with design intent, we label this problem 'design alignment'. A critical first step towards aligning generative CAD models is to generate constraints which fully-constrain all geometric primitives, without over-constraining or distorting sketch geometry. Using alignment techniques to train an existing constraint generation model with feedback from a constraint solver, we are able to fully-constrain 93% of sketches compared to 34% when using a naive supervised fine-tuning (SFT) baseline and only 8.9% without SFT. Our approach can be applied to any existing constraint generation model and sets the stage for further research bridging alignment strategies between the language and design domains. Additional results can be found at https://autodeskailab.github.io/aligning-constraint-generation/.

The Elementary Shortest-Path Problem(ESPP) seeks a minimum cost path from s to t that visits each vertex at most once. The presence of negative-cost cycles renders the problem NP-hard. We present a probabilistic method for finding near-optimal ESPP, enabled by an unsupervised graph neural network that jointly learns node value estimates and edge-selection probabilities via a surrogate loss function. The loss provides a high probability certificate of finding near-optimal ESPP solutions by simultaneously reducing negative-cost cycles and embedding the desired algorithmic alignment. At inference time, a decoding algorithm transforms the learned edge probabilities into an elementary path. Experiments on graphs of up to 100 nodes show that the proposed method surpasses both unsupervised baselines and classical heuristics, while exhibiting high performance in cross-size and cross-topology generalization on unseen synthetic graphs.