The cutting plane method is an augmentative constrained optimization procedure that is often used with continuous-domain optimization techniques such as linear and convex programs. We investigate the viability of a similar idea within message passing - for integral solutions in the context of two combinatorial problems: 1) For Traveling Salesman Problem (TSP), we propose a factor-graph based on Held-Karp formulation, with an exponential number of constraint factors, each of which has an exponential but sparse tabular form.

Metric labeling is a special case of energy minimization for pairwise Markov random fields. The energy function consists of arbitrary unary potentials, and pairwise potentials that are proportional to a given metric distance function over the label set.

In many RL applications, ensuring an agent's actions adhere to constraints is crucial for safety. Most previous methods in Action-Constrained Reinforcement Learning (ACRL) employ a projection layer after the policy network to correct the action. However projection-based methods suffer from issues like the zero gradient problem and higher runtime due to the usage of optimization solvers. Recently methods were proposed to train generative models to learn a differentiable mapping between latent variables and feasible actions to address this issue. However, generative models require training using samples from the constrained action space, which itself is challenging. To address such limitations, first, we define a target distribution for feasible actions based on constraint violation signals, and train normalizing flows by minimizing the KL divergence between an approximated distribution over feasible actions and the target. This eliminates the need to generate feasible action samples, greatly simplifying the flow model learning. Second, we integrate the learned flow model with existing deep RL methods, which restrict it to exploring only the feasible action space. Third, we extend our approach beyond ACRL to handle state-wise constraints by learning the constraint violation signal from the environment. Empirically, our approach has significantly fewer constraint violations while achieving similar or better quality in several control tasks than previous best methods.

Auto-bidding problem under a strict return-on-spend constraint (ROSC) is considered, where an algorithm has to make decisions about how much to bid for an ad slot depending on the revealed value, and the hidden allocation and payment function that describes the probability of winning the ad-slot depending on its bid. The objective of an algorithm is to maximize the expected utility (product of ad value and probability of winning the ad slot) summed across all time slots subject to the total expected payment being less than the total expected utility, called the ROSC. A (surprising) impossibility result is derived that shows that no online algorithm can achieve a sub-linear regret even when the value, allocation and payment function are drawn i.i.d. from an unknown distribution. The problem is non-trivial even when the revealed value remains constant across time slots, and an algorithm with regret guarantee that is optimal up to logarithmic factor is derived.

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 $O(\sqrt{T})$ and a CCV of $\min\{\cV, O(\sqrt{T}\log T) \}$, where $\cV$ 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. For special cases of constraint sets, $\cV=O(1)$. Compared to the state of the art results, static regret of $O(\sqrt{T})$ and CCV of $O(\sqrt{T}\log T)$, that were universal, the new result on CCV is instance dependent, which is derived by exploiting the geometric properties of the constraint sets.

Recent research has shown that machine learning models are vulnerable to privacy attacks targeting their training data. Differential privacy (DP) has become a widely adopted countermeasure, as it offers rigorous privacy protections. In this paper, we introduce a reconstruction attack targeting state-of-the-art $\varepsilon$-DP random forests. By leveraging a constraint programming model that incorporates knowledge of the forest's structure and DP mechanism characteristics, our approach formally reconstructs the most likely dataset that could have produced a given forest. Through extensive computational experiments, we examine the interplay between model utility, privacy guarantees, and reconstruction accuracy across various configurations. Our results reveal that random forests trained with meaningful DP guarantees can still leak substantial portions of their training data. Specifically, while DP reduces the success of reconstruction attacks, the only forests fully robust to our attack exhibit predictive performance no better than a constant classifier. Building on these insights, we provide practical recommendations for the construction of DP random forests that are more resilient to reconstruction attacks and maintain non-trivial predictive performance.

The success of Constraint Programming relies partly on the global constraints and implementation of the associated filtering algorithms. Recently, new ideas emerged to improve these implementations in practice, especially regarding the all different constraint. In this paper, we consider the cardinality constraint with costs. The cardinality constraint is a generalization of the all different constraint that specifies the number of times each value must be taken by a given set of variables in a solution. The version with costs introduces an assignment cost and bounds the total sum of assignment costs. The arc consistency filtering algorithm of this constraint is difficult to use in practice, as it systematically searches for many shortest paths. We propose a new approach that works with upper bounds on shortest paths based on landmarks. This approach can be seen as a preprocessing. It is fast and avoids, in practice, a large number of explicit computations of shortest paths.

We investigate the logical reasoning capabilities of large language models (LLMs) and their scalability in complex non-monotonic reasoning. To this end, we introduce ZebraLogic, a comprehensive evaluation framework for assessing LLM reasoning performance on logic grid puzzles derived from constraint satisfaction problems (CSPs). ZebraLogic enables the generation of puzzles with controllable and quantifiable complexity, facilitating a systematic study of the scaling limits of models such as Llama, o1 models, and DeepSeek-R1. By encompassing a broad range of search space complexities and diverse logical constraints, ZebraLogic provides a structured environment to evaluate reasoning under increasing difficulty. Our results reveal a significant decline in accuracy as problem complexity grows -- a phenomenon we term the curse of complexity. This limitation persists even with larger models and increased inference-time computation, suggesting inherent constraints in current LLM reasoning capabilities. Additionally, we explore strategies to enhance logical reasoning, including Best-of-N sampling, backtracking mechanisms, and self-verification prompts. Our findings offer critical insights into the scalability of LLM reasoning, highlight fundamental limitations, and outline potential directions for improvement.

Circuits in deterministic decomposable negation normal form (d-DNNF) are representations of Boolean functions that enable linear-time model counting. This paper strengthens our theoretical knowledge of what classes of functions can be efficiently transformed, or compiled, into d-DNNF. Our main contribution is the fixed-parameter tractable (FPT) compilation of conjunctions of specific constraints parameterized by incidence treewidth. This subsumes the known result for CNF. The constraints in question are all functions representable by constant-width ordered binary decision diagrams (OBDDs) for all variable orderings. For instance, this includes parity constraints and cardinality constraints with constant threshold. The running time of the FPT compilation is singly exponential in the incidence treewidth but hides large constants in the exponent. To balance that, we give a more efficient FPT algorithm for model counting that applies to a sub-family of the constraints and does not require compilation.

We consider bandits with anytime knapsacks (BwAK), a novel version of the BwK problem where there is an \textit{anytime} cost constraint instead of a total cost budget. This problem setting introduces additional complexities as it mandates adherence to the constraint throughout the decision-making process. We propose SUAK, an algorithm that utilizes upper confidence bounds to identify the optimal mixture of arms while maintaining a balance between exploration and exploitation. SUAK is an adaptive algorithm that strategically utilizes the available budget in each round in the decision-making process and skips a round when it is possible to violate the anytime cost constraint. In particular, SUAK slightly under-utilizes the available cost budget to reduce the need for skipping rounds. We show that SUAK attains the same problem-dependent regret upper bound of $ O(K \log T)$ established in prior work under the simpler BwK framework. Finally, we provide simulations to verify the utility of SUAK in practical settings.