We consider the problem of estimating inverse temperature parameter $β$ of an $n$-dimensional truncated Ising model using a single sample. Given a graph $G = (V,E)$ with $n$ vertices, a truncated Ising model is a probability distribution over the $n$-dimensional hypercube $\{-1,1\}^n$ where each configuration $\mathbfσ$ is constrained to lie in a truncation set $S \subseteq \{-1,1\}^n$ and has probability $\Pr(\mathbfσ) \propto \exp(β\mathbfσ^\top A\mathbfσ)$ with $A$ being the adjacency matrix of $G$. We adopt the recent setting of [Galanis et al. SODA'24], where the truncation set $S$ can be expressed as the set of satisfying assignments of a $k$-SAT formula. Given a single sample $\mathbfσ$ from a truncated Ising model, with inverse parameter $β^*$, underlying graph $G$ of bounded degree $Δ$ and $S$ being expressed as the set of satisfying assignments of a $k$-SAT formula, we design in nearly $O(n)$ time an estimator $\hatβ$ that is $O(Δ^3/\sqrt{n})$-consistent with the true parameter $β^*$ for $k \gtrsim \log(d^2k)Δ^3.$ Our estimator is based on the maximization of the pseudolikelihood, a notion that has received extensive analysis for various probabilistic models without [Chatterjee, Annals of Statistics '07] or with truncation [Galanis et al. SODA '24]. Our approach generalizes recent techniques from [Daskalakis et al. STOC '19, Galanis et al. SODA '24], to confront the more challenging setting of the truncated Ising model.

In this paper, we create optimal, collision-free, time-dependent trajectories through cluttered dynamic environments. The many spatial and temporal constraints make finding an initial guess for a numerical solver difficult. Graphs of Convex Sets (GCS) and the recently developed Space-Time Graphs of Convex Sets (ST-GCS) enable us to generate minimum distance collision-free trajectories without providing an initial guess to the solver. We also explore the derivation of general GCS-compatible constraints and document an intuitive strategy for adapting general constraints to the framework. We show that ST-GCS produces equivalent trajectories to the standard GCS formulation when the environment is static, as well as globally optimal trajectories in cluttered dynamic environments.

Integer Linear Programs (ILPs) are central to real-world optimizations but notoriously difficult to solve. Learning to Optimize (L2O) has emerged as a promising paradigm, with Graph Neural Networks (GNNs) serving as the standard backbone. However, standard anonymous GNNs are limited in expressiveness for ILPs, and the common enhancement of augmenting nodes with globally unique identifiers (UIDs) typically introduces spurious correlations that severely harm generalization. To address this tradeoff, we propose a parsimonious Local-UID scheme based on d-hop uniqueness coloring, which ensures identifiers are unique only within each node's d-hop neighborhood. Building on this scheme, we introduce ColorGNN, which incorporates color information via color-conditioned embeddings, and ColorUID, a lightweight feature-level variant. We prove that for d-layer networks, Local-UIDs achieve the expressive power of Global-UIDs while offering stronger generalization. Extensive experiments show that our approach (i) yields substantial gains on three ILP benchmarks, (ii) exhibits strong OOD generalization on linear programming datasets, and (iii) further improves a general graph-level task when paired with a state-of-the-art method.

Abstract--In Constraint Programming, solving discrete minimization problems with hard and soft constraints can be done either using (i) soft global constraints, (ii) a reformulation into a linear program, or (iii) a reformulation into local cost functions. Conversely, the approach (ii) provides a global view with strong bounds, but the size of the reformulation can be problematic. We focus on approach (iii) in which soft arc consistency (SAC) algorithms produce bounds of intermediate quality. Recently, the introduction of linear constraints as local cost functions increases their modeling expressiveness. We adapt an existing SAC algorithm to handle linear constraints. We show that our algorithm significantly improves the lower bounds compared to the original algorithm on several benchmarks, reducing solving time in some cases. Graphical models provide a powerful framework for modeling a variety of combinatorial problems, addressing tasks that range from satisfaction problems to probabilistic models. They employ local functions defined over'small' subset of variables to represent diverse interactions among them. For example, to model the Constraint Satisfaction Problem (CSP) [2], each local function is a constraint evaluating to true (satisfied) or false (falsified).

Recent advances have significantly improved our understanding of the sample complexity of learning in average-reward Markov decision processes (AMDPs) under the generative model. However, much less is known about the constrained average-reward MDP (CAMDP), where policies must satisfy long-run average constraints. In this work, we address this gap by studying the sample complexity of learning an $ε$-optimal policy in CAMDPs under a generative model. We propose a model-based algorithm that operates under two settings: (i) relaxed feasibility, which allows small constraint violations, and (ii) strict feasibility, where the output policy satisfies the constraint. We show that our algorithm achieves sample complexities of $\tilde{O}\left(\frac{S A (B+H)}{ ε^2}\right)$ and $\tilde{O} \left(\frac{S A (B+H)}{ε^2 ζ^2} \right)$ under the relaxed and strict feasibility settings, respectively. Here, $ζ$ is the Slater constant indicating the size of the feasible region, $H$ is the span bound of the bias function, and $B$ is the transient time bound. Moreover, a matching lower bound of $\tildeΩ\left(\frac{S A (B+H)}{ ε^2ζ^2}\right)$ for the strict feasibility case is established, thus providing the first minimax-optimal bounds for CAMDPs. Our results close the theoretical gap in understanding the complexity of constrained average-reward MDPs.

Leveraging machine learning methods to solve constraint satisfaction problems has shown promising, but they are mostly limited to a static situation where the problem description is completely known and fixed from the beginning. In this work we present a new approach to constraint satisfaction and optimization in dynamically changing environments, particularly when variables in the problem are statistically independent. We frame it as a reinforcement learning problem and introduce a conditional policy generator by borrowing the idea of class conditional generative adversarial networks (GANs). Assuming that the problem includes both static and dynamic constraints, the former are used in a reward formulation to guide the policy training such that it learns to map to a probabilistic distribution of solutions satisfying static constraints from a noise prior, which is similar to a generator in GANs. On the other hand, dynamic constraints in the problem are encoded to different class labels and fed with the input noise. The policy is then simultaneously updated for maximum likelihood of correctly classifying given the dynamic conditions in a supervised manner. We empirically demonstrate a proof-of-principle experiment with a multi-modal constraint satisfaction problem and compare between unconditional and conditional cases.

Relational object rearrangement (ROR) tasks (e.g., insert flower to vase) require a robot to manipulate objects with precise semantic and geometric reasoning. Existing approaches either rely on pre-collected demonstrations that struggle to capture complex geometric constraints or generate goal-state observations to capture semantic and geometric knowledge, but fail to explicitly couple object transformation with action prediction, resulting in errors due to generative noise. To address these limitations, we propose Imagine2Act, a 3D imitation-learning framework that incorporates semantic and geometric constraints of objects into policy learning to tackle high-precision manipulation tasks. We first generate imagined goal images conditioned on language instructions and reconstruct corresponding 3D point clouds to provide robust semantic and geometric priors. These imagined goal point clouds serve as additional inputs to the policy model, while an object-action consistency strategy with soft pose supervision explicitly aligns predicted end-effector motion with generated object transformation. This design enables Imagine2Act to reason about semantic and geometric relationships between objects and predict accurate actions across diverse tasks. Experiments in both simulation and the real world demonstrate that Imagine2Act outperforms previous state-of-the-art policies. More visualizations can be found at https://sites.google.com/view/imagine2act.

Existing reasoning datasets saturate and fail to test abstract, multi-step problems, especially pathfinding and complex rule constraint satisfaction. We introduce SPaRC (Spatial Pathfinding Reasoning Challenge), a dataset of 1,000 2D grid pathfinding puzzles to evaluate spatial and symbolic reasoning, requiring step-by-step planning with arithmetic and geometric rules. Humans achieve near-perfect accuracy (98.0%; 94.5% on hard puzzles), while the best reasoning models, such as o4-mini, struggle (15.8%; 1.1% on hard puzzles). Models often generate invalid paths (>50% of puzzles for o4-mini), and reasoning tokens reveal they make errors in navigation and spatial logic. Unlike humans, who take longer on hard puzzles, models fail to scale test-time compute with difficulty. Allowing models to make multiple solution attempts improves accuracy, suggesting potential for better spatial reasoning with improved training and efficient test-time scaling methods. SPaRC can be used as a window into models' spatial reasoning limitations and drive research toward new methods that excel in abstract, multi-step problem-solving.

We propose a new formulation for the multi-robot task allocation problem that incorporates (a) complex precedence relationships between tasks, (b) efficient intra-task coordination, and (c) cooperation through the formation of robot coalitions. A task graph specifies the tasks and their relationships, and a set of reward functions models the effects of coalition size and preceding task performance. Maximizing task rewards is NP-hard; hence, we propose network flow-based algorithms to approximate solutions efficiently. A novel online algorithm performs iterative re-allocation, providing robustness to task failures and model inaccuracies to achieve higher performance than offline approaches. We comprehensively evaluate the algorithms in a testbed with random missions and reward functions and compare them to a mixed-integer solver and a greedy heuristic. Additionally, we validate the overall approach in an advanced simulator, modeling reward functions based on realistic physical phenomena and executing the tasks with realistic robot dynamics. Results establish efficacy in modeling complex missions and efficiency in generating high-fidelity task plans while leveraging task relationships.