Display Ads and the generalized assignment problem are two well-studied online packing problems with important applications in ad allocation and other areas.

However,such predictions, although usually accurate, can be arbitrarily poor.

We study the online unweighted bipartite matching problem in the random arrival order model, with $n$ offline and $n$ online vertices, in the learning-augmented setting: The algorithm is provided with untrusted predictions of the types (neighborhoods) of the online vertices. We build upon the work of Choo et al. (ICML 2024, pp. 8762-8781) who proposed an approach that uses a prefix of the arrival sequence as a sample to determine whether the predictions are close to the true arrival sequence and then either follows the predictions or uses a known baseline algorithm that ignores the predictions and is $β$-competitive. Their analysis is limited to the case that the optimal matching has size $n$, i.e., every online vertex can be matched. We generalize their approach and analysis by removing any assumptions on the size of the optimal matching while only requiring that the size of the predicted matching is at least $αn$ for any constant $0 < α\le 1$. Our learning-augmented algorithm achieves $(1-o(1))$-consistency and $(β-o(1))$-robustness. Additionally, we show that the competitive ratio degrades smoothly between consistency and robustness with increasing prediction error.

Although LLMs have demonstrated improved performance by scaling parallel test-time compute, doing so relies on generating reasoning paths that are both diverse and accurate. For challenging problems, the forking tokens that trigger diverse yet correct reasoning modes are typically deep in the sampling tree. Consequently, common strategies to encourage diversity, such as temperature scaling, encounter a worsened trade-off between diversity and accuracy. Motivated by this challenge, we treat parallel reasoning as a set-of-next-token-prediction problem, and incorporate a set-based global loss into Supervised Fine-Tuning (SFT) using self-supervised bipartite matching between our global forking tokens and unique reasoning traces. We observe that, while naive fine-tuning with multiple reasoning traces collapses these unique reasoning modes, our proposed method, Set Supervised Fine-Tuning (SSFT), preserves these modes and produces emergent global forking tokens. Experiments on multiple reasoning benchmarks show that our SSFT consistently outperforms SFT under both Pass@1 and Cons@k metrics.

Modern generative models excel at producing realistic samples--images, text, molecules-- but often lack guarantees about structural properties. A protein generator may produce plausible sequences that violate stability constraints; a network topology generator may create graphs that fail connectivity requirements; a molecule generator may output structures violating chemical valence rules. Standard GAN discriminators provide a global "real vs. fake" signal, but they cannot pinpoint which specific structural constraint failed or guarantee that generated samples satisfy formal specifications. Meanwhile, mathematical logic has developed precise tools for reasoning about structural properties. Ehrenfeucht-Fraïssé (EF) games [1, 2] characterize when two structures are indistinguishable by logical formulas up to a given complexity (quantifier depth k). First-order (FO) and monadic second-order (MSO) logics can express rich structural properties--connectivity, bipartiteness, planarity, acyclicity--that are crucial in applications but invisible to standard discriminators.

We present Sadcher, a real-time task assignment framework for heterogeneous multi-robot teams that incorporates dynamic coalition formation and task precedence constraints. Sadcher is trained through Imitation Learning and combines graph attention and transformers to predict assignment rewards between robots and tasks. Based on the predicted rewards, a relaxed bipartite matching step generates high-quality schedules with feasibility guarantees. We explicitly model robot and task positions, task durations, and robots' remaining processing times, enabling advanced temporal and spatial reasoning and generalization to environments with different spatiotemporal distributions compared to training. Trained on optimally solved small-scale instances, our method can scale to larger task sets and team sizes. Sadcher outperforms other learning-based and heuristic baselines on randomized, unseen problems for small and medium-sized teams with computation times suitable for real-time operation. We also explore sampling-based variants and evaluate scalability across robot and task counts. In addition, we release our dataset of 250,000 optimal schedules: https://autonomousrobots.nl/paper_websites/sadcher_MRTA/

Display Ads and the generalized assignment problem are two well-studied online packing problems with important applications in ad allocation and other areas.