Differentiating Through Dual Prices: End-to-End Policy Learning Under Capacity Constraints

Many social services assign scarce resources, such as housing assistance or hospital interventions, to people who arrive one at a time: each arrival must receive a decision immediately, and the long-run usage of every resource must stay within its capacity. We study how to learn such an assignment policy from logged observational data. The standard pipeline is decision-blind: fit one outcome model per arm by regression, price each capacitated resource from the fitted models, and assign each arrival the arm whose predicted outcome minus price is largest. We instead train the outcome models end-to-end, differentiating an off-policy estimate of the deployed policy's value through the dual prices themselves. We study two formulations: an exact nonconvex one, and a convex relaxation whose optimum always satisfies the capacity constraints in expectation and which is suboptimal by at most a term linear in the smoothing temperature and logarithmic in the number of arms. Every method is evaluated in a queueing simulation with resources replenished at their capacity rates. Across six datasets, the two end-to-end variants take the top slots on a deployment-adjusted value index at every delay cost, including zero; when capacities are binding, decision-blind baselines frequently violate them and incur much longer queueing delays. On the largest dataset, a hospital cohort of seventy thousand patients, end-to-end training also achieves significantly higher policy value, a margin that survives a capacity-matched neural baseline. Flexible decision-blind regression remains the stronger pure predictor where ground truth is measurable; end-to-end training is best suited to settings where resources are genuinely scarce and feasibility matters.

A Gold-Standard Study of What Makes a Lightweight Game-Playing Agent Strong

Reinforcement learning agents for imperfect-information card games are only as strong as the opponents they train against, and they are hard to grade, since they beat a random opponent over 99 percent of the time and only tie copies of themselves. So we build a strong, fixed, rule-based expert for Gin Rummy and use it only as a yardstick, never for training. It beats every agent we trained 70 to 99 percent of the time. Across more than a hundred runs, we isolate what makes a lightweight agent stronger. Trust region updates, a well-aimed reward, a curriculum of tougher opponents, warm starting, and keeping the best checkpoint all help, and stacking them lifts a self-play champion from about 30 to 36 percent against the expert. Several ideas did not pay off. Short-term and longer-term reward shaping, learned state embeddings, imitation and DAgger, and a live large language model opponent were each unhelpful, too slow, or too heavy to train at scale. Comparing MLP, convolutional, set-based, attention, and recurrent encoders shows that extra capacity does little to break the ceiling, suggesting the limit is information rather than network size. We add standard baselines (neural fictitious self-play and information set Monte Carlo search) and confirm the approach carries over to Leduc Hold'em, where the optimum is computable. The result is a lightweight, game-agnostic recipe that trains competitive agents without training on the expert, for any game a small model can handle, reported with robust statistics and released as a reusable package.

Early Stopping for Large Reasoning Models via Confidence Dynamics

Large reasoning models rely on long chain-of-thought generation to solve complex problems, but extended reasoning often incurs substantial computational cost and can even degrade performance due to overthinking. A key challenge is determining when the model should stop reasoning and produce the final answer. In this work, we study the confidence of intermediate answers during reasoning and observe two characteristic behaviors: correct reasoning trajectories often reach high-confidence answers early, while incorrect rollouts tend to produce long, unproductive reasoning traces and exhibit less reliable confidence dynamics. Motivated by these observations, we propose CoDE-Stop (Confidence Dynamics Early Stop), an early stopping method that leverages the dynamics of intermediate answer confidence to decide when to terminate reasoning, requiring no additional training and easily integrating into existing models. We evaluate CoDE-Stop on diverse reasoning and science benchmarks across multiple models. Compared to prior early stopping methods, it achieves a more favorable accuracy-compute tradeoff and reduces total token usage by 25-50% compared to standard full-length reasoning. In addition, we provide analyses of confidence dynamics during reasoning, offering insights into how confidence changes in both correct and incorrect trajectories.

Sampling and Loss Weights in Multi-Domain Training

In the training of large deep neural networks, there is a need for vast amounts of training data. To meet this need, data is collected from multiple domains, such as Wikipedia and GitHub. These domains are heterogeneous in both data quality and the diversity of information they provide. This raises the question of how much we should rely on each domain. Several methods have attempted to address this issue by assigning sampling weights to each data domain using heuristics or approximations. As a first step toward a deeper understanding of the role of data mixing, this work revisits the problem by studying two kinds of weights: sampling weights, which control how much each domain contributes in a batch, and loss weights, which scale the loss from each domain during training. Through a rigorous study of linear regression, we show that these two weights play complementary roles. First, they can reduce the variance of gradient estimates in iterative methods such as stochastic gradient descent (SGD). Second, they can improve generalization performance by reducing the generalization gap. We provide both theoretical and empirical support for these claims. We further study the joint dynamics of sampling weights and loss weights, examining how they can be combined to capture both contributions.

Rewriting the Budget: A General Framework for Black-Box Attacks Under Cost Asymmetry

Traditional decision-based black-box adversarial attacks on image classifiers aim to generate adversarial examples by slightly modifying input images while keeping the number of queries low, where each query involves sending an input to the model and observing its output. Most existing methods assume that all queries have equal cost. However, in practice, queries may incur asymmetric costs; for example, in content moderation systems, certain output classes may trigger additional review, enforcement, or penalties, making them more costly than others. While prior work has considered such asymmetric cost settings, effective algorithms for this scenario remain underdeveloped. In this paper, we propose a general framework for decision-based attacks under asymmetric query costs, which we refer to as asymmetric black-box attacks. We modify two core components of existing attacks: the search strategy and the gradient estimation process. Specifically, we propose Asymmetric Search (AS), a more conservative variant of binary search that reduces reliance on high-cost queries, and Asymmetric Gradient Estimation (AGREST), which shifts the sampling distribution to favor low-cost queries. We design efficient algorithms that minimize total attack cost by balancing different query types, in contrast to earlier methods such as stealthy attacks that focus only on limiting expensive (high-cost) queries. Our method can be integrated into a range of existing black-box attacks with minimal changes. We perform both theoretical analysis and empirical evaluation on standard image classification benchmarks. Across various cost regimes, our method consistently achieves lower total query cost and smaller perturbations than existing approaches, with improvements of up to 40% in some settings.

Blacksmith: Fast Adversarial Training of Vision Transformers via a Mixture of Single-step and Multi-step Methods

Despite the remarkable success achieved by deep learning algorithms in various domains, such as computer vision, they remain vulnerable to adversarial perturbations. Adversarial Training (AT) stands out as one of the most effective solutions to address this issue; however, single-step AT can lead to Catastrophic Overfitting (CO). This scenario occurs when the adversarially trained network suddenly loses robustness against multi-step attacks like Projected Gradient Descent (PGD). Although several approaches have been proposed to address this problem in Convolutional Neural Networks (CNNs), we found out that they do not perform well when applied to Vision Transformers (ViTs). In this paper, we propose Blacksmith, a novel training strategy to overcome the CO problem, specifically in ViTs. Our approach utilizes either of PGD-2 or Fast Gradient Sign Method (FGSM) randomly in a mini-batch during the adversarial training of the neural network. This will increase the diversity of our training attacks, which could potentially mitigate the CO issue. To manage the increased training time resulting from this combination, we craft the PGD-2 attack based on only the first half of the layers, while FGSM is applied end-to-end. Through our experiments, we demonstrate that our novel method effectively prevents CO, achieves PGD-2 level performance, and outperforms other existing techniques including N-FGSM, which is the state-of-the-art method in fast training for CNNs.