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Many decision-making processes involve evaluating and selecting items, including scientific peer review, job hiring, school admissions, and investment decisions. These domains feature error-prone evaluations and uncertainty about outcomes, which undermine deterministic selection rules. Consequently, randomized selection mechanisms are gaining traction. However, current randomized approaches are ad hoc and, as we prove, inappropriate for their purported objectives. We propose a principled framework for randomized decision-making based on interval estimates of item quality. We introduce MERIT (Maximin Efficient Randomized Interval Top-k), which maximizes the worst-case expected number of top candidates selected under uncertainty represented by overlapping intervals. MERIT provides optimal resource allocation under an interpretable robustness notion. We develop a polynomial-time, practically efficient algorithm and prove our approach satisfies desirable axiomatic properties not guaranteed by existing methods. Experiments on synthetic peer review data from grant funding and conferences demonstrate that MERIT matches existing algorithms' expected utility under fully probabilistic models while outperforming them under our worst-case formulation.

Data-adaptive two-sample testing assesses if two samples come from the same distribution, using a discrepancy learned from the data (e.g., via kernel-based feature representations). Such methods typically rely on data splitting to decouple learning from testing and control type I error. However, this paradigm is ill-suited to few-shot settings with severe sample-size imbalance: abundant reference samples are available, while only a handful of query samples arrive. In this paper, we show how this imbalance can be leveraged constructively. Using abundant reference data, we learn reference-dependent representations that summarize salient structure of the reference distribution and provide informative signals for detecting departures. We incorporate a collection of representation families that capture both global and local structure, and adaptively weight them using only reference samples via an uncertainty-guided principle. Theoretically, we establish permutation-based type I error control and show consistency of the aggregated test: as the sample sizes grow, the test power converges to one whenever the representation set contains at least one consistent representation. Empirically, our aggregation achieves strong performance across a range of benchmarks while retaining type I error control.

Increasingly, copious amounts of consumer data are used to learn high-revenue mechanisms via machine learning. Existing research on mechanism design via machine learning assumes that there is a distribution over the buyers' values for the items for sale and that the learning algorithm's input is a training set sampled from this distribution. This setup makes the strong assumption that no noise is introduced during data collection. In order to help place mechanism design via machine learning on firm foundations, we investigate the extent to which this learning process is robust to noise. Optimizing revenue using noisy data is challenging because revenue functions are extremely volatile: an infinitesimal change in the buyers' values can cause a steep drop in revenue. Nonetheless, we provide guarantees when arbitrarily correlated noise is added to the training set; we only require that the noise has bounded magnitude or is sub-Gaussian. We conclude with an application of our guarantees to multi-task mechanism design, where there are multiple distributions over buyers' values and the goal is to learn a high-revenue mechanism per distribution. To our knowledge, we are the first to study mechanism design via machine learning with noisy data as well as multi-task mechanism design.

When making decisions under uncertainty, individuals often deviate from rational behavior, which can be evaluated across three dimensions: risk preference, probability weighting, and loss aversion.

Despite the great success of deep learning, recent works show that large deep neural networks are often highly redundant and can be significantly reduced in size. However, the theoretical question of how much we can prune a neural network given a specified tolerance of accuracy drop is still open. This paper provides one answer to this question by proposing a greedy optimization based pruning method. The proposed method has the guarantee that the discrepancy between the pruned network and the original network decays with exponentially fast rate w.r.t. the size of the pruned network, under weak assumptions that apply for most practical settings. Empirically, our method improves prior arts on pruning various network architectures including ResNet, MobilenetV2/V3 on ImageNet.

The strong lottery ticket hypothesis has highlighted the potential for training deep neural networks by pruning, which has inspired interesting practical and theoretical insights into how neural networks can represent functions. For networks with ReLU activation functions, it has been proven that a target network with depth L can be approximated by the subnetwork of a randomly initialized neural network that has double the target's depth 2L and is wider by a logarithmic factor. We show that a depth L+1 is sufficient. This result indicates that we can expect to find lottery tickets at realistic, commonly used depths while only requiring logarithmic overparametrization. Our novel construction approach applies to a large class of activation functions and is not limited to ReLUs. Code is available on Github (RelationalML/LT-existence).

The search for efficient, sparse deep neural network models is most prominently performed by pruning: training a dense, overparameterized network and removing parameters, usually via following a manually-crafted heuristic. Additionally, the recent Lottery Ticket Hypothesis conjectures that, for a typically-sized neural network, it is possible to find small sub-networks which, when trained from scratch on a comparable budget, match the performance of the original dense counterpart. We revisit fundamental aspects of pruning algorithms, pointing out missing ingredients in previous approaches, and develop a method, Continuous Sparsification, which searches for sparse networks based on a novel approximation of an intractable $\ell_0$ regularization. We compare against dominant heuristic-based methods on pruning as well as ticket search -- finding sparse subnetworks that can be successfully re-trained from an early iterate. Empirical results show that we surpass the state-of-the-art for both objectives, across models and datasets, including VGG trained on CIFAR-10 and ResNet-50 trained on ImageNet. In addition to setting a new standard for pruning, Continuous Sparsification also offers fast parallel ticket search, opening doors to new applications of the Lottery Ticket Hypothesis.

We introduce TwIST, a distributed training framework for efficient large language model (LLM) sparsification. TwIST trains multiple subnetworks in parallel, periodically aggregates their parameters, and resamples new subnetworks during training. This process identifies high-quality subnetworks ("golden tickets") without requiring post-training procedures such as calibration or Hessian-based recovery. As a result, TwIST enables zero-cost pruning at deployment time while achieving perplexity competitive with state-of-the-art post-training sparsification methods. The benefits are most pronounced under aggressive sparsity (e.g., 50%+), where TwIST significantly outperforms baseline methods; for example, reaching 23.14 PPL compared to 31.64 for the closest prior approach. Unlike unstructured pruning, TwIST produces structured, dense matrices that offer practical inference speedups and memory reductions on commodity hardware (e.g., CPUs) that do not support efficient sparse computation. TwIST provides an efficient training-time path to deployable sparse LLMs without additional fine-tuning or recovery overhead.

When making decisions under uncertainty, individuals often deviate from rational behavior, which can be evaluated across three dimensions: risk preference, probability weighting, and loss aversion.