We study the problem of designing procurement auctions for the strategic uncapacitated facility location problem: a company needs to procure a set of facility locations in order to serve its customers and each facility location is owned by a strategic agent. Each owner has a private cost for providing access to their facility (e.g., renting it or selling it to the company) and needs to be compensated accordingly. The goal is to design truthful auctions that decide which facilities the company should procure and how much to pay the corresponding owners, aiming to minimize the total cost, i.e., the monetary cost paid to the owners and the connection cost suffered by the customers (their distance to the nearest facility). We evaluate the performance of these auctions using the frugality ratio. We first analyze the performance of the classic VCG auction in this context and prove that its frugality ratio is exactly 3. We then leverage the learning-augmented framework and design auctions that are augmented with predictions regarding the owners' private costs. Specifically, we propose a family of learning-augmented auctions that achieve significant payment reductions when the predictions are accurate, leading to much better frugality ratios. At the same time, we demonstrate that these auctions remain robust even if the predictions are arbitrarily inaccurate, and maintain reasonable frugality ratios even under adversarially chosen predictions. We finally provide a family of "error-tolerant" auctions that maintain improved frugality ratios even if the predictions are only approximately accurate, and we provide upper bounds on their frugality ratio as a function of the prediction error.

Optimization modeling is one of the most crucial but technical parts of operations research (OR). To automate the modeling process, existing works have leveraged large language models (LLMs), prompting them to break down tasks into steps for generating variables, constraints, and objectives. However, due to the highly complex mathematical structures inherent in OR problems, standard fixed-step decomposition often fails to achieve high performance. To address this challenge, we introduce OptiTree, a novel tree search approach designed to enhance modeling capabilities for complex problems through adaptive problem decomposition into simpler subproblems. Specifically, we develop a modeling tree that organizes a wide range of OR problems based on their hierarchical problem taxonomy and complexity, with each node representing a problem category and containing relevant high-level modeling thoughts. Given a problem to model, we recurrently search the tree to identify a series of simpler subproblems and synthesize the global modeling thoughts by adaptively integrating the hierarchical thoughts. Experiments show that OptiTree significantly improves the modeling accuracy compared to the state-of-theart, achieving over 10% improvements on the challenging benchmarks.

Federated learning is a distributed learning paradigm where multiple agents, each only with access to local data, jointly learn a global model. There has recently been an explosion of research aiming not only to improve the accuracy rates of federated learning, but also provide certain guarantees around social good properties such as total error. One branch of this research has taken a game-theoretic approach, and in particular, prior work has viewed federated learning as a hedonic game, where error-minimizing players arrange themselves into federating coalitions. This past work proves the existence of stable coalition partitions, but leaves open a wide range of questions, including how far from optimal these stable solutions are. In this work, we motivate and define a notion of optimality given by the average error rates among federating agents (players).

The distance from calibration, introduced by Błasiok, Gopalan, Hu, and Nakkiran (STOC 2023), has recently emerged as a central measure of miscalibration for probabilistic predictors. We study the fundamental problems of computing and estimating this quantity, given either an exact description of the data distribution or only sample access to it. We give an efficient algorithm that exactly computes the calibration distance when the distribution has a uniform marginal and noiseless labels, which improves the $O(1/\sqrt{|\mathcal{X}|})$ additive approximation of Qiao and Zheng (COLT 2024) for this special case. Perhaps surprisingly, the problem becomes $\mathsf{NP}$-hard when either of the two assumptions is removed. We extend our algorithm to a polynomial-time approximation scheme for the general case. For the estimation problem, we show that $Θ(1/ε^3)$ samples are sufficient and necessary for the empirical calibration distance to be upper bounded by the true distance plus $ε$. In contrast, a polynomial dependence on the domain size -- incurred by the learning-based baseline -- is unavoidable for two-sided estimation. Our positive results are based on simple sparsifications of both the distribution and the target predictor, which significantly reduce the search space for computation and lead to stronger concentration for the estimation problem. To prove the hardness results, we introduce new techniques for certifying lower bounds on the calibration distance -- a problem that is hard in general due to its $\textsf{co-NP}$-completeness.

We create GTA (a benchmark forGeneral Tool Agents) to evaluate the general tool-use ability ofLLMs inreal-worldscenarios. Who created the dataset (e.g., which team, research group) and on behalf of which entity(e.g.,company,institution,organization)?

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