Our algorithm employsonecolumn forsubgradient descent ineach iteration, whereas thedual project subgradient algorithm requires the whole constraint matrix and conducts matrix multiplication in each iteration. In addition, a class of backpressure/max-weight algorithms [25] are developed in the control/queueing literature and the backpressure algorithm can be interpreted from a view of pressuregradient.

This paper takes a closer look at Git Re-Basin, an interesting new approach to merge trained models. We propose a hierarchical model merging scheme that significantly outperforms the standard MergeMany algorithm. With our new algorithm, we find that Re-Basin induces adversarial and perturbation robustness into the merged models, with the effect becoming stronger the more models participate in the hierarchical merging scheme. However, in our experiments Re-Basin induces a much bigger performance drop than reported by the original authors.

In the random-order model for online learning, the sequence of losses is chosen upfront by an adversary and presented to the learner after a random permutation. Any random-order input is \emph{asymptotically} equivalent to a stochastic i.i.d. one, but, for finite times, it may exhibit significant {\em non-stationarity}, which can hinder the performance of stochastic learning algorithms. While algorithms for adversarial inputs naturally maintain their regret guarantees in random order, simple no-regret algorithms exist for the stochastic model that fail against random-order instances. In this paper, we propose a general template to adapt stochastic learning algorithms to the random-order model without substantially affecting their regret guarantees. This allows us to recover improved regret bounds for prediction with delays, online learning with constraints, and bandits with switching costs. Finally, we investigate online classification and prove that, in random order, learnability is characterized by the VC dimension rather than the Littlestone dimension, thus providing a further separation from the general adversarial model.

We consider the problem of fairly allocating sequentially arriving items to a set of individuals. For this problem, the recently-introduced P ACE algorithm leverages the dual averaging algorithm to approximate competitive equilibria and thus generate online fair allocations. P ACE is simple, distributed, and parameter-free, making it appealing for practical use in large-scale systems. However, current performance guarantees for P ACE require i.i.d.

Artificial Intelligence (AI) has achieved remarkable success in specialized tasks but struggles with efficient skill acquisition and generalization. The Abstraction and Reasoning Corpus (ARC) benchmark evaluates intelligence based on minimal training requirements. While Large Language Models (LLMs) have recently improved ARC performance, they rely on extensive pre-training and high computational costs. We introduce MADIL (MDL-based AI), a novel approach leveraging the Minimum Description Length (MDL) principle for efficient inductive learning. MADIL performs pattern-based decomposition, enabling structured generalization. While its performance (7% at ArcPrize 2024) remains below LLM-based methods, it offers greater efficiency and interpretability. This paper details MADIL's methodology, its application to ARC, and experimental evaluations.

Fine-tuning of Large Language Models (LLMs) has become the default practice for improving model performance on a given task. However, performance improvement comes at the cost of training on vast amounts of annotated data which could be sensitive leading to significant data privacy concerns. In particular, the healthcare domain is one of the most sensitive domains exposed to data privacy issues. In this paper, we present PatientDx, a framework of model merging that allows the design of effective LLMs for health-predictive tasks without requiring fine-tuning nor adaptation on patient data. Our proposal is based on recently proposed techniques known as merging of LLMs and aims to optimize a building block merging strategy. PatientDx uses a pivotal model adapted to numerical reasoning and tunes hyperparameters on examples based on a performance metric but without training of the LLM on these data. Experiments using the mortality tasks of the MIMIC-IV dataset show improvements up to 7% in terms of AUROC when compared to initial models. Additionally, we confirm that when compared to fine-tuned models, our proposal is less prone to data leak problems without hurting performance. Finally, we qualitatively show the capabilities of our proposal through a case study. Our best model is publicly available at https://huggingface.co/ Jgmorenof/mistral\_merged\_0\_4.

We study a ranking and selection (R&S) problem when all solutions share common parametric Bayesian input models updated with the data collected from multiple independent data-generating sources. Our objective is to identify the best system by designing a sequential sampling algorithm that collects input and simulation data given a budget. We adopt the most probable best (MPB) as the estimator of the optimum and show that its posterior probability of optimality converges to one at an exponential rate as the sampling budget increases. Assuming that the input parameters belong to a finite set, we characterize the $\epsilon$-optimal static sampling ratios for input and simulation data that maximize the convergence rate. Using these ratios as guidance, we propose the optimal sampling algorithm for R&S (OSAR) that achieves the $\epsilon$-optimal ratios almost surely in the limit. We further extend OSAR by adopting the kernel ridge regression to improve the simulation output mean prediction. This not only improves OSAR's finite-sample performance, but also lets us tackle the case where the input parameters lie in a continuous space with a strong consistency guarantee for finding the optimum. We numerically demonstrate that OSAR outperforms a state-of-the-art competitor.

By merging models, AI systems can combine the distinct strengths of separate language models, achieving a balance between multiple capabilities without requiring substantial retraining. However, the integration process can be intricate due to differences in training methods and fine-tuning, typically necessitating specialized knowledge and repeated refinement. This paper explores model merging techniques across a spectrum of complexity, examining where automated methods like evolutionary strategies stand compared to hyperparameter-driven approaches such as DARE, TIES-Merging and simpler methods like Model Soups. In addition, we introduce Differentiable Adaptive Merging (DAM), an efficient, adaptive merging approach as an alternative to evolutionary merging that optimizes model integration through scaling coefficients, minimizing computational demands. Our findings reveal that even simple averaging methods, like Model Soups, perform competitively when model similarity is high, underscoring each technique's unique strengths and limitations. We open-sourced DAM, including the implementation code and experiment pipeline, on GitHub: https://github.com/arcee-ai/DAM.