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General Machine Learning · Causality

Anish Dhir, Ruby Sedgwick, Avinash Kori, Ben Glocker, Mark van der Wilk

Current causal discovery approaches require restrictive model assumptions in the absence of interventional data to ensure structure identifiability. These assumptions often do not hold in real-world applications leading to a loss of guarantees and poor performance in practice. Recent work has shown that, in the bivariate case, Bayesian model selection can greatly improve performance by exchanging restrictive modelling for more flexible assumptions, at the cost of a small probability of making an error. Our work shows that this approach is useful in the important multivariate case as well. We propose a scalable algorithm leveraging a continuous relaxation of the discrete model selection problem. Specifically, we employ the Causal Gaussian Process Conditional Density Estimator (CGP-CDE) as a Bayesian non-parametric model, using its hyperparameters to construct an adjacency matrix. This matrix is then optimised using the marginal likelihood and an acyclicity regulariser, giving the maximum a posteriori causal graph. We demonstrate the competitiveness of our approach, showing it is advantageous to perform multivariate causal discovery without infeasible assumptions using Bayesian model selection.

Optimization

Huizhuo Yuan, Yifeng Liu, Shuang Wu, zhou Xun, Quanquan Gu

Training deep neural networks--and more recently, large models--demands efficient and scalable optimizers. Adaptive gradient algorithms like Adam, AdamW, and their variants have been central to this task. Despite the development of numerous variance reduction algorithms in the past decade aimed at accelerating stochastic optimization in both convex and nonconvex settings, variance reduction has not found widespread success in training deep neural networks or large language models. Consequently, it has remained a less favored approach in modern AI. In this paper, to unleash the power of variance reduction for efficient training of large models, we propose a unified optimization framework, MARS (**M**ake v**A**riance **R**eduction **S**hine), which reconciles preconditioned gradient methods with variance reduction via a scaled stochastic recursive momentum technique. Within our framework, we introduce three instances of MARS that leverage preconditioned gradient updates based on AdamW, Lion, and Shampoo, respectively. We also draw a connection between our algorithms and existing optimizers. Experimental results on training GPT-2 models indicate that MARS consistently outperforms AdamW by a large margin.

Theory · Optimization

Chansophea Wathanak In, Yi Li, David Woodruff, Xuan Wu

Robustness to outliers is important in machine learning. Many classical problems, including subspace embedding, clustering, and low-rank approximation, lack scalable, outlier-resilient algorithms. This paper considers machine learning problems of the form $\min_{x\in \mathbb{R}^d} F(x)$, where $F(x)=\sum_{i=1}^n F_i(x)$, and their robust counterparts $\min_{x\in\mathbb{R}^d} F^{(m)}(x)$, where $F^{(m)}(x)$ denotes the sum of all but the $m$ largest $F_i(x)$ values. We develop a general framework for constructing $\epsilon$-coresets for such robust problems, where an $\epsilon$-coreset is a weighted subset of functions $\{F_1(x),\dots,F_n(x)\}$ that provides a $(1+\epsilon)$-approximation to $F(x)$. Specifically, if the original problem $F$ has total sensitivity $T$ and admits a vanilla $\epsilon$-coreset of size $S$, our algorithm constructs an $\epsilon$-coreset of size $\tilde{O}(\frac{mT}{\epsilon})+S$ for the robust objective $F^{(m)}$. This coreset size can be shown to be near-tight for $\ell_2$ subspace embedding. Our coreset algorithm has scalable running time and leads to new or improved algorithms for the robust optimization problems. Empirical evaluations demonstrate that our coresets outperform uniform sampling on real-world data sets.

Reinforcement Learning

Zachary Roch, George Atia, Yue Wang

Robust reinforcement learning (RL) under the average reward criterion, which seeks to optimize long-term system performance in uncertain environments, remains a largely unexplored area. To address this challenge, we propose a reduction-based framework that transforms robust average reward optimization into the more extensively studied robust discounted reward optimization by employing a specific discount factor. Our framework provides two key advantages. **Data Efficiency**: We design a model-based reduction algorithm that achieves near-optimal sample complexity, enabling efficient identification of optimal robust policies; **Scalability**: By bypassing the inherent challenges of scaling up average reward optimization, our framework facilitates the design of scalable, convergent algorithms for robust average reward optimization leveraging function approximation. Our algorithmic design, supported by theoretical and empirical analyses, provides a concrete solution to robust average reward RL with the first data efficiency and scalability guarantees, highlighting the framework’s potential to optimize long-term performance under model uncertainty in practical problems.

Reinforcement Learning · Deep RL

Haitong Ma, Tianyi Chen, Kai Wang, Na Li, Bo Dai

Diffusion policies have achieved superior performance in imitation learning and offline reinforcement learning (RL) due to their rich expressiveness. However, the conventional diffusion training procedure requires samples from target distribution, which is impossible in online RL since we cannot sample from the optimal policy. Backpropagating policy gradient through the diffusion process incurs huge computational costs and instability, thus being expensive and not scalable. To enable efficient training of diffusion policies in online RL, we generalize the conventional denoising score matching by reweighting the loss function. The resulting Reweighted Score Matching (RSM) preserves the optimal solution and low computational cost of denoising score matching, while eliminating the need to sample from the target distribution and allowing learning to optimize value functions. We introduce two tractable reweighted loss functions to solve two commonly used policy optimization problems, policy mirror descent and max-entropy policy, resulting in two practical algorithms named Diffusion Policy Mirror Descent (DPMD) and Soft Diffusion Actor-Critic (SDAC). We conducted comprehensive comparisons on MuJoCo benchmarks. The empirical results show that the proposed algorithms outperform recent diffusion-policy online RLs on most tasks, and the DPMD improves more than 120% over soft actor-critic on Humanoid and Ant.

Optimization · Zero-order and Black-box Optimization

Mujin Cheon, Jay Lee, Dong-Yeun Koh, Calvin Tsay

To avoid myopic behavior, multi-step lookahead Bayesian optimization (BO) algorithms consider the sequential nature of BO and have demonstrated promising results in recent years. However, owing to the curse of dimensionality, most of these methods make significant approximations or suffer scalability issues. This paper presents a novel reinforcement learning (RL)-based framework for multi-step lookahead BO in high-dimensional black-box optimization problems. The proposed method enhances the scalability and decision-making quality of multi-step lookahead BO by efficiently solving the sequential dynamic program of the BO process in a near-optimal manner using RL. We first introduce an Attention-DeepSets encoder to represent the state of knowledge to the RL agent and subsequently propose a multi-task, fine-tuning procedure based on end-to-end (encoder-RL) on-policy learning. We evaluate the proposed method, EARL-BO (Encoder Augmented RL for BO), on synthetic benchmark functions and hyperparameter tuning problems, finding significantly improved performance compared to existing multi-step lookahead and high-dimensional BO methods.

Applications · Language, Speech and Dialog

Jimmy Wang, Tom Zollo, Richard Zemel, Hongseok Namkoong

Eliciting information to reduce uncertainty about a latent entity is a critical task in many application domains, e.g., assessing individual student learning outcomes, diagnosing underlying diseases, or learning user preferences. Though natural language is a powerful medium for this purpose, large language models (LLMs) and existing fine-tuning algorithms lack mechanisms for strategically gathering information to refine their own understanding of the latent entity. To harness the generalization power and world knowledge of LLMs in developing effective information-gathering strategies, we propose an adaptive elicitation framework that actively reduces uncertainty on the latent entity. Since probabilistic modeling of an abstract latent entity is difficult, our framework adopts a predictive view of uncertainty, using a meta-learned language model to simulate future observations and enable scalable uncertainty quantification over complex natural language. Through autoregressive forward simulation, our model quantifies how new questions reduce epistemic uncertainty, enabling the development of sophisticated information-gathering strategies to choose the most informative next queries. In experiments on the 20 questions game, dynamic opinion polling, and adaptive student assessment, our method consistently outperforms baselines in identifying critical unknowns and improving downstream predictions, illustrating the promise of strategic information gathering in natural language settings.

General Machine Learning · Scalable Algorithms

Yang Jiao, Kai Yang, Chengtao Jian

Trilevel learning (TLL) with zeroth order constraints is a fundamental problem in machine learning, arising in scenarios where gradient information is inaccessible due to data privacy or model opacity, such as in federated learning, healthcare, and financial systems. These problems are notoriously difficult to solve due to their inherent complexity and the lack of first order information. Moreover, in many practical scenarios, data may be distributed across various nodes, necessitating strategies to address trilevel learning problems without centralizing data on servers to uphold data privacy. To this end, an effective distributed trilevel zeroth order learning framework DTZO is proposed in this work to address the trilevel learning problems with level-wise zeroth order constraints in a distributed manner. The proposed DTZO is versatile and can be adapted to a wide range of (grey-box) trilevel learning problems with partial zeroth order constraints. In DTZO, the cascaded polynomial approximation can be constructed without relying on gradients or sub-gradients, leveraging a novel cut, i.e., zeroth order cut. Furthermore, we theoretically carry out the non-asymptotic convergence rate analysis for the proposed DTZO in achieving the $\epsilon$-stationary point. Extensive experiments have been conducted to demonstrate and validate the superior performance of the proposed DTZO.

General Machine Learning · Transfer, Multitask and Meta-learning

Jing Xu, Jiazheng Li, Jingzhao Zhang

Model merging offers an effective way to integrate the capabilities of multiple fine-tuned models. However, the performance degradation of the merged model remains a challenge, particularly when none or few data are available. This paper first highlights the necessity of domain-specific data for model merging by proving that data-agnostic algorithms can have arbitrarily bad worst-case performances. Building on this theoretical insight, we explore the relationship between model merging and distillation, introducing a novel few-shot merging algorithm, ProDistill (Progressive Layer-wise Distillation). Unlike common belief that layer-wise training hurts performance, we show that layer-wise teacher-student distillation not only enhances the scalability but also improves model merging performance. We conduct extensive experiments to show that compared to existing few-shot merging methods,ProDistill achieves state-of-the-art performance, with up to 6.14\% and 6.61\% improvements in vision and NLU tasks. Furthermore, we extend the experiments to models with over 10B parameters, showcasing the exceptional scalability of ProDistill.

General Machine Learning · Clustering

Arhit Chakrabarti, Yang Ni, Debdeep Pati, Bani Mallick

We consider the problem of clustering grouped data for which the observations may include group-specific variables in addition to the variables that are shared across groups. This type of data is quite common; for example, in cancer genomic studies, molecular information is available for all cancers whereas cancer-specific clinical information may only be available for certain cancers. Existing grouped clustering methods only consider the shared variables but ignore valuable information from the group-specific variables. To allow for these group-specific variables to aid in the clustering, we propose a novel Bayesian nonparametric approach, termed global-local (GLocal) Dirichlet process, that models the "global-local" structure of the observations across groups. We characterize the GLocal Dirichlet process using the stick-breaking representation and the representation as a limit of a finite mixture model. We theoretically quantify the approximation errors of the truncated prior, the corresponding finite mixture model, and the associated posterior distribution. We develop a fast variational Bayes algorithm for scalable posterior inference, which we illustrate with extensive simulations and a TCGA pan-gastrointestinal cancer dataset.

Social Aspects · Privacy

Justin Chen, Vincent Cohen-Addad, Alessandro Epasto, Morteza Zadimoghaddam

In the differentially private partition selection problem (a.k.a. set union, key discovery), users hold subsets of items from an unbounded universe. The goal is to output as many items as possible from the union of the users' sets while maintaining user-level differential privacy. Solutions to this problem are a core building block for many privacy-preserving ML applications including vocabulary extraction in a private corpus, computing statistics over categorical data and learning embeddings over user-provided items. We propose an algorithm for this problem, MaxAdaptiveDegree (MAD), which adaptively reroutes weight from items with weight far above the threshold needed for privacy to items with smaller weight, thereby increasing the probability that less frequent items are output. Our algorithm can be efficiently implemented in massively parallel computation systems allowing scalability to very large datasets. We prove that our algorithm stochastically dominates the standard parallel algorithm for this problem. We also develop a two-round version of our algorithm, MAD2R, where results of the computation in the first round are used to bias the weighting in the second round to maximize the number of items output. In experiments, our algorithms provide the best results among parallel algorithms and scale to datasets with hundreds of billions of items, up to three orders of magnitude larger than those analyzed in prior works.

General Machine Learning · Scalable Algorithms

Supratim Shit, Gurmehak chadha, Surendra kumar, Bapi Chatterjee

Coreset, as a summary of training data, offers an efficient approach for reducing data processing and storage complexity during training. In the emerging vertical federated learning (VFL) setting, where scattered clients store different data features, it directly reduces communication complexity. In this work, we introduce coresets construction for regularized logistic regression both in centralized and VFL settings. Additionally, we improve the coreset size for regularized linear regression in the VFL setting. We also eliminate the dependency of the coreset size on a property of the data due to the VFL setting. The improvement in the coreset sizes is due to our novel coreset construction algorithms that capture the reduced model complexity due to the added regularization and its subsequent analysis. In experiments, we provide extensive empirical evaluation that backs our theoretical claims. We also report the performance of our coresets by comparing the models trained on the complete data and on the coreset.

Reinforcement Learning · Deep RL

Bryan L. M. de Oliveira, Luana G. B. Martins, Bruno Brandão, Murilo L. da Luz, Telma Woerle de Lima Soares, Luckeciano C. Melo

Effective visual representation learning is crucial for reinforcement learning (RL) agents to extract task-relevant information from raw sensory inputs and generalize across diverse environments. However, existing RL benchmarks lack the ability to systematically evaluate representation learning capabilities in isolation from other learning challenges. To address this gap, we introduce the Sliding Puzzles Gym (SPGym), a novel benchmark that transforms the classic 8-tile puzzle into a visual RL task with images drawn from arbitrarily large datasets. SPGym's key innovation lies in its ability to precisely control representation learning complexity through adjustable grid sizes and image pools, while maintaining fixed environment dynamics, observation, and action spaces. This design enables researchers to isolate and scale the visual representation challenge independently of other learning components. Through extensive experiments with model-free and model-based RL algorithms, we uncover fundamental limitations in current methods' ability to handle visual diversity. As we increase the pool of possible images, all algorithms exhibit in- and out-of-distribution performance degradation, with sophisticated representation learning techniques often underperforming simpler approaches like data augmentation. These findings highlight critical gaps in visual representation learning for RL and establish SPGym as a valuable tool for driving progress in robust, generalizable decision-making systems.

General Machine Learning · Scalable Algorithms

Zhaolu Liu, Robert Peach, Mauricio Barahona

Kernel-based hypothesis tests offer a flexible, non-parametric tool to detect high-order interactions in multivariate data, beyond pairwise relationships. Yet the scalability of such tests is limited by the computationally demanding permutation schemes used to generate null approximations. Here we introduce a family of permutation-free high-order tests for joint independence and partial factorisations of $d$ variables. Our tests eliminate the need for permutation-based approximations by leveraging V-statistics and a novel cross-centring technique to yield test statistics with a standard normal limiting distribution under the null. We present implementations of the tests and showcase their efficacy and scalability through synthetic datasets. We also show applications inspired by causal discovery and feature selection, which highlight both the importance of high-order interactions in data and the need for efficient computational methods.

Reinforcement Learning · Batch/Offline

Andrei Polubarov, Nikita Lyubaykin, Alexander Derevyagin, Ilya Zisman, Denis Tarasov, Alexander Nikulin, Vladislav Kurenkov

In-Context Reinforcement Learning (ICRL) represents a promising paradigm for developing generalist agents that learn at inference time through trial-and-error interactions, analogous to how large language models adapt contextually, but with a focus on reward maximization. However, the scalability of ICRL beyond toy tasks and single-domain settings remains an open challenge. In this work, we present the first steps toward scaling ICRL by introducing a fixed, cross-domain model capable of learning behaviors through in-context reinforcement learning. Our results demonstrate that Algorithm Distillation, a framework designed to facilitate ICRL, offers a compelling and competitive alternative to expert distillation to construct versatile action models. These findings highlight the potential of ICRL as a scalable approach for generalist decision-making systems.

General Machine Learning · Everything Else

Tam Le, Truyen Nguyen, Hideitsu Hino, Kenji Fukumizu

We investigate the Sobolev IPM problem for probability measures supported on a graph metric space. Sobolev IPM is an important instance of integral probability metrics (IPM), and is obtained by constraining a critic function within a unit ball defined by the Sobolev norm. In particular, it has been used to compare probability measures and is crucial for several theoretical works in machine learning. However, to our knowledge, there are no efficient algorithmic approaches to compute Sobolev IPM effectively, which hinders its practical applications. In this work, we establish a relation between Sobolev norm and weighted $L^p$-norm, and leverage it to propose a *novel regularization* for Sobolev IPM. By exploiting the graph structure, we demonstrate that the regularized Sobolev IPM provides a *closed-form* expression for fast computation. This advancement addresses long-standing computational challenges, and paves the way to apply Sobolev IPM for practical applications, even in large-scale settings. Additionally, the regularized Sobolev IPM is negative definite. Utilizing this property, we design positive-definite kernels upon the regularized Sobolev IPM, and provide preliminary evidences of their advantages for comparing probability measures on a given graph for document classification and topological data analysis.

General Machine Learning · Scalable Algorithms

Jinbin Zhang, Nasib Ullah, Erik Schultheis, Rohit Babbar

Large output spaces, also referred to as Extreme multilabel classification (XMC), is a setting that arises, e.g., in large-scale tagging and product-to-product recommendation, and is characterized by the number of labels ranging from hundreds of thousands to millions. This means that the linear classification head, usually only a tiny fraction of the overall model, turns into the main driver for compute and memory demand. Current state-of-the-art XMC methods predominantly rely on FP16-FP32 mixed-precision training, which we show can be unstable, and inefficient in terms of memory usage and computational overhead. Meanwhile, existing low-precision methods typically retain higher precision for the classification layer. In this work, we propose ELMO, a pure low-precision training framework for XMC models using BFloat16 and Float8 data types. By leveraging Kahan summation and stochastic rounding, we demonstrate that XMC models can be effectively trained entirely in Float8, without relying on single-precision master weights or tensor scaling. Low-precision training, combined with our proposed memory optimizations---gradient fusion and chunking---enables significant reductions in GPU memory usage. For example, we train a 3-million-label XMC model with only 6.6 GiB of GPU memory, compared to the 39.7GiB required by the optimized SOTA method, Renee without compromising accuracy.

Reinforcement Learning · Multi-agent

Tianxu Li, Kun Zhu

Recent works have increasingly focused on learning decentralized policies for agents as a solution to the scalability challenges in Multi-Agent Reinforcement Learning (MARL), where agents typically share the parameters of a policy network to make action decisions. However, this parameter sharing can impede efficient exploration, as it may lead to similar behaviors among agents. Different from previous mutual information-based methods that promote multi-agent diversity, we introduce a novel multi-agent exploration method called Trajectory Entropy Exploration (TEE). Our method employs a particle-based entropy estimator to maximize the entropy of different agents' trajectories in a contrastive trajectory representation space, resulting in diverse trajectories and efficient exploration. This entropy estimator avoids challenging density modeling and scales effectively in high-dimensional multi-agent settings. We integrate our method with MARL algorithms by deploying an intrinsic reward for each agent to encourage entropy maximization. To validate the effectiveness of our method, we test our method in challenging multi-agent tasks from several MARL benchmarks. The results demonstrate that our method consistently outperforms existing state-of-the-art methods.

Deep Learning · Large Language Models

Ruizhe Shi, Runlong Zhou, Simon Du

Direct Preference Optimization (DPO) has emerged as a stable, scalable, and efficient solution for language model alignment.Despite its empirical success, the optimization properties, particularly the impact of samplers on its convergence rates, remain under-explored. In this paper, we provide a rigorous analysis of DPO's convergence rates with different sampling strategies under the exact gradient setting, revealing a surprising separation: uniform sampling achieves $\textbf{linear}$ convergence, while our proposed online sampler achieves $\textbf{quadratic}$ convergence. We further adapt the sampler to practical settings by incorporating posterior distributions and logit mixing, demonstrating improvements over previous methods. For example, it outperforms vanilla DPO by over $7.4$% on Safe-RLHF dataset. Our results not only offer insights into the theoretical understanding of DPO but also pave the way for further algorithm designs.

Deep Learning · Large Language Models

Guanting Dong, Keming Lu, Chengpeng Li, Tingyu Xia, Bowen Yu, Chang Zhou, Jingren Zhou

One core capability of large language models~(LLMs) is to follow natural language instructions. However, the issue of automatically constructing high-quality training data to enhance the complex instruction-following abilities of LLMs without manual annotation remains unresolved. In this paper, we introduce AutoIF, the first scalable and reliable method for automatically generating instruction-following training data. AutoIF transforms the validation of instruction-following data quality into code verification, requiring LLMs to generate instructions, the corresponding code to verify the correctness of the instruction responses, and unit test samples to cross-validate the code's correctness. Then, execution feedback-based rejection sampling can generate data for Supervised Fine-Tuning (SFT) and Reinforcement Learning from Human Feedback (RLHF) training. AutoIF achieves significant improvements across three training algorithms, SFT, Offline DPO, and Online DPO, when applied to the advanced open-source LLMs, Qwen2 and LLaMA3, in self-alignment and strong-to-weak distillation settings. Using two widely-used and three challenging general instruction-following benchmarks, we demonstrate that AutoIF significantly improves LLM performance across a wide range of natural instruction constraints. Notably, AutoIF is the first to surpass 90\% accuracy in IFEval’s loose instruction accuracy, without compromising general, math and coding capabilities. Further analysis of quality, scaling, combination, and data efficiency highlights AutoIF's strong generalization and alignment potential. Our code are available at https://github.com/QwenLM/AutoIF