Multi-agent imitation learning with function approximation: Linear Markov games and beyond

In this work, we present the first theoretical analysis of multi-agent imitation learning (MAIL) in linear Markov games where both the transition dynamics and each agent's reward function are linear in some given features. We demonstrate that by leveraging this structure, it is possible to replace the state-action level "all policy deviation concentrability coefficient" (Freihaut et al., arXiv:2510.09325) with a concentrability coefficient defined at the feature level which can be much smaller than the state-action analog when the features are informative about states' similarity. Furthermore, to circumvent the need for any concentrability coefficient, we turn to the interactive setting. We provide the first, computationally efficient, interactive MAIL algorithm for linear Markov games and show that its sample complexity depends only on the dimension of the feature map $d$. Building on these theoretical findings, we propose a deep MAIL interactive algorithm which clearly outperforms BC on games such as Tic-Tac-Toe and Connect4.

Matching Multiple Experts: On the Exploitability of Multi-Agent Imitation Learning

Multi-agent imitation learning (MA-IL) aims to learn optimal policies from expert demonstrations of interactions in multi-agent interactive domains. Despite existing guarantees on the performance of the resulting learned policies, characterizations of how far the learned polices are from a Nash equilibrium are missing for offline MA-IL. In this paper, we demonstrate impossibility and hardness results of learning low-exploitable policies in general $n$-player Markov Games. We do so by providing examples where even exact measure matching fails, and demonstrating a new hardness result on characterizing the Nash gap given a fixed measure matching error. We then show how these challenges can be overcome using strategic dominance assumptions on the expert equilibrium. Specifically, for the case of dominant strategy expert equilibria, assuming Behavioral Cloning error $ε_{\text{BC}}$, this provides a Nash imitation gap of $\mathcal{O}\left(nε_{\text{BC}}/(1-γ)^2\right)$ for a discount factor $γ$. We generalize this result with a new notion of best-response continuity, and argue that this is implicitly encouraged by standard regularization techniques.

Easy Data Unlearning Bench

Evaluating machine unlearning methods remains technically challenging, with recent benchmarks requiring complex setups and significant engineering overhead. We introduce a unified and extensible benchmarking suite that simplifies the evaluation of unlearning algorithms using the KLoM (KL divergence of Margins) metric. Our framework provides precomputed model ensembles, oracle outputs, and streamlined infrastructure for running evaluations out of the box. By standardizing setup and metrics, it enables reproducible, scalable, and fair comparison across unlearning methods. We aim for this benchmark to serve as a practical foundation for accelerating research and promoting best practices in machine unlearning. Our code and data are publicly available.

MaD-Mix: Multi-Modal Data Mixtures via Latent Space Coupling for Vision-Language Model Training

Vision-Language Models (VLMs) are typically trained on a diverse set of multi-modal domains, yet current practices rely on costly manual tuning. We propose MaD-Mix, a principled and computationally efficient framework that derives multi-modal data mixtures for VLM training. MaD-Mix formulates data mixing as modality-aware domain alignment maximization and obtains closed-form multi-modal alignment scores from the Fenchel dual through inter-modal coupling variables. MaD-Mix systematically handles domains with missing modalities, allowing for the integration of language-only domains. Empirical evaluations across 0.5B and 7B models demonstrate that MaD-Mix accelerates VLM training across diverse benchmarks. MaD-Mix matches human-tuned data mixtures using 22% fewer training steps in image-text instruction tuning. In complex tri-modal video-image-text scenarios, where manual tuning becomes impractical, MaD-Mix boosts average accuracy over uniform weights, with negligible mixture computation overhead (< 1 GPU-hour), enabling scalable mixture design for modern VLM pipelines.

Provably avoiding over-optimization in Direct Preference Optimization without knowing the data distribution

We introduce PEPO (Pessimistic Ensemble based Preference Optimization), a single-step Direct Preference Optimization (DPO)-like algorithm to mitigate the well-known over-optimization issue in preference learning without requiring the knowledge of the data-generating distribution or learning an explicit reward model. PEPO achieves pessimism via an ensemble of preference-optimized policies trained on disjoint data subsets and then aggregates them through a worst case construction that favors the agreement across models. In the tabular setting, PEPO achieves sample complexity guarantees depending only on a single-policy concentrability coefficient, thus avoiding the all-policy concentrability which affects the guarantees of algorithms prone to over-optimization, such as DPO. The theoretical findings are corroborated by a convincing practical performance, while retaining the simplicity and the practicality of DPO-style training.

Direct Preference Optimization with Rating Information: Practical Algorithms and Provable Gains

The class of direct preference optimization (DPO) algorithms has emerged as a promising approach for solving the alignment problem in foundation models. These algorithms work with very limited feedback in the form of pairwise preferences and fine-tune models to align with these preferences without explicitly learning a reward model. While the form of feedback used by these algorithms makes the data collection process easy and relatively more accurate, its ambiguity in terms of the quality of responses could have negative implications. For example, it is not clear if a decrease (increase) in the likelihood of preferred (dispreferred) responses during the execution of these algorithms could be interpreted as a positive or negative phenomenon. In this paper, we study how to design algorithms that can leverage additional information in the form of rating gap, which informs the learner how much the chosen response is better than the rejected one. We present new algorithms that can achieve faster statistical rates than DPO in presence of accurate rating gap information. Moreover, we theoretically prove and empirically show that the performance of our algorithms is robust to inaccuracy in rating gaps. Finally, we demonstrate the solid performance of our methods in comparison to a number of DPO-style algorithms across a wide range of LLMs and evaluation benchmarks.

Training Neural Networks at Any Scale

This article reviews modern optimization methods for training neural networks with an emphasis on efficiency and scale. We present state-of-the-art optimization algorithms under a unified algorithmic template that highlights the importance of adapting to the structures in the problem. We then cover how to make these algorithms agnostic to the scale of the problem. Our exposition is intended as an introduction for both practitioners and researchers who wish to be involved in these exciting new developments.

BLUR: A Bi-Level Optimization Approach for LLM Unlearning

Enabling large language models (LLMs) to unlearn knowledge and capabilities acquired during training has proven vital for ensuring compliance with data regulations and promoting ethical practices in generative AI. Although there are growing interests in developing various unlearning algorithms, it remains unclear how to best formulate the unlearning problem. The most popular formulation uses a weighted sum of forget and retain loss, but it often leads to performance degradation due to the inherent trade-off between forget and retain losses. In this work, we argue that it is important to model the hierarchical structure of the unlearning problem, where the forget problem (which \textit{unlearns} certain knowledge and/or capabilities) takes priority over the retain problem (which preserves model utility). This hierarchical structure naturally leads to a bi-level optimization formulation where the lower-level objective focuses on minimizing the forget loss, while the upper-level objective aims to maintain the model's utility. Based on this new formulation, we propose a novel algorithm, termed Bi-Level UnleaRning (\texttt{BLUR}), which not only possesses strong theoretical guarantees but more importantly, delivers superior performance. In particular, our extensive experiments demonstrate that \texttt{BLUR} consistently outperforms all the state-of-the-art algorithms across various unlearning tasks, models, and metrics. Codes are available at https://github.com/OptimAI-Lab/BLURLLMUnlearning.

Accelerating Spectral Clustering under Fairness Constraints

Fairness of decision-making algorithms is an increasingly important issue. In this paper, we focus on spectral clustering with group fairness constraints, where every demographic group is represented in each cluster proportionally as in the general population. We present a new efficient method for fair spectral clustering (Fair SC) by casting the Fair SC problem within the difference of convex functions (DC) framework. To this end, we introduce a novel variable augmentation strategy and employ an alternating direction method of multipliers type of algorithm adapted to DC problems. We show that each associated subproblem can be solved efficiently, resulting in higher computational efficiency compared to prior work, which required a computationally expensive eigendecomposition. Numerical experiments demonstrate the effectiveness of our approach on both synthetic and real-world benchmarks, showing significant speedups in computation time over prior art, especially as the problem size grows. This work thus represents a considerable step forward towards the adoption of fair clustering in real-world applications.

DiffCAP: Diffusion-based Cumulative Adversarial Purification for Vision Language Models

Vision Language Models (VLMs) have shown remarkable capabilities in multimodal understanding, yet their susceptibility to perturbations poses a significant threat to their reliability in real-world applications. Despite often being imperceptible to humans, these perturbations can drastically alter model outputs, leading to erroneous interpretations and decisions. This paper introduces DiffCAP, a novel diffusion-based purification strategy that can effectively neutralize adversarial corruptions in VLMs. We observe that adding minimal noise to an adversarially corrupted image significantly alters its latent embedding with respect to VLMs. Building on this insight, DiffCAP cumulatively injects random Gaussian noise into adversarially perturbed input data. This process continues until the embeddings of two consecutive noisy images reach a predefined similarity threshold, indicating a potential approach to neutralize the adversarial effect. Subsequently, a pretrained diffusion model is employed to denoise the stabilized image, recovering a clean representation suitable for the VLMs to produce an output. Through extensive experiments across six datasets with three VLMs under varying attack strengths in three task scenarios, we show that DiffCAP consistently outperforms existing defense techniques by a substantial margin. Notably, DiffCAP significantly reduces both hyperparameter tuning complexity and the required diffusion time, thereby accelerating the denoising process. Equipped with strong theoretical and empirical support, DiffCAP provides a robust and practical solution for securely deploying VLMs in adversarial environments.