As machine learning (ML) applications grow increasingly complex in recent years, modern ML frameworks often need to address multiple potentially conflicting objectives with coupled decision variables across different layers. This creates a compelling need for multi-objective bilevel learning (MOBL). So far, however, the field of MOBL remains in its infancy and many important problems remain under-explored. This motivates us to fill this gap and systematically investigate the theoretical and algorithmic foundation of MOBL. Specifically, we consider MOBL problems with multiple conflicting objectives guided by preferences at the upper-level subproblem, where part of the inputs depend on the optimal solution of the lower-level subproblem. Our goal is to develop efficient MOBL optimization algorithms to (1) identify a preference-guided Pareto-stationary solution with low oracle complexity; and (2) enable systematic Pareto front exploration. To this end, we propose a unifying algorithmic framework called weighted-Chebyshev multi-hyper-gradient-descent (WC-MHGD) for both deterministic and stochastic settings with finite-time Pareto-stationarity convergence rate guarantees, which not only implies low oracle complexity but also induces systematic Pareto front exploration. We further conduct extensive experiments to confirm our theoretical results.

Large language models (LLMs) have demonstrated impressive natural language processing abilities but face challenges such as hallucination and outdated knowledge. Retrieval-Augmented Generation (RAG) has emerged as a state-of-the-art approach to mitigate these issues. While RAG enhances LLM outputs, it remains vulnerable to poisoning attacks. Recent studies show that injecting poisoned texts into the knowledge database can compromise RAG systems, but most existing attacks assume that the attacker can insert a sufficient number of poisoned texts per query to outnumber correct-answer texts in retrieval, an assumption that is often unrealistic. To address this limitation, we propose CorruptRAG, a practical poisoning attack against RAG systems in which the attacker injects only a single poisoned text, enhancing both feasibility and stealth. Extensive experiments conducted on multiple large-scale datasets demonstrate that CorruptRAG achieves higher attack success rates than existing baselines.

Retrieval-Augmented Generation (RAG) integrates external knowledge into large language models to improve response quality. However, recent work has shown that RAG systems are highly vulnerable to poisoning attacks, where malicious texts are inserted into the knowledge database to influence model outputs. While several defenses have been proposed, they are often circumvented by more adaptive or sophisticated attacks. This paper presents RAGOrigin, a black-box responsibility attribution framework designed to identify which texts in the knowledge database are responsible for misleading or incorrect generations. Our method constructs a focused attribution scope tailored to each misgeneration event and assigns a responsibility score to each candidate text by evaluating its retrieval ranking, semantic relevance, and influence on the generated response. The system then isolates poisoned texts using an unsupervised clustering method. We evaluate RAGOrigin across seven datasets and fifteen poisoning attacks, including newly developed adaptive poisoning strategies and multi-attacker scenarios. Our approach outperforms existing baselines in identifying poisoned content and remains robust under dynamic and noisy conditions. These results suggest that RAGOrigin provides a practical and effective solution for tracing the origins of corrupted knowledge in RAG systems. Our code is available at: https://github.com/zhangbl6618/RAG-Responsibility-Attribution

Split Learning (SL) offers a framework for collaborative model training that respects data privacy by allowing participants to share the same dataset while maintaining distinct feature sets. However, SL is susceptible to backdoor attacks, in which malicious clients subtly alter their embeddings to insert hidden triggers that compromise the final trained model. To address this vulnerability, we introduce SecureSplit, a defense mechanism tailored to SL. SecureSplit applies a dimensionality transformation strategy to accentuate subtle differences between benign and poisoned embeddings, facilitating their separation. With this enhanced distinction, we develop an adaptive filtering approach that uses a majority-based voting scheme to remove contaminated embeddings while preserving clean ones. Rigorous experiments across four datasets (CIFAR-10, MNIST, CINIC-10, and ImageNette), five backdoor attack scenarios, and seven alternative defenses confirm the effectiveness of SecureSplit under various challenging conditions.

Federated Learning (FL) allows multiple clients to collaboratively train a model without sharing their private data. However, FL is vulnerable toByzantine attacks, where adversaries manipulate client models to compromise the federated model, andprivacy inference attacks, where adversaries exploit client models to infer private data. Existing defenses against both backdoor and privacy inference attacks introduce significant computational and communication overhead, creating a gap between theory and practice. To address this, we propose ABBR, a practical framework for Byzantine-robust and privacy-preserving FL. We are the first to utilize dimensionality reduction to speed up the private computation of complex filtering rules in privacy-preserving FL. Additionally, we analyze the accuracy loss of vector-wise filtering in low-dimensional space and introduce an adaptive tuning strategy to minimize the impact of malicious models that bypass filtering on the global model. We implement ABBR with state-of-the-art Byzantine-robust aggregation rules and evaluate it on public datasets, showing that it runs significantly faster, has minimal communication overhead, and maintains nearly the same Byzantine-resilience as the baselines.

Decentralized bilevel optimization (DBO) provides a powerful framework for multi-agent systems to solve local bilevel tasks in a decentralized fashion without the need for a central server. However, most existing DBO methods rely on lower-level strong convexity (LLSC) to guarantee unique solutions and a well-defined hypergradient for stationarity measure, hindering their applicability in many practical scenarios not satisfying LLSC. To overcome this limitation, we introduce a new single-loop DBO algorithm called diminishing quadratically-regularized bilevel decentralized optimization (DUET), which eliminates the need for LLSC by introducing a diminishing quadratic regularization to the lower-level (LL) objective. We show that DUET achieves an iteration complexity of $O(1/T^{1-5p-\frac{11}{4}\tau})$ for approximate KKT-stationary point convergence under relaxed assumptions, where $p$ and $\tau $ are control parameters for LL learning rate and averaging, respectively. In addition, our DUET algorithm incorporates gradient tracking to address data heterogeneity, a key challenge in DBO settings. To the best of our knowledge, this is the first work to tackle DBO without LLSC under decentralized settings with data heterogeneity. Numerical experiments validate the theoretical findings and demonstrate the practical effectiveness of our proposed algorithms.

Decentralized min-max optimization allows multi-agent systems to collaboratively solve global min-max optimization problems by facilitating the exchange of model updates among neighboring agents, eliminating the need for a central server. However, sharing model updates in such systems carry a risk of exposing sensitive data to inference attacks, raising significant privacy concerns. To mitigate these privacy risks, differential privacy (DP) has become a widely adopted technique for safeguarding individual data. Despite its advantages, implementing DP in decentralized min-max optimization poses challenges, as the added noise can hinder convergence, particularly in non-convex scenarios with complex agent interactions in min-max optimization problems. In this work, we propose an algorithm called DPMixSGD (Differential Private Minmax Hybrid Stochastic Gradient Descent), a novel privacy-preserving algorithm specifically designed for non-convex decentralized min-max optimization. Our method builds on the state-of-the-art STORM-based algorithm, one of the fastest decentralized min-max solutions. We rigorously prove that the noise added to local gradients does not significantly compromise convergence performance, and we provide theoretical bounds to ensure privacy guarantees. To validate our theoretical findings, we conduct extensive experiments across various tasks and models, demonstrating the effectiveness of our approach.

Federated learning (FL) is a privacy-preserving machine learning technique that facilitates collaboration among participants across demographics. FL enables model sharing, while restricting the movement of data. Since FL provides participants with independence over their training data, it becomes susceptible to poisoning attacks. Such collaboration also propagates bias among the participants, even unintentionally, due to different data distribution or historical bias present in the data. This paper proposes an intentional fairness attack, where a client maliciously sends a biased model, by increasing the fairness loss while training, even considering homogeneous data distribution. The fairness loss is calculated by solving an optimization problem for fairness metrics such as demographic parity and equalized odds. The attack is insidious and hard to detect, as it maintains global accuracy even after increasing the bias. We evaluate our attack against the state-of-the-art Byzantine-robust and fairness-aware aggregation schemes over different datasets, in various settings. The empirical results demonstrate the attack efficacy by increasing the bias up to 90%, even in the presence of a single malicious client in the FL system.

Recently, multi-objective optimization (MOO) has gained attention for its broad applications in ML, operations research, and engineering. However, MOO algorithm design remains in its infancy and many existing MOO methods suffer from unsatisfactory convergence rate and sample complexity performance. To address this challenge, in this paper, we propose an algorithm called STIMULUS (**st**ochastic path-**i**ntegrated **mul**ti-gradient rec**u**rsive e**s**timator), a new and robust approach for solving MOO problems. Different from the traditional methods, STIMULUS introduces a simple yet powerful recursive framework for updating stochastic gradient estimates to improve convergence performance with low sample complexity. In addition, we introduce an enhanced version of \algns, termed \algmns, which incorporates a momentum term to further expedite convergence. We establish $\mathcal{O}(1/T)$ convergence rates of the proposed methods for non-convex settings and $\mathcal{O}(\exp{-\mu T})$ for strongly convex settings, where $T$ is the total number of iteration rounds. Additionally, we achieve the state-of-the-art $O\left(n+\sqrt{n}\epsilon^{-1}\right)$ sample complexities for non-convex settings and $\mathcal{O}\left(n+ \sqrt{n} \ln ({\mu/\epsilon})\right)$ for strongly convex settings, where $\epsilon>0$ is a desired stationarity error. Moreover, to alleviate the periodic full gradient evaluation requirement in STIMULUS and STIMULUS-M, we further propose enhanced versions with adaptive batching called STIMULUS$^+$/ STIMULUS-M$^+$ and provide their theoretical analysis.

Large language models (LLMs) integrated with retrieval-augmented generation (RAG) systems improve accuracy by leveraging external knowledge sources. However, recent research has revealed RAG's susceptibility to poisoning attacks, where the attacker injects poisoned texts into the knowledge database, leading to attacker-desired responses. Existing defenses, which predominantly focus on inference-time mitigation, have proven insufficient against sophisticated attacks. In this paper, we introduce RAGForensics, the first traceback system for RAG, designed to identify poisoned texts within the knowledge database that are responsible for the attacks. RAGForensics operates iteratively, first retrieving a subset of texts from the database and then utilizing a specially crafted prompt to guide an LLM in detecting potential poisoning texts. Empirical evaluations across multiple datasets demonstrate the effectiveness of RAGForensics against state-of-the-art poisoning attacks. This work pioneers the traceback of poisoned texts in RAG systems, providing a practical and promising defense mechanism to enhance their security.

Learning an accurate value function for a given policy is a critical step in solving reinforcement learning (RL) problems. So far, however, the convergence speed and sample complexity performances of most existing policy evaluation algorithms remain unsatisfactory, particularly with non-linear function approximation. This challenge motivates us to develop a new path-integrated primal-dual stochastic gradient (PILOT) method, that is able to achieve a fast convergence speed for RL policy evaluation with nonlinear function approximation. To further alleviate the periodic full gradient evaluation requirement, we further propose an enhanced method with an adaptive-batch adjustment called PILOT$^+$. The main advantages of our methods include: i) PILOT allows the use of {\em{constant}} step sizes and achieves the $\mathcal{O}(1/K)$ convergence rate to first-order stationary points of non-convex policy evaluation problems; ii) PILOT is a generic {\em{single}}-timescale algorithm that is also applicable for solving a large class of non-convex strongly-concave minimax optimization problems; iii) By adaptively adjusting the batch size via historical stochastic gradient information, PILOT$^+$ is more sample-efficient empirically without loss of theoretical convergence rate. Our extensive numerical experiments verify our theoretical findings and showcase the high efficiency of the proposed PILOT and PILOT$^+$ algorithms compared with the state-of-the-art methods.

In recent years, decentralized bilevel optimization has gained significant attention thanks to its versatility in modeling a wide range of multi-agent learning problems, such as multi-agent reinforcement learning and multi-agent meta-learning. However, one unexplored and fundamental problem in this area is how to solve decentralized stochastic bilevel optimization problems with domain constraints while achieving low sample and communication complexities. This problem often arises from multi-agent learning problems with safety constraints. As shown in this paper, constrained decentralized bilevel optimization is far more challenging than its unconstrained counterpart due to the complex coupling structure, which necessitates new algorithm design and analysis techniques. Toward this end, we investigate a class of constrained decentralized bilevel optimization problems, where multiple agents collectively solve a nonconvex-strongly-convex bilevel problem with constraints in the upper-level variables. We propose an algorithm called Prometheus (proximal tracked stochastic recursive estimator) that achieves the first $\mathcal{O}(\epsilon^{-1})$ results in both sample and communication complexities for constrained decentralized bilevel optimization, where $\epsilon>0$ is a desired stationarity error. Collectively, the results in this work contribute to a theoretical foundation for low sample- and communication-complexity constrained decentralized bilevel learning.

Decentralized bilevel optimization has received increasing attention recently due to its foundational role in many emerging multi-agent learning paradigms (e.g., multi-agent meta-learning and multi-agent reinforcement learning) over peer-to-peer edge networks. However, to work with the limited computation and communication capabilities of edge networks, a major challenge in developing decentralized bilevel optimization techniques is to lower sample and communication complexities. This motivates us to develop a new decentralized bilevel optimization called DIAMOND (decentralized single-timescale stochastic approximation with momentum and gradient-tracking). The contributions of this paper are as follows: i) our DIAMOND algorithm adopts a single-loop structure rather than following the natural double-loop structure of bilevel optimization, which offers low computation and implementation complexity; ii) compared to existing approaches, the DIAMOND algorithm does not require any full gradient evaluations, which further reduces both sample and computational complexities; iii) through a careful integration of momentum information and gradient tracking techniques, we show that the DIAMOND algorithm enjoys $\mathcal{O}\left( {{ \in ^{ - 3/2}}} \right)$ in sample and communication complexities for achieving an ϵ-stationary solution, both of which are independent of the dataset sizes and significantly outperform existing works. Extensive experiments also verify our theoretical findings.

Recently, min-max optimization problems have received increasing attention due to their wide range of applications in machine learning (ML). However, most existing min-max solution techniques are either single-machine or distributed algorithms coordinated by a central server. In this paper, we focus on the decentralized min-max optimization for learning with domain constraints, where multiple agents collectively solve a nonconvex-strongly-concave min-max saddle point problem without coordination from any server. Decentralized min-max optimization problems with domain constraints underpins many important ML applications, including multi-agent ML fairness assurance, and policy evaluations in multi-agent reinforcement learning. We propose an algorithm called PRECISION (proximal gradient-tracking and stochastic recursive variance reduction) that enjoys a convergence rate of O(1/T), where T is the maximum number of iterations. To further reduce sample complexity, we propose PRECISION+ with an adaptive batch size technique. We show that the fast O(1/T) convergence of PRECISION and PRECISION+ to an ε-stationary point imply O(ε-2) communication complexity and [EQUATION] sample complexity, where m is the number of agents and n is the size of dataset at each agent. To our knowledge, this is the first work that achieves O(ε-2) in both sample and communication complexities in decentralized min-max learning with domain constraints. Our experiments also corroborate the theoretical results.

In recent years, multi-objective optimization (MOO) emerges as a foundational problem underpinning many multi-agent multi-task learning applications. However, existing algorithms in MOO literature remain limited to centralized learning settings, which do not satisfy the distributed nature and data privacy needs of such multi-agent multi-task learning applications. This motivates us to propose a new federated multi-objective learning (FMOL) framework with multiple clients distributively and collaboratively solving an MOO problem while keeping their training data private. Notably, our FMOL framework allows a different set of objective functions across different clients to support a wide range of applications, which advances and generalizes the MOO formulation to the federated learning paradigm for the first time. For this FMOL framework, we propose two new federated multi-objective optimization (FMOO) algorithms called federated multi-gradient descent averaging (FMGDA) and federated stochastic multi-gradient descent averaging (FSMGDA). Both algorithms allow local updates to significantly reduce communication costs, while achieving the {\em same} convergence rates as those of their algorithmic counterparts in the single-objective federated learning. Our extensive experiments also corroborate the efficacy of our proposed FMOO algorithms.

In recent years, decentralized bilevel optimization problems have received increasing attention in the networking and machine learning communities. However, for decentralized bilevel optimization over networks with limited computation and communication capabilities, how to achieve low sample and communication complexities are two fundamental challenges. In this paper, we make the first attempt to investigate the class of decentralized bilevel optimization problems with nonconvex and strongly-convex structure corresponding to the outer and inner subproblems, respectively. Our main contributions in this paper are two-fold: i) We first propose a deterministic algorithm called interact (inner-gradient-descent-outer-tracked-gradient) that requires the sample complexity of O(nϵ-1) and communication complexity of O(ϵ-1) to solve the bilevel optimization problem, where n and ϵ > 0 are the number of samples at each agent and the desired stationarity gap, respectively. ii) To relax the need for full gradient evaluations in each iteration, we propose a stochastic variance-reduced version of interact (svr-interact), which improves the sample complexity to [EQUATION] while achieving the same communication complexity as the deterministic algorithm. Our numerical experiments also corroborate our theoretical findings.

To increase the training speed of distributed learning, recent years have witnessed a significant amount of interest in developing both synchronous and asynchronous distributed stochastic variance-reduced optimization methods. However, all existing synchronous and asynchronous distributed training algorithms suffer from various limitations in either convergence speed or implementation complexity. This motivates us to propose an algorithm called synthesis (semi-asynchronous path-integrated stochastic gradient search), which leverages the special structure of the variance-reduction framework to overcome the limitations of both synchronous and asynchronous distributed learning algorithms, while retaining their salient features. We consider two implementations of synthesis under distributed and shared memory architectures. We show that our synthesis algorithms have [EQUATION] computational complexities for achieving an ϵ-stationary point in non-convex learning under distributed and shared memory architectures, respectively, where N denotes the total number of training samples and Δ represents the maximum delay of the workers. Moreover, we investigate the generalization performance of synthesis by establishing algorithmic stability bounds for quadratic strongly convex and non-convex optimization. We further conduct extensive numerical experiments to verify our theoretical findings.

Federated learning (FL) has received a surge of interest in recent years thanks to its benefits in data privacy protection, efficient communication, and parallel data processing. Also, with appropriate algorithmic designs, one could achieve the desirable linear speedup for convergence effect in FL. However, most existing works on FL are limited to systems with i.i.d. data and centralized parameter servers and results on decentralized FL with heterogeneous datasets remains limited. Moreover, whether or not the linear speedup for convergence is achievable under fully decentralized FL with data heterogeneity remains an open question. In this paper, we address these challenges by proposing a new algorithm, called NET-FLEET, for fully decentralized FL systems with data heterogeneity. The key idea of our algorithm is to enhance the local update scheme in FL (originally intended for communication efficiency) by incorporating a recursive gradient correction technique to handle heterogeneous datasets. We show that, under appropriate parameter settings, the proposed NET-FLEET algorithm achieves a linear speedup for convergence. We further conduct extensive numerical experiments to evaluate the performance of the proposed NET-FLEET algorithm and verify our theoretical findings.

Federated min-max learning has received increasing attention in recent years thanks to its wide range of applications in various learning paradigms. Similar to the conventional federated learning for empirical risk minimization problems, communication complexity also emerges as one of the most critical concerns that affects the future prospect of federated min-max learning. To lower the communication complexity of federated min-max learning, a natural approach is to utilize the idea of infrequent communications (through multiple local updates) same as in conventional federated learning. However, due to the more complicated inter-outer problem structure in federated min-max learning, theoretical understandings of communication complexity for federated min-max learning with infrequent communications remain very limited in the literature. This is particularly true for settings with non-i.i.d. datasets and partial client participation. To address this challenge, in this paper, we propose a new algorithmic framework called \ul{s}tochastic \ul{s}ampling \ul{a}veraging \ul{g}radient \ul{d}escent \ul{a}scent ($\mathsf{SAGDA}$), which i) assembles stochastic gradient estimators from randomly sampled clients as control variates and ii) leverages two learning rates on both server and client sides. We show that $\mathsf{SAGDA}$ achieves a linear speedup in terms of both the number of clients and local update steps, which yields an $\mathcal{O}(\epsilon^{-2})$ communication complexity that is orders of magnitude lower than the state of the art. Interestingly, by noting that the standard federated stochastic gradient descent ascent (FSGDA) is in fact a control-variate-free special version of $\mathsf{SAGDA}$, we immediately arrive at an $\mathcal{O}(\epsilon^{-2})$ communication complexity result for FSGDA. Therefore, through the lens of $\mathsf{SAGDA}$, we also advance the current understanding on communication complexity of the standard FSGDA method for federated min-max learning.

Cooperative multi-agent reinforcement learning (MARL) has received increasing attention in recent years and has found many scientific and engineering applications. However, a key challenge arising from many cooperative MARL algorithm designs (e.g., the actor-critic framework) is the policy evaluation problem, which can only be conducted in a {\em decentralized} fashion. In this paper, we focus on decentralized MARL policy evaluation with nonlinear function approximation, which is often seen in deep MARL. We first show that the empirical decentralized MARL policy evaluation problem can be reformulated as a decentralized nonconvex-strongly-concave minimax saddle point problem. We then develop a decentralized gradient-based descent ascent algorithm called GT-GDA that enjoys a convergence rate of $\mathcal{O}(1/T)$. To further reduce the sample complexity, we propose two decentralized stochastic optimization algorithms called GT-SRVR and GT-SRVRI, which enhance GT-GDA by variance reduction techniques. We show that all algorithms all enjoy an $\mathcal{O}(1/T)$ convergence rate to a stationary point of the reformulated minimax problem. Moreover, the fast convergence rates of GT-SRVR and GT-SRVRI imply $\mathcal{O}(\epsilon^{-2})$ communication complexity and $\mathcal{O}(m\sqrt{n}\epsilon^{-2})$ sample complexity, where $m$ is the number of agents and $n$ is the length of trajectories. To our knowledge, this paper is the first work that achieves both $\mathcal{O}(\epsilon^{-2})$ sample complexity and $\mathcal{O}(\epsilon^{-2})$ communication complexity in decentralized policy evaluation for cooperative MARL. Our extensive experiments also corroborate the theoretical performance of our proposed decentralized policy evaluation algorithms.