L-Lipschitz continuous gradient, if there exists a constant L > 0, such that null f (x) f (y)null Lnull x y null, x,y. If f is m-strongly convex and has an L-Lipschitz continuous gradient, then it is obvious that m L. Let λ be the Lagrange multiplier. Using Jensen's inequality, we have r We next prove the convergence of the algorithm with the proposed weight assignment rule. An edge between two agents means they are neighbors. This is to model the realistic scenario in which some of the agents may have less data samples and they may learn slowly than others.

We also characterize the lower and upper bounds of the predictive variance.

Decentralized cooperative multi-agent multi-armed bandits (DeCMA2B) considers how multiple agents collaborate in a decentralized multi-armed bandit setting. Though this problem has been extensively studied in previous work, most existing methods remain susceptible to various adversarial attacks. In this paper, we first study DeCMA2B with adversarial corruption, where an adversary can corrupt reward observations of all agents with a limited corruption budget. We propose a robust algorithm, called DeMABAR, which ensures that each agent's individual regret suffers only an additive term proportional to the corruption budget. Then we consider a more realistic scenario where the adversary can only attack a small number of agents. Our theoretical analysis shows that the DeMABAR algorithm can also almost completely eliminate the influence of adversarial attacks and is inherently robust in the Byzantine setting, where an unknown fraction of the agents can be Byzantine, i.e., may arbitrarily select arms and communicate wrong information. We also conduct numerical experiments to illustrate the robustness and effectiveness of the proposed method.

L-Lipschitz continuous gradient, if there exists a constant L > 0, such that null f (x) f (y)null Lnull x y null, x,y. If f is m-strongly convex and has an L-Lipschitz continuous gradient, then it is obvious that m L. Let λ be the Lagrange multiplier. Using Jensen's inequality, we have r We next prove the convergence of the algorithm with the proposed weight assignment rule. An edge between two agents means they are neighbors. This is to model the realistic scenario in which some of the agents may have less data samples and they may learn slowly than others.

However, distributed algorithms for learning relatedness among tasks are not resilient in the presence of Byzantine agents. In this paper, we present an approach for Byzantine resilient distributed multi-task learning. We propose an efficient online weight assignment rule by measuring the accumulated loss using an agent's data and its neighbors' models. A small accumulated loss indicates a large similarity between the two tasks.

We also characterize the lower and upper bounds of the predictive variance.

Collaboration among multiple large language model (LLM) agents is a promising approach to overcome inherent limitations of single-agent systems, such as hallucinations and single points of failure. As LLM agents are increasingly deployed on open blockchain platforms, multi-agent systems capable of tolerating malicious (Byzantine) agents have become essential. Recent Byzantine-robust multi-agent systems typically rely on leader-driven coordination, which suffers from two major drawbacks. First, they are inherently vulnerable to targeted attacks against the leader. If consecutive leaders behave maliciously, the system repeatedly fails to achieve consensus, forcing new consensus rounds, which is particularly costly given the high latency of LLM invocations. Second, an underperforming proposal from the leader can be accepted as the final answer even when higher-quality alternatives are available, as existing methods finalize the leader's proposal once it receives a quorum of votes. To address these issues, we propose DecentLLMs, a novel decentralized consensus approach for multi-agent LLM systems, where worker agents generate answers concurrently and evaluator agents independently score and rank these answers to select the best available one. This decentralized architecture enables faster consensus despite the presence of Byzantine agents and consistently selects higher-quality answers through Byzantine-robust aggregation techniques. Experimental results demonstrate that DecentLLMs effectively tolerates Byzantine agents and significantly improves the quality of selected answers.