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Multi-user environments present significant challenges in coordinating diverse preferences and resolving conflicts around shared resources. Current systems use a single-agent approach that struggles to balance individual needs with collective objectives. We introduce MALLM, a novel framework that deploys personalized LLM-based agents for each user on edge devices. MALLM integrates multi-sensor data fusion with a structured multi-agent decision-making mechanism, processing all data locally for enhanced privacy. Our edge-computing architecture enables real-time deliberation through evidence-based argumentation and consensus formation algorithms. The system continuously refines user profiles through sensor data while managing computational resources e!ciently. We evaluate MALLM through two case studies-health monitoring and personalized comfort management- demonstrating improved conflict resolution and resource e!ciency compared to conventional approaches. Our results show that MALLM e''ectively balances competing user priorities while preserving privacy in complex shared environments. 

We study a variant of online optimization in which the learner receives k-rounddelayed feedback about hitting cost and there is a multi-step nonlinear switching cost, i.e., costs depend on multiple previous actions in a nonlinear manner. Our main result shows that a novel Iterative Regularized Online Balanced Descent (iROBD) algorithm has a constant, dimension-free competitive ratio that is $O(L^2k )$, where L is the Lipschitz constant of the switching cost. Additionally, we provide lower bounds that illustrate the Lipschitz condition is required and the dependencies on k and L are tight. Finally, via reductions, we show that this setting is closely related to online control problems with delay, nonlinear dynamics, and adversarial disturbances, where iROBD directly offers constant-competitive online policies.