Then OMAC (Algorithm 1) specifiedby Table 3 hasthe followingACEguarantee (withprobabilityatleast1 ): ACE 1 r W2+ o(T) T +O( log (NT / ) log (N) N ).

We present an online multi-task learning approach for adaptive nonlinear control, which we call Online Meta-Adaptive Control (OMAC). The goal is to control a nonlinear system subject to adversarial disturbance and unknown \emph{environment-dependent} nonlinear dynamics, under the assumption that the environment-dependent dynamics can be well captured with some shared representation. Our approach is motivated by robot control, where a robotic system encounters a sequence of new environmental conditions that it must quickly adapt to. A key emphasis is to integrate online representation learning with established methods from control theory, in order to arrive at a unified framework that yields both control-theoretic and learning-theoretic guarantees. We provide instantiations of our approach under varying conditions, leading to the first non-asymptotic end-to-end convergence guarantee for multi-task nonlinear control. OMAC can also be integrated with deep representation learning. Experiments show that OMAC significantly outperforms conventional adaptive control approaches which do not learn the shared representation, in inverted pendulum and 6-DoF drone control tasks under varying wind conditions.

The goal is to control a nonlinear system subject to adversarial disturbance and unknown environment-dependent nonlinear dynamics, under the assumption that the environment-dependent dynamics can be well captured with some shared representation. Our approach is motivated by robot control, where a robotic system encounters a sequence of new environmental conditions that it must quickly adapt to.

Agents powered by advanced large language models (LLMs) have demonstrated impressive capabilities across diverse complex applications. Recently, Multi-Agent Systems (MAS), wherein multiple agents collaborate and communicate with each other, have exhibited enhanced capabilities in complex tasks, such as high-quality code generation and arithmetic reasoning. However, the development of such systems often relies on handcrafted methods, and the literature on systematic design and optimization of LLM-based MAS remains limited. In this work, we introduce OMAC, a general framework designed for holistic optimization of LLM-based MAS. Specifically, we identify five key optimization dimensions for MAS, encompassing both agent functionality and collaboration structure. Building upon these dimensions, we first propose a general algorithm, utilizing two actors termed the Semantic Initializer and the Contrastive Comparator, to optimize any single dimension. Then, we present an algorithm for joint optimization across multiple dimensions. Extensive experiments demonstrate the superior performance of OMAC on code generation, arithmetic reasoning, and general reasoning tasks against state-of-the-art approaches.

We present an online multi-task learning approach for adaptive nonlinear control, which we call Online Meta-Adaptive Control (OMAC). The goal is to control a nonlinear system subject to adversarial disturbance and unknown \emph{environment-dependent} nonlinear dynamics, under the assumption that the environment-dependent dynamics can be well captured with some shared representation. Our approach is motivated by robot control, where a robotic system encounters a sequence of new environmental conditions that it must quickly adapt to. A key emphasis is to integrate online representation learning with established methods from control theory, in order to arrive at a unified framework that yields both control-theoretic and learning-theoretic guarantees. We provide instantiations of our approach under varying conditions, leading to the first non-asymptotic end-to-end convergence guarantee for multi-task nonlinear control.

Offline reinforcement learning (RL) that learns policies from offline datasets without environment interaction has received considerable attention in recent years. Compared with the rich literature in the single-agent case, offline multi-agent RL is still a relatively underexplored area. Most existing methods directly apply offline RL ingredients in the multi-agent setting without fully leveraging the decomposable problem structure, leading to less satisfactory performance in complex tasks. We present OMAC, a new offline multi-agent RL algorithm with coupled value factorization. OMAC adopts a coupled value factorization scheme that decomposes the global value function into local and shared components, and also maintains the credit assignment consistency between the state-value and Q-value functions. Moreover, OMAC performs in-sample learning on the decomposed local state-value functions, which implicitly conducts max-Q operation at the local level while avoiding distributional shift caused by evaluating out-of-distribution actions. Based on the comprehensive evaluations of the offline multi-agent StarCraft II micro-management tasks, we demonstrate the superior performance of OMAC over the state-of-the-art offline multi-agent RL methods.

We present an online multi-task learning approach for adaptive nonlinear control, which we call Online Meta-Adaptive Control (OMAC). The goal is to control a nonlinear system subject to adversarial disturbance and unknown $\textit{environment-dependent}$ nonlinear dynamics, under the assumption that the environment-dependent dynamics can be well captured with some shared representation. Our approach is motivated by robot control, where a robotic system encounters a sequence of new environmental conditions that it must quickly adapt to. A key emphasis is to integrate online representation learning with established methods from control theory, in order to arrive at a unified framework that yields both control-theoretic and learning-theoretic guarantees. We provide instantiations of our approach under varying conditions, leading to the first non-asymptotic end-to-end convergence guarantee for multi-task adaptive nonlinear control. OMAC can also be integrated with deep representation learning. Experiments show that OMAC significantly outperforms conventional adaptive control approaches which do not learn the shared representation.