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Network Markov Decision Processes (MDPs), which are the de-facto model for multi-agent control, pose a significant challenge to efficient learning caused by the exponential growth of the global state-action space with the number of agents. In this work, utilizing the exponential decay property of network dynamics, we first derive scalable spectral local representations for multiagent reinforcement learning in network MDPs, which induces a network linear subspace for the local $$Q$$-function of each agent. Building on these local spectral representations, we design a scalable algorithmic framework for multiagent reinforcement learning in continuous state-action network MDPs, and provide end-to-end guarantees for the convergence of our algorithm. Empirically, we validate the effectiveness of our scalable representation-based approach on two benchmark problems, and demonstrate the advantages of our approach over generic function approximation approaches to representing the local $$Q$$-functions. 

The problem of controller reduction has a rich history in control theory. Yet, many questions remain open. In particular, there exist very few results on the order reduction of general non-observer based controllers and the subsequent quantification of the closed-loop performance. Recent developments in model-free policy optimization for Linear Quadratic Gaussian (LQG) control have highlighted the importance of this question. In this paper, we first propose a new set of sufficient conditions ensuring that a perturbed controller remains internally stabilizing. Based on this result, we illustrate how to perform order reduction of general (non-observer based) output feedback controllers using balanced truncation and modal truncation. We also provide explicit bounds on the LQG performance of the reduced-order controller. Furthermore, for single-input-single-output (SISO) systems, we introduce a new controller reduction technique by truncating unstable modes. We illustrate our theoretical results with numerical simulations. Our results will serve as valuable tools to design direct policy search algorithms for control problems with partial observations. 

Abstract Current biotechnologies can simultaneously measure multiple high-dimensional modalities (e.g., RNA, DNA accessibility, and protein) from the same cells. A combination of different analytical tasks (e.g., multi-modal integration and cross-modal analysis) is required to comprehensively understand such data, inferring how gene regulation drives biological diversity and functions. However, current analytical methods are designed to perform a single task, only providing a partial picture of the multi-modal data. Here, we present UnitedNet, an explainable multi-task deep neural network capable of integrating different tasks to analyze single-cell multi-modality data. Applied to various multi-modality datasets (e.g., Patch-seq, multiome ATAC + gene expression, and spatial transcriptomics), UnitedNet demonstrates similar or better accuracy in multi-modal integration and cross-modal prediction compared with state-of-the-art methods. Moreover, by dissecting the trained UnitedNet with the explainable machine learning algorithm, we can directly quantify the relationship between gene expression and other modalities with cell-type specificity. UnitedNet is a comprehensive end-to-end framework that could be broadly applicable to single-cell multi-modality biology. This framework has the potential to facilitate the discovery of cell-type-specific regulation kinetics across transcriptomics and other modalities. 

We consider a class of multi-agent optimization problems, where each agent is associated with an action vector and a local cost that depends on the joint actions of all agents, and the goal is to minimize the average of the local costs. Such problems arise in many control applications such as wind farm operation and mobile sensor coverage. In many of these applications, while we have access to (zeroth-order) information about function values, it can be difficult to obtain (first-order) gradient information. In this paper, we propose a zeroth-order feedback optimization (ZFO) algorithm based on two-point gradient estimators for the considered class of problems, and provide the convergence rate to a first-order stationary point for nonconvex problems. We complement our theoretical analysis with numerical simulations on a wind farm power maximization problem.