We study the performance of the gradient play algorithm for multi-agent tabular Markov decision processes (MDPs), which are also known as stochastic games (SGs), where each agent tries to maximize its own total discounted reward by making decisions independently based on current state information which is shared between agents. Policies are directly parameterized by the probability of choosing a certain action at a given state. We show that Nash equilibria (NEs) and first order stationary policies are equivalent in this setting, and give a non-asymptotic global convergence rate analysis to an -NE for a subclass of multi-agent MDPs called Markov potential games, which includes the cooperative setting with identical rewards among agents as an important special case. Our result shows that the number of iterations to reach an -NE scales linearly, instead of exponentially, with the number of agents. Local geometry and local stability are also considered. For Markov potential games, we prove that strict NEs are local maxima of the total potential function and fully-mixed NEs are saddle points. We also give a local convergence rate around strict NEs for more general settings.Preprint. Under review.

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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.

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