This paper investigates decentralized multitask learning over networks when the underlying task relationships are unknown. While existing graph-regularized multitask frameworks typically assume a known structure, practical settings often require learning inter-task dependencies directly from distributed data. We propose a decentralized two-phase strategy that first estimates a generalized graph Laplacian from noisy non-cooperative stochastic gradient iterates, and subsequently exploits the learned graph to enable cooperative multitask diffusion learning. This framework is motivated by a Gaussian Markov random field prior, which gives rise to a decentralized maximum likelihood estimator for the graph Laplacian. The analysis quantifies the Laplacian estimation error and its propagation to the steady-state performance of the multitask diffusion recursion, and introduces a topology sensitivity index to capture the effect of network heterogeneity. Simulation results corroborate the theoretical findings and demonstrate that cooperation enabled by the learned task graph significantly improves performance over non-cooperative learning, while approaching the true-graph baseline when the estimation stepsize is sufficiently small.
Most existing multitask learning approaches are limited by their reliance on task-specific loss functions tailored to the scale and type of each outcome. When outcomes differ across tasks, these losses are generally not directly comparable, which makes it difficult to formulate a unified objective and may limit information sharing across tasks. We propose a multitask transformation framework in which task-specific responses may differ through unknown monotone transformations. Motivated by high-dimensional biological applications in which the predictor dimension may diverge with the sample size while only a common subset of predictors is informative, we consider shared sparsity across tasks. Under this framework, we estimate the target functions and identify important predictors by optimizing a smoothed rank-based criterion with a group-Lasso penalty, implemented through a multitask deep neural network with a shared first layer. We establish the nonasymptotic excess-risk bounds, and variable-selection consistency for the proposed estimator. Simulation studies show that the proposed method achieves competitive prediction and variable-selection performance compared with competing approaches. Analyses of gene-expression studies with continuous, binary, and mixed outcomes further illustrate that the proposed method improves prediction and identifies biologically meaningful shared predictors.