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Linear contextual bandit is a popular online learning problem. It has been mostly studied in centralized learning settings. With the surging demand of large-scale decentralized model learning, e.g., federated learning, how to retain regret minimization while reducing communication cost becomes an open challenge. In this paper, we study linear contextual bandit in a federated learning setting. We propose a general framework with asynchronous model update and communication for a collection of homogeneous clients and heterogeneous clients, respectively. Rigorous theoretical analysis is provided about the regret and communication cost under this distributed learning framework; and extensive empirical evaluations demonstrate the effectiveness of our solution. 

Traditionally, Bayesian network structure learning is often carried out at a central site, in which all data is gathered. However, in practice, data may be distributed across different parties (e.g., companies, devices) who intend to collectively learn a Bayesian network, but are not willing to disclose information related to their data owing to privacy or security concerns. In this work, we present a federated learning approach to estimate the structure of Bayesian network from data that is horizontally partitioned across different parties. We develop a distributed structure learning method based on continuous optimization, using the alternating direction method of multipliers (ADMM), such that only the model parameters have to be exchanged during the optimization process. We demonstrate the flexibility of our approach by adopting it for both linear and nonlinear cases. Experimental results on synthetic and real datasets show that it achieves an improved performance over the other methods, especially when there is a relatively large number of clients and each has a limited sample size. 

Recently, structure learning of directed acyclic graphs (DAGs) has been formulated as a continuous optimization problem by leveraging an algebraic characterization of acyclicity. The constrained problem is solved using the augmented Lagrangian method (ALM) which is often preferred to the quadratic penalty method (QPM) by virtue of its standard convergence result that does not require the penalty coefficient to go to infinity, hence avoiding ill-conditioning. However, the convergence properties of these methods for structure learning, including whether they are guaranteed to return a DAG solution, remain unclear, which might limit their practical applications. In this work, we examine the convergence of ALM and QPM for structure learning in the linear, nonlinear, and confounded cases. We show that the standard convergence result of ALM does not hold in these settings, and demonstrate empirically that its behavior is akin to that of the QPM which is prone to ill-conditioning. We further establish the convergence guarantee of QPM to a DAG solution, under mild conditions. Lastly, we connect our theoretical results with existing approaches to help resolve the convergence issue, and verify our findings in light of an empirical comparison of them. 

Bayesian Networks are useful for analyzing the properties of systems with large populations of interacting agents (e.g., in social modeling applications and distributed service applications). These networks typically have large functions (CPTs), making exact inference intractable. However, often these models have additive symmetry. In this paper we show how summation-based CPTs, especially in the presence of symmetry, can be computed efficiently through the usage of the Fast Fourier Transform (FFT). In particular, we propose an efficient method using the FFT for reducing the size of Conditional Probability Tables (CPTs) in Bayesian Networks with summation-based causal independence (CI). We show how to apply it directly towards the acceleration of Bucket Elimination, and we subsequently provide experimental results demonstrating the computational speedup provided by our method.