We present the problem of conservative distributed multi-task learning in
stochastic linear contextual bandits with heterogeneous agents. This extends
conservative linear bandits to a distributed setting where M agents tackle
different but related tasks while adhering to stage-wise performance
constraints. The exact context is unknown, and only a context distribution is
available to the agents as in many practical applications that involve a
prediction mechanism to infer context, such as stock market prediction and
weather forecast. We propose a distributed upper confidence bound (UCB)
algorithm, DiSC-UCB. Our algorithm constructs a pruned action set during each
round to ensure the constraints are met. Additionally, it includes synchronized
sharing of estimates among agents via a central server using well-structured
synchronization steps. We prove the regret and communication bounds on the
algorithm. We extend the problem to a setting where the agents are unaware of
the baseline reward. For this setting, we provide a modified algorithm,
DiSC-UCB2, and we show that the modified algorithm achieves the same regret and
communication bounds. We empirically validated the performance of our algorithm
on synthetic data and real-world Movielens-100K data.

我们研究了具有异质代理的随机线性情境赌博机的保守式分布式多任务学习问题，提出了一种名为 DiSC-UCB 的分布式上置信界算法，并证明了该算法的遗憾和通信界限。此外，我们还将问题扩展到代理人不知道基准奖励的情况，并通过修改算法 DiSC-UCB2 来实现相同的遗憾和通信界限，我们通过合成数据和真实世界 Movielens-100K 数据对算法的性能进行了实证验证。

分布式多任务学习：面向随机赌博机的背景分布与阶段约束

Distributed Multi-Task Learning for Stochastic Bandits with Context  Distribution and Stage-wise Constraints

We consider the problem of distributed multi-task learning, where each
machine learns a separate, but related, task. Specifically, each machine learns
a linear predictor in high-dimensional space,where all tasks share the same
small support. We present a communication-efficient estimator based on the
debiased lasso and show that it is comparable with the optimal centralized
method.

本研究关注分布式多任务学习问题，提出了一种基于 debaised lasso 的通信高效估计方法，能够在高维空间中学习线性预测器，并与最佳集中式方法相媲美。