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