Distributed Stochastic Bandit Learning with Context Distributions
- URL: http://arxiv.org/abs/2207.14391v1
- Date: Thu, 28 Jul 2022 22:00:11 GMT
- Title: Distributed Stochastic Bandit Learning with Context Distributions
- Authors: Jiabin Lin and Shana Moothedath
- Abstract summary: We study the problem of distributed multi-arm contextual bandit with unknown contexts.
In our model, an adversary chooses a distribution on the set of possible contexts and the agents observe only the context distribution and the exact context is unknown to the agents.
Our goal is to develop a distributed algorithm that selects a sequence of optimal actions to maximize the cumulative reward.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study the problem of distributed stochastic multi-arm contextual bandit
with unknown contexts, in which M agents work collaboratively to choose optimal
actions under the coordination of a central server in order to minimize the
total regret. In our model, an adversary chooses a distribution on the set of
possible contexts and the agents observe only the context distribution and the
exact context is unknown to the agents. Such a situation arises, for instance,
when the context itself is a noisy measurement or based on a prediction
mechanism as in weather forecasting or stock market prediction. Our goal is to
develop a distributed algorithm that selects a sequence of optimal actions to
maximize the cumulative reward. By performing a feature vector transformation
and by leveraging the UCB algorithm, we propose a UCB algorithm for stochastic
bandits with context distribution and prove that our algorithm achieves a
regret and communications bounds of $O(d\sqrt{MT}log^2T)$ and $O(M^{1.5}d^3)$,
respectively, for linearly parametrized reward functions. We also consider a
case where the agents observe the actual context after choosing the action. For
this setting we presented a modified algorithm that utilizes the additional
information to achieve a tighter regret bound. Finally, we validated the
performance of our algorithms and compared it with other baseline approaches
using extensive simulations on synthetic data and on the real world movielens
dataset.
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