# On Distributed Multi-player Multiarmed Bandit Problems in Abruptly Changing Environment

## TL;DR

This paper addresses the challenge of multi-player multi-armed bandit problems in environments that change abruptly, proposing new algorithms that achieve sublinear regret growth over time.

## Contribution

The paper introduces two novel algorithms, RR-SW-UCB# and SW-DLP, with rigorous analysis showing they attain sublinear regret in abruptly changing environments.

## Key findings

- Expected cumulative group regret is upper bounded by sublinear functions of time.
- Algorithms' time average regret asymptotically converges to zero.
- Numerical results support the theoretical analysis.

## Abstract

We study the multi-player stochastic multiarmed bandit (MAB) problem in an abruptly changing environment. We consider a collision model in which a player receives reward at an arm if it is the only player to select the arm. We design two novel algorithms, namely, Round-Robin Sliding-Window Upper Confidence Bound\# (RR-SW-UCB\#), and the Sliding-Window Distributed Learning with Prioritization (SW-DLP). We rigorously analyze these algorithms and show that the expected cumulative group regret for these algorithms is upper bounded by sublinear functions of time, i.e., the time average of the regret asymptotically converges to zero. We complement our analytic results with numerical illustrations.