Adapting to Decision-Relevant Non-Stationarity in Decentralized Heterogeneous Bandits
TL;DR
This work introduces Decision-Relevant Fresh Comparison (DRFC), which uses new, balanced samples from all agents to compare arms at the network level and switches only when fresh global evidence indicates that the common best arm has changed, and proves a high-probability dynamic regret bound with no adaptation term depending on $\Stloc$.
Abstract
Decentralized bandit systems often contain heterogeneous agents: rewards can change at individual agents even when the best action for the network stays the same. These local changes may cancel when rewards are averaged across agents, so the number of local changes $\Stloc$ can be much larger than the number of changes in the best common arm $\Stdec$. We introduce Decision-Relevant Fresh Comparison (DRFC), which uses new, balanced samples from all agents to compare arms at the network level and switches only when fresh global evidence indicates that the common best arm has changed. We prove a high-probability dynamic regret bound with no adaptation term depending on $\Stloc$, and show that every algorithm must still pay for identifying genuine decision switches and propagating them through the communication graph. Under a distinct time-average benchmark, an anytime-valid sliding-window extension handles gradual drift; experiments on synthetic, semi-real, and MovieLens-1M replays show that DRFC ignores decision-irrelevant local changes while the extension avoids false switches.