Flickering Multi-Armed Bandits

TL;DR

This paper introduces Flickering Multi-Armed Bandits (FMAB), modeling decision-making with changing action availability constrained by local neighborhoods, and provides algorithms with regret bounds for such environments.

Contribution

It formalizes FMAB with stochastic graph models, proposes a lazy random walk exploration algorithm, and establishes regret bounds and lower bounds for learning costs under local constraints.

Findings

Proposed a two-phase lazy random walk algorithm for FMAB.

Established high-probability sublinear regret bounds.

Proved near-optimality via information-theoretic lower bounds.

Abstract

We introduce Flickering Multi-Armed Bandits (FMAB) to model sequential decision-making in environments with changing action availability, where accessibility of the next action is restricted to a subset dependent on the agent's current choice. We formalize these constraints through stochastically evolving graphs where actions are limited to local neighborhoods. This mobility-constrained structure imposes a dual challenge: the statistical requirement of information acquisition and the physical overhead of navigation. We analyze FMAB under i.i.d. Erd\H{o}s--R'enyi and Edge-Markovian process, proposing a two-phase lazy random walk algorithm for robust exploration. We establish high-probability sublinear regret bounds and prove near-optimality via a matching information-theoretic lower bound. Our results characterize the intrinsic cost of learning under local-move constraints, complemented by a robotic disaster-response simulation.