Regret Analysis of Sleeping Competing Bandits

2026-03-20

AI Summary

This work addresses the limitation of classical competitive multi-armed bandit models, which fail to capture the realistic scenario where agents and arms may become arbitrarily unavailable over time. To this end, we formally introduce the Dormant Competitive Multi-Armed Bandit model, which incorporates intermittent availability and extends the definition of regret accordingly. Leveraging tools from online learning and stable matching theory, we propose a novel algorithm that achieves stable matching under dynamic availability constraints. Our theoretical analysis shows that the algorithm is asymptotically optimal when the number of arms $K$ greatly exceeds the number of agents $N$, with an upper regret bound of $O(NK \log T_i / \Delta^2)$ and a matching lower bound of $\Omega(N(K - N + 1) \log T_i / \Delta^2)$.

Technology Category

• Machine Learning: Online Learning & Bandits
• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The Competing Bandits framework is a recently emerging area that integrates multi-armed bandits in online learning with stable matching in game theory. While conventional models assume that all players and arms are constantly available, in real-world problems, their availability can vary arbitrarily over time. In this paper, we formulate this setting as Sleeping Competing Bandits. To analyze this problem, we naturally extend the regret definition used in existing competing bandits and derive regret bounds for the proposed model. We propose an algorithm that simultaneously achieves an asymptotic regret bound of $\mathrm{O}\left(NK\log T_{i}/Δ^2\right)$ under reasonable assumptions, where $N$ is the number of players, $K$ is the number of arms, $T_{i}$ is the number of rounds of each player $p_i$, and $Δ$ is the minimum reward gap. We also provide a regret lower bound of $\mathrmΩ\left( N(K-N+1)\log T_{i}/Δ^2 \right)$ under the same assumptions. This implies that our algorithm is asymptotically optimal in the regime where the number of arms $K$ is relatively larger than the number of players $N$.

Problem

• Sleeping Competing Bandits
• multi-armed bandits
• stable matching
• online learning
• regret analysis

Innovation

• Sleeping Competing Bandits
• regret analysis
• asymptotic optimality
• online learning
• stable matching