Stochastic Resource Allocation in Dynamic Environments: Non-Stationary Bandits and Knapsack Constraints

Abstract

Stochastic resource allocation is a critical area of study in operations research and decision-making, particularly in dynamic environments characterized by uncertainty and changing conditions. This paper explores the complexities associated with non-stationary bandit problems and knapsack constraints, providing a comprehensive review of current methodologies, challenges, and potential solutions. We begin by outlining the theoretical foundations of non-stationary bandits, highlighting their significance in real-world applications such as online advertising, healthcare resource management, and adaptive learning systems. Subsequently, we delve into knapsack constraints, discussing their implications for resource allocation strategies. We propose a framework that integrates non-stationary bandit strategies with knapsack problem formulations, demonstrating how this approach can enhance decision-making in dynamic contexts. Through empirical analysis and simulations, we illustrate the effectiveness of our proposed framework, offering insights into its practical applications. The paper concludes with a discussion on future research directions and the importance of adaptive strategies in stochastic resource allocation.