Online Clustering of Dueling Bandits

The contextual multi-armed bandit (MAB) is a widely used framework for problems requiring sequential decision-making under uncertainty, such as recommendation systems. In applications involving a large number of users, the performance of contextual MAB can be significantly improved by facilitating collaboration among multiple users. This has been achieved by the clustering of bandits (CB) methods, which adaptively group the users into different clusters and achieve collaboration by allowing the users in the same cluster to share data. However, classical CB algorithms typically rely on numerical reward feedback, which may not be practical in certain real-world applications. For instance, in recommendation systems, it is more realistic and reliable to solicit preference feedback between pairs of recommended items rather than absolute rewards. To address this limitation, we introduce the first "clustering of dueling bandit algorithms" to enable collaborative decision-making based on preference feedback. We propose two novel algorithms: (1) Clustering of Linear Dueling Bandits (COLDB) which models the user reward functions as linear functions of the context vectors, and (2) Clustering of Neural Dueling Bandits (CONDB) which uses a neural network to model complex, non-linear user reward functions. Both algorithms are supported by rigorous theoretical analyses, demonstrating that user collaboration leads to improved regret bounds. Extensive empirical evaluations on synthetic and real-world datasets further validate the effectiveness of our methods, establishing their potential in real-world applications involving multiple users with preference-based feedback.

Meta-Prompt Optimization for LLM-Based Sequential Decision Making

Large language models (LLMs) have recently been employed as agents to solve sequential decision-making tasks such as Bayesian optimization and multi-armed bandits (MAB). These works usually adopt an LLM for sequential action selection by providing it with a fixed, manually designed meta-prompt. However, numerous previous works have found that the prompt has a significant impact on the performance of the LLM, which calls for a method to automatically optimize the meta-prompt for LLM-based agents. Unfortunately, the non-stationarity in the reward observations during LLM-based sequential decision-making makes meta-prompt optimization highly challenging. To address this challenge, we draw inspirations from adversarial bandit algorithms, which are inherently capable of handling non-stationary reward observations. Building on this foundation, we propose our EXPonential-weight algorithm for prompt Optimization} (EXPO) to automatically optimize the task description and meta-instruction in the meta-prompt for LLM-based agents. We also extend EXPO to additionally optimize the exemplars (i.e., history of interactions) in the meta-prompt to further enhance the performance, hence introducing our EXPO-ES algorithm. We use extensive experiments to show that our algorithms significantly improve the performance of LLM-based sequential decision-making.