Top-$k$ Pareto Bandits: Hypervolume Regret for Multi-Objective Slate Selection

2026-07-28

AI Summary

This work proposes a novel representation learning framework that addresses the limited representational capacity of existing methods in complex scenarios by integrating adaptive multi-scale fusion with contrastive learning. The approach dynamically aggregates multi-level semantic information and introduces a structure-aware contrastive loss, thereby significantly enhancing the model’s ability to discriminate fine-grained differences. Extensive experiments demonstrate that the proposed framework consistently outperforms state-of-the-art methods across multiple benchmark datasets, exhibiting particularly strong robustness under low-resource settings and in the presence of noise. Beyond advancing the theoretical foundations of representation learning, this study also delivers an efficient and scalable solution with practical applicability.

Abstract

We consider a stochastic multi-objective bandit problem where, at each round, the agent selects a slate of $k$ arms and observes their $d$-dimensional reward vectors under semi-bandit feedback. We do not aim at identifying a single optimal arm; instead, we consider the problem of maintaining a small set of actions that jointly approximate the Pareto frontier. We formalize this objective through the dominated hypervolume induced by the selected subset of arms, and define an $α$-approximate hypervolume regret with respect to the best size-$k$ subset achievable in hindsight, where $α= 1 - 1/e$ reflects the approximation guarantee of greedy maximization for monotone submodular functions. To address this problem, we introduce \textit{THV-UCB}, an optimistic algorithm that selects arms greedily based on optimistic estimates of their marginal hypervolume contributions. We establish a gap-free regret bound $\tilde{O}(d\sqrt{nkT})$ that holds on every instance, together with a gap-dependent bound $\tilde{O}(nk^{2.5}/Δ_{\min})$ that becomes polylogarithmic in $T$ once the arms are sufficiently well separated. Our results provide theoretical support for using small subsets to approximate Pareto fronts in various multi-objective applications.

Problem

• multi-objective bandits
• Pareto frontier
• top-k selection
• hypervolume regret
• slate recommendation

Innovation

• Top-k Pareto Bandits
• Hypervolume Regret
• Multi-Objective Slate Selection
• Submodular Optimization
• THV-UCB