OpenNovelty.org

Multi-Armed Bandits with Minimum Aggregated Revenue Constraints

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Multi-Armed Bandit with ConstraintsExploration-ExploitationRegretConstraint Violation
Abstract:

We examine a multi-armed bandit problem with contextual information, where the objective is to ensure that each arm receives a minimum aggregated reward across contexts while simultaneously maximizing the total cumulative reward. This framework captures a broad class of real-world applications where fair revenue allocation is critical and contextual variation is inherent. The cross-context aggregation of minimum reward constraints, while enabling better performance and easier feasibility, introduces significant technical challenges—particularly the absence of closed-form optimal allocations typically available in standard MAB settings. We design and analyze algorithms that either optimistically prioritize performance or pessimistically enforce constraint satisfaction. For each algorithm, we derive problem-dependent upper bounds on both regret and constraint violations. Furthermore, we establish a lower bound demonstrating that the dependence on the time horizon in our results is optimal in general and revealing fundamental limitations of the free exploration principle leveraged in prior work.

Disclaimer
This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper contributes algorithms and analysis for contextual multi-armed bandits with minimum aggregated revenue constraints per arm across contexts. It occupies a singleton leaf in the taxonomy ('Contextual Bandits with Aggregated Revenue Constraints'), indicating a relatively sparse research direction within the broader constrained bandits landscape. While the taxonomy contains twenty-seven papers across multiple branches—including knapsack constraints, conservative baselines, and federated settings—this specific combination of contextual aggregation and revenue guarantees appears underexplored, with no sibling papers sharing the exact problem formulation.

The taxonomy reveals neighboring work in closely related directions. The sibling leaf 'Multi-Armed Bandits with Guaranteed Revenue Per Arm' addresses revenue guarantees without contextual aggregation, while 'Conservative Bandits with Baseline Constraints' enforces uniform per-round safety rather than cumulative cross-context targets. Nearby branches include 'Bandits with Knapsacks' (focusing on resource consumption rather than revenue floors) and 'Contextual Bandits with Metric and Lipschitz Structure' (exploiting geometric properties without explicit constraints). The taxonomy's scope notes clarify that aggregated revenue constraints differ fundamentally from per-round baselines or knapsack budgets, positioning this work at the intersection of contextual learning and cumulative fairness.

Among thirty candidates examined via semantic search, none clearly refutes the paper's three main contributions. The first contribution (OLP and OPLP algorithms integrating linear programming with optimistic/pessimistic estimation) examined ten candidates with zero refutable overlaps. The second (refined sub-optimality gap notion and analytical techniques) and third (lower bound refuting free exploration in contextual settings) each examined ten candidates, also with zero refutations. This suggests that within the limited search scope, the algorithmic designs, analytical framework, and lower-bound results appear novel relative to the sampled prior work, though the search does not claim exhaustive coverage of all relevant literature.

Based on the limited search scope of thirty semantically similar papers, the work appears to occupy a relatively unexplored niche combining contextual structure with aggregated revenue constraints. The singleton taxonomy leaf and absence of refutable overlaps suggest novelty, though the analysis does not rule out relevant work outside the top-thirty semantic matches or in adjacent communities (e.g., operations research, fairness-aware learning). The taxonomy context indicates that while constrained bandits is an active area, this specific cross-context aggregation formulation has received less attention than knapsack or conservative baseline variants.

Taxonomy

Core-task Taxonomy Papers
27
3
Claimed Contributions
30
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: contextual multi-armed bandits with minimum aggregated revenue constraints. The field of constrained bandits has evolved to address settings where decision-makers must balance exploration and exploitation while satisfying resource or revenue guarantees. The taxonomy reveals several main branches: Constrained Bandits with Resource or Revenue Guarantees focuses on problems where arms must meet budget, cost, or revenue thresholds, often incorporating knapsack-like constraints (e.g., Linear Knapsacks[12]) or conservative baseline requirements (e.g., Conservative Bandits[15]); Contextual and Structured Bandits examines how side information and problem geometry—such as metric spaces (Metric Space Bandits[2]) or Lipschitz continuity (Lipschitz Bandits[3])—can improve learning; Federated and Distributed Bandits studies collaborative learning across agents or devices (Federated Linear Contextual[7], Distributed Exploration[9]); Best-Arm Identification and Pure Exploration targets fixed-confidence or fixed-budget scenarios (Best Arm Complexity[4]); Regret Bounds and Lower Bounds provides theoretical foundations; Application-Driven Bandit Problems connects theory to domains like auctions (Auctions Meet Bandits[18]) and e-commerce (Ecommerce Diversification[22]); and Specialized Bandit Structures covers niche settings such as combinatorial or preference-based feedback. Within the constrained bandits branch, a particularly active line of work addresses minimum revenue or performance guarantees, where the learner must ensure that cumulative rewards meet or exceed a threshold over time. Minimum Aggregated Revenue[0] sits squarely in this cluster, extending contextual bandits to enforce aggregated revenue constraints—a setting closely related to Guaranteed Revenue[1], which also tackles revenue floors, and to conservative approaches like Conservative Bandits[15] that require performance above a known baseline. Compared to works focusing on small per-round cost constraints (Small Cost Constraints[10]) or exposure fairness (Exposure Constraints[14]), Minimum Aggregated Revenue[0] emphasizes cumulative revenue targets in a contextual framework, blending the structural richness of Contextual Bandits[11] with the safety and feasibility concerns central to constrained optimization. This positioning highlights ongoing questions about how to efficiently explore while maintaining hard guarantees, and how contextual information can be leveraged to tighten regret bounds under such constraints.

Claimed Contributions

Two novel algorithms (OLP and OPLP) integrating linear programming with optimistic/pessimistic estimation

The authors propose two algorithms that combine linear programming with confidence-bound estimation to navigate the trade-off between performance and constraint satisfaction in contextual bandits with minimum aggregated revenue constraints. OLP achieves poly-logarithmic regret with O(√T) constraint violation, while OPLP achieves the inverse.

10 retrieved papers
Novel analytical techniques with refined sub-optimality gap notion

The authors develop new analytical methods that introduce a refined notion of sub-optimality gap leveraging the structure of the underlying linear program. This methodology quantifies the complexity of learning the optimal policy and extends naturally to MAB problems requiring global linear constraints.

10 retrieved papers
Lower bound establishing near-optimality and refuting free exploration in contextual setting

The authors prove a lower bound demonstrating that the √T dependence in their results is optimal and that the free exploration property from non-contextual settings no longer holds in the contextual case, reinstating the exploration-exploitation trade-off.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Within the taxonomy built over the current TopK core-task papers, the original paper is assigned to a leaf with no direct siblings and no cousin branches under the same grandparent topic. In this retrieved landscape, it appears structurally isolated, which is one partial signal of novelty, but still constrained by search coverage and taxonomy granularity.

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Two novel algorithms (OLP and OPLP) integrating linear programming with optimistic/pessimistic estimation

The authors propose two algorithms that combine linear programming with confidence-bound estimation to navigate the trade-off between performance and constraint satisfaction in contextual bandits with minimum aggregated revenue constraints. OLP achieves poly-logarithmic regret with O(√T) constraint violation, while OPLP achieves the inverse.

Contribution

Novel analytical techniques with refined sub-optimality gap notion

The authors develop new analytical methods that introduce a refined notion of sub-optimality gap leveraging the structure of the underlying linear program. This methodology quantifies the complexity of learning the optimal policy and extends naturally to MAB problems requiring global linear constraints.

Contribution

Lower bound establishing near-optimality and refuting free exploration in contextual setting

The authors prove a lower bound demonstrating that the √T dependence in their results is optimal and that the free exploration property from non-contextual settings no longer holds in the contextual case, reinstating the exploration-exploitation trade-off.

Table of Contents