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Towards Safe and Optimal Online Bidding: A Modular Look-ahead Lyapunov Framework

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
online biddingbudget constraintsROI constraintsLyapunov optimization
Abstract:

This paper studies online bidding subject to simultaneous budget and return-on-investment (ROI) constraints, which encodes the goal of balancing high volume and profitability. We formulate the problem as a general constrained online learning problem that can be applied to diverse bidding settings (e.g., first-price or second-price auctions) and feedback regimes (e.g., full or partial information), among others. We introduce L2FOB, a Look-ahead Lyapunov Framework for Online Bidding with strong empirical and theoretical performance. By combining optimistic reward and pessimistic cost estimation with the look-ahead virtual queue mechanism, L2FOB delivers safe and optimal bidding decisions. We provide adaptive guarantees: L2FOB achieves O(E_r(T,p)+(ν∗/ρ)E_c(T,p))O (\mathcal{E}\_r(T,p)+(\nu^* / \rho) \mathcal{E}\_c(T,p)) regret and O(E_r(T,p)+E_c(T,p))O (\mathcal{E}\_r(T,p)+\mathcal{E}\_c(T,p)) anytime ROI constraint violation, where Er(T,p)\mathcal{E}_r(T,p) and Ec(T,p)\mathcal{E}_c(T,p) are cumulative estimation errors over TT rounds, ρ\rho is the average per-round budget, and ν∗\nu^* is the offline optimal average reward. We instantiate L2FOB in several online bidding settings, demonstrating guarantees that match or improve upon the best-known results. These results are derived from the novel look-ahead design and Lyapunov stability analysis. Numerical experiments further validate our theoretical guarantees.

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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.
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Overview

Overall Novelty Assessment

The paper proposes L2FOB, a look-ahead Lyapunov framework for online bidding under simultaneous budget and ROI constraints. According to the taxonomy, it resides in the 'Single-Advertiser Online Learning with Budget and ROI Constraints' leaf, which contains five papers total. This leaf is part of the 'Algorithmic Frameworks for Constrained Online Bidding' branch, indicating a moderately populated research direction focused on regret-minimization algorithms for constrained advertisers. The taxonomy shows this is an active area with established foundational work and ongoing refinements.

The taxonomy structure reveals several neighboring research directions. The sibling category 'Safe and Robust Constraint Satisfaction' (two papers) addresses high-probability constraint guarantees, while 'Return-on-Spend Constrained Bidding' (three papers) focuses on settings without known impression values. The 'Reinforcement Learning for Real-Time Bidding' leaf (three papers) applies RL techniques to similar objectives but in dynamic auction environments. The paper's approach using Lyapunov drift and optimistic-pessimistic estimation positions it at the intersection of online learning and safe constraint handling, bridging algorithmic frameworks with robust satisfaction concerns.

Among twenty candidates examined, the unified problem formulation contribution found one refutable candidate among eight examined, and the adaptive guarantees contribution found one refutable candidate among seven examined. The L2FOB framework itself showed no refutable candidates among five examined, suggesting relative novelty in its specific look-ahead mechanism design. The statistics indicate that while the core algorithmic framework may have some overlap with existing formulations, the specific combination of optimistic rewards, pessimistic costs, and look-ahead virtual queues appears less directly anticipated in the limited search scope.

Based on the top-twenty semantic matches examined, the work appears to offer meaningful contributions within an established research direction. The analysis covers a focused slice of the literature rather than an exhaustive survey, so the novelty assessment reflects positioning among closely related papers. The taxonomy context suggests the paper advances a moderately crowded subfield where incremental algorithmic improvements and tighter theoretical guarantees constitute valuable progress.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
20
Contribution Candidate Papers Compared
2
Refutable Paper

Research Landscape Overview

Core task: online bidding under budget and return-on-investment constraints. The field addresses how advertisers can optimize their bids in dynamic auction environments while respecting hard budget limits and maintaining target ROI thresholds. The taxonomy organizes research into five main branches. Algorithmic Frameworks for Constrained Online Bidding develops learning algorithms and regret bounds for single or multiple advertisers facing budget and ROI constraints, often drawing on online convex optimization and Lyapunov techniques. Auction Mechanism Design for Constrained Bidders studies how platforms can design truthful or efficient mechanisms when bidders have such constraints, exploring pricing rules and allocation schemes. Real-Time Bidding Systems and Practical Implementations focuses on deployed systems, pacing strategies, and reinforcement learning methods tailored to display advertising. Advanced Bidding Strategies and Specialized Settings examines extensions such as multi-channel campaigns, non-stationary environments, and privacy-preserving approaches. Related Auction and Incentive Mechanisms covers broader auction theory and crowdsourcing incentives that inform constrained bidding design. A particularly active line of work within Algorithmic Frameworks centers on single-advertiser online learning with both budget and ROI constraints, where the main challenge is balancing exploration and constraint satisfaction over time. Early contributions like Online ROI Bidding[1] established foundational regret guarantees, while more recent efforts such as No-Regret Budget ROI[3] and Budget ROI Learning[9] refine these bounds under various feedback models. Safe Lookahead Lyapunov[0] sits squarely in this cluster, emphasizing safe constraint handling via Lyapunov drift analysis and lookahead techniques to ensure feasibility even under adversarial arrivals. Compared to Weak Adaptivity Learning[2], which explores limited feedback settings, Safe Lookahead Lyapunov[0] focuses more directly on proactive constraint management. Meanwhile, works like Autobidding Budget ROI[6] and Multi-channel Autobidding[5] extend these ideas to multi-agent or multi-channel scenarios, highlighting ongoing questions about scalability, non-stationarity, and the interplay between platform mechanisms and advertiser algorithms.

Claimed Contributions

L2FOB: Look-ahead Lyapunov Framework for Online Bidding

The authors propose L2FOB, a modular algorithmic framework that combines optimistic reward and pessimistic cost estimation with a look-ahead virtual queue mechanism to deliver safe and optimal bidding decisions under budget and ROI constraints. The framework uses convex potential functions and potential-shaped multipliers to provide flexible violation control.

5 retrieved papers
Unified problem formulation for constrained online bidding

The authors present a unified formulation of online bidding as a general constrained online learning problem where reward and cost are treated as general functions of context and bid. This formulation applies to different auction models and feedback regimes by leveraging general online regression oracles.

8 retrieved papers
Can Refute
Adaptive theoretical guarantees without Slater's condition

The authors establish adaptive regret and violation bounds that scale with cumulative estimation errors and do not require Slater's condition (existence of a strictly feasible policy). The guarantees are anytime, meaning they hold over the entire time horizon, and account for hard stopping due to budget constraints.

7 retrieved papers
Can Refute

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

L2FOB: Look-ahead Lyapunov Framework for Online Bidding

The authors propose L2FOB, a modular algorithmic framework that combines optimistic reward and pessimistic cost estimation with a look-ahead virtual queue mechanism to deliver safe and optimal bidding decisions under budget and ROI constraints. The framework uses convex potential functions and potential-shaped multipliers to provide flexible violation control.

Contribution

Unified problem formulation for constrained online bidding

The authors present a unified formulation of online bidding as a general constrained online learning problem where reward and cost are treated as general functions of context and bid. This formulation applies to different auction models and feedback regimes by leveraging general online regression oracles.

Contribution

Adaptive theoretical guarantees without Slater's condition

The authors establish adaptive regret and violation bounds that scale with cumulative estimation errors and do not require Slater's condition (existence of a strictly feasible policy). The guarantees are anytime, meaning they hold over the entire time horizon, and account for hard stopping due to budget constraints.

Table of Contents

Towards Safe and Optimal Online Bidding: A Modular Look-ahead Lyapunov Framework | Novelty Validation