[论文解读] Robust Temporal Guarantees in Budgeted Sequential Auctions

Giannis Fikioris, Robert Kleinberg+3 more|arXiv (Cornell University)|Feb 20, 2026

Advanced Bandit Algorithms Research被引用 0

一句话总结

一个简单的基于原始学习的预算序列拍卖算法提供鲁棒的保证：拥有ρ分预算的出价方在对手对抗下大致赢得ρT轮，在自对弈中实现近似相等、低时序偏差的胜出分布。

ABSTRACT

In modern advertising platforms, learning algorithms are deployed by budget-constrained bidders to maximize their accumulated value. These algorithms often offer classical utility guarantees like no-regret, i.e., the agent's utility is at least the utility achieved by some benchmark in which it is assumed that every other agent's bidding remains the same. These guarantees offer compelling properties: They are optimal against stationary competition distributions, and in unconstrained settings, the resulting empirical distribution of play induced by no-regret dynamics approximates a Coarse Correlated Equilibrium. However, no-regret algorithms are easily manipulable, and in budgeted settings, no stronger notion of regret (such as swap regret) is currently known that would limit such manipulation. We propose a very simple learning algorithm for budgeted sequential auctions where agents maximize their total number of wins and show that it has surprisingly appealing properties. We analyze this algorithm from two perspectives. First, we show that when an agent with a $ρ$ fraction of the total budget uses this algorithm, then she is guaranteed to win at least $ρT - O(\sqrt T)$ of the total $T$ rounds. This result holds for adversarial behavior by the other agents, as long as they respect their own budget restrictions. Second, we examine the scenario when all the agents follow our algorithm. By the first result, every agent's total wins are proportional to her budget, up to the additive $O(\sqrt T)$ term. In addition, we show that this result holds in a much stronger sense: after an initial period of $O(\sqrt T \log T)$ rounds, every agent gets the same guarantee over any time interval. For intervals of length $O(\sqrt T)$, we show that the deviation from the desired number of wins is an additive constant.

研究动机与目标

• 在超越无后悔框架的全球预算约束下，激发拍卖中的学习。
• 提出一个原始、确定性的出价更新规则并分析其预算安全性。
• 在尊重预算的对手中建立最坏情形的胜利保证。
• 证明自对弈性质：胜出分布成比例且随时间的偏差较小。

提出的方法

• 提出一个确定性的出价更新：b^{(t+1)} = b^{(t)} + η(ρ_i − p_i^{(t)}).
• 设定 η = 1/√T 以获得强的渐近保证。
• 证明出价保持非负且预算不超支（引理 2.1）。
• 将优化器行为建模为整数规划并通过拉格朗日松弛进行分析，以界定优化者收益（定理 3.1）。
• 刻画收敛性：在凸函数 f(b) 上的子梯度下降解释，唯一最小值在 b = 1（方程 5，命题 4.3–4.5）。
• 提供多主体自对弈分析：启动后，每个具有份额ρ_i 的代理在任意长度 τ = Θ(√T) 的区间内胜出约为 ρ_iτ。

实验结果

研究问题

• RQ1 简单的原始出价规则是否能在预算存在的对手面前保证等比例的胜出份额？
• RQ2 当所有代理都遵循该规则时，这样的原始动力学是否会导致胜出分布的低时间偏差？
• RQ3 出价收敛到稳定区间的速度有多快，对基于区间的胜出保证有何影响？
• RQ4 对使用此规则的预算学习者，优化器的操控理论极限是什么？
• RQ5 结果如何推广到自对弈与在预算约束下的多区间情形？

主要发现

• 拥有预算ρ_i T的代理在对手为预算尊重的任意对手面前，至少赢得 ρ_i T − O(√T) 的轮数。
• 若所有代理都使用该算法，且每个代理的总胜出近似与其预算成正比，且有一个 O(√T) 的启动项。
• 在初始 O(√T log T) 轮后，每个代理在任意时间区间内获得近似相等的保证；在长度为 O(√T) 的区间内，偏差为 O(1)。
• 在等预算设置下，代理最终以轮换制方式获胜，任意区间内的偏差不超过 (n−1)/n。
• 在适当的轮次后，出价收敛到以 1 为中心、宽度为 O(η) 的区间，从而在小区间内获得 O(1) 的偏差界。