We study the problem of learning to bid when the bidder's value is dynamic, i.e., when the current value depends on past outcomes. Specifically, we consider a bidder participating in repeated second-price auctions whose value depends on the time elapsed since their last successful bid, with auctions arriving in continuous time and only aggregated feedback revealed at the end of the horizon. Such a bidder must (1) balance the immediate benefit of winning the current auction against its impact on future values and (2) learn unknown environmental parameters. We derive regret bounds for a class of learning methods that combine plug-in estimators with a differential-equation characterization of the optimal policy, and show that a specific confidence bound algorithm learns the optimal policy with a near optimal regret of $\widetilde{O}(\log N)$ for piecewise linear primitives, and $\widetilde{O}(N^{1/3})$ for general, smooth primitives, achieving these regrets without explicit randomization. These theoretical results are supported by numerical experiments.

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Logged advertising auctions make offline reserve-price evaluation attractive but risky. Replay tables can identify policies with large apparent yield gains, yet they can also hide weak threshold support, multiple-comparison effects, subgroup harm, and bidder-response uncertainty. Existing replay and off-policy evaluation methods estimate or rank policy values, but they do not directly answer the operational question of whether the available evidence is strong enough to justify validation. This paper develops a support-aware offline decision framework for reserve-policy selection. Rather than outputting a single point-estimate winner, the framework converts logged evidence into a conservative decision object consisting of certified policies, statistically dominated alternatives, and unresolved candidates requiring further validation. The main theoretical result gives a unified finite-catalog guarantee showing that, under simultaneous uncertainty control and conservative support gates, the framework preserves the best gate-passing policy while eliminating only policies with certified regret. Supporting results characterize support-localized replay generalization, establish information-theoretic threshold-resolution limits, and quantify when heterogeneous bidder response can overturn localized replay rankings. Experiments on iPinYou real-time-bidding logs show that the leading reserve rule achieves a 47.66% replay lift in season two, a 40.71% simultaneous lower-bound lift, and a 43.87% frozen out-of-time replay lift in season three. The framework reduces a 19-policy catalog to a two-policy validation shortlist while certifying non-harm across 44 advertiser, exchange, and region segments. The results support the central claim that offline reserve-policy evaluation should produce certified validation decisions rather than point-estimate rankings alone.

Shilling is the use of artificial bids to make competition appear stronger and push prices upward. We study repeated first-price auctions in which shilling affects feedback but not allocation: the learner wins or loses against the real competing bid, but after a loss observes the maximum of the real bid and an independent shill bid. Thus the manipulation changes what the learner observes and hence how it learns to bid, without changing the outcome of the current auction. We analyze regret with respect to the best bid benchmark, assuming that the shill-bid distribution is known. Even then, shilling can mask the real bid, while useful side information appears only through intermittent low-shill events. Our algorithm combines a robust interval-elimination branch, which ignores the shilled report and achieves the dynamic-pricing rate $\tilde{\mathcal{O}}(T^{2/3})$, with an optimistic branch that debiases losing-side reports and exploits the resulting suffix information when it is reliable and achieves the first-price auctions rate $\tilde{\mathcal{O}}(\sqrt{T})$. A validation and racing procedure lets the algorithm use these optimistic updates without knowing the right scale or feedback geometry in advance. We complement the upper bounds with a matching lower bound, up to logarithmic factors, in the single-active-region case. Overall, the results show that even feedback-only shilling can sharply alter the statistical difficulty of repeated bidding.

We revisit the classical problem of designing Budget-Feasible Mechanisms (BFMs) for submodular valuation functions, which has been extensively studied since the seminal paper of Singer [FOCS'10] due to its wide applications in crowdsourcing and social marketing. We propose TripleEagle, a novel algorithmic framework for designing BFMs, based on which we present several simple yet effective BFMs that achieve better approximation ratios than the state-of-the-art work for both monotone and non-monotone submodular valuation functions. Moreover, our BFMs are the first in the literature to achieve linear complexities while ensuring obvious strategyproofness, making them more practical than the previous BFMs. We conduct extensive experiments to evaluate the empirical performance of our BFMs, and the experimental results strongly demonstrate the efficiency and effectiveness of our approach.

Increasingly, copious amounts of consumer data are used to learn high-revenue mechanisms via machine learning. Existing research on mechanism design via machine learning assumes that there is a distribution over the buyers' values for the items for sale and that the learning algorithm's input is a training set sampled from this distribution. This setup makes the strong assumption that no noise is introduced during data collection. In order to help place mechanism design via machine learning on firm foundations, we investigate the extent to which this learning process is robust to noise. Optimizing revenue using noisy data is challenging because revenue functions are extremely volatile: an infinitesimal change in the buyers' values can cause a steep drop in revenue. Nonetheless, we provide guarantees when arbitrarily correlated noise is added to the training set; we only require that the noise has bounded magnitude or is sub-Gaussian. We conclude with an application of our guarantees to multi-task mechanism design, where there are multiple distributions over buyers' values and the goal is to learn a high-revenue mechanism per distribution. To our knowledge, we are the first to study mechanism design via machine learning with noisy data as well as multi-task mechanism design.

Double Auction enables decentralized transfer of goods between multiple buyers and sellers, thus underpinning functioning of many online marketplaces. Buyers and sellers compete in these markets through bidding, but do not often know their own valuation a-priori. As the allocation and pricing happens through bids, the profitability of participants, hence sustainability of such markets, depends crucially on learning respective valuations through repeated interactions. We initiate the study of Double Auction markets under bandit feedback on both buyers' and sellers' side. We show with confidence bound based bidding, and'Average Pricing' there is an efficient price discovery among the participants.

Incrementality, which measures the causal effect of showing an ad to a potential customer (e.g. a user in an internet platform) versus not, is a central object for advertisers in online advertising platforms. This paper investigates the problem of how an advertiser can learn to optimize the bidding sequence in an online manner without knowing the incrementality parameters in advance. We formulate the offline version of this problem as a specially structured episodic Markov Decision Process (MDP) and then, for its online learning counterpart, propose a novel reinforcement learning (RL) algorithm with regret at most eO(H2 T), which depends on the number of rounds H and number of episodes T, but does not depend on the number of actions (i.e., possible bids). A fundamental difference between our learning problem from standard RL problems is that the realized reward feedback from conversion incrementality is mixed and delayed. To handle this difficulty we propose and analyze a novel pairwise moment-matching algorithm to learn the conversion incrementality, which we believe is of independent interest.

A shrinking market is a ubiquitous challenge faced by various industries. In this paper we formulate the first formal model of shrinking markets in multi-item settings, and study how mechanism design and machine learning can help preserve revenue in an uncertain, shrinking market. Via a sample-based learning mechanism, we prove the first guarantees on how much revenue can be preserved by truthful multi-item, multi-bidder auctions (for limited supply) when only a random unknown fraction of the population participates in the market. We first present a general reduction that converts any sufficiently rich auction class into a randomized auction robust to market shrinkage. Our main technique is a novel combinatorial construction called a winner diagram that concisely represents all possible executions of an auction on an uncertain set of bidders. Via a probabilistic analysis of winner diagrams, we derive a general possibility result: a sufficiently rich class of auctions always contains an auction that is robust to market shrinkage and market uncertainty. Our result has applications to important practically-constrained settings such as auctions with a limited number of winners. We then show how to efficiently learn an auction that is robust to market shrinkage by leveraging practically-efficient routines for solving the winner determination problem.