Bandit Sequential Posted Pricing via Half-Concavity

• URL: http://arxiv.org/abs/2312.12794v2
• Date: Wed, 12 Jun 2024 21:02:06 GMT
• Title: Bandit Sequential Posted Pricing via Half-Concavity
• Authors: Sahil Singla, Yifan Wang,
• Abstract summary: We study sequential posted pricing in the bandit learning model. In each round the seller posts $n$ prices for the $n$ buyers and the first buyer with a valuation higher than the price takes the item. Our main results obtain nearly-optimal regret bounds for single-item sequential posted pricing.
• Score: 12.373936155910934
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Sequential posted pricing auctions are popular because of their simplicity in practice and their tractability in theory. A usual assumption in their study is that the Bayesian prior distributions of the buyers are known to the seller, while in reality these priors can only be accessed from historical data. To overcome this assumption, we study sequential posted pricing in the bandit learning model, where the seller interacts with $n$ buyers over $T$ rounds: In each round the seller posts $n$ prices for the $n$ buyers and the first buyer with a valuation higher than the price takes the item. The only feedback that the seller receives in each round is the revenue. Our main results obtain nearly-optimal regret bounds for single-item sequential posted pricing in the bandit learning model. In particular, we achieve an $\tilde{O}(\mathsf{poly}(n)\sqrt{T})$ regret for buyers with (Myerson's) regular distributions and an $\tilde{O}(\mathsf{poly}(n)T^{{2}/{3}})$ regret for buyers with general distributions, both of which are tight in the number of rounds $T$. Our result for regular distributions was previously not known even for the single-buyer setting and relies on a new half-concavity property of the revenue function in the value space. For $n$ sequential buyers, our technique is to run a generalized single-buyer algorithm for all the buyers and to carefully bound the regret from the sub-optimal pricing of the suffix buyers.

Related papers

• No-Regret Algorithms in non-Truthful Auctions with Budget and ROI Constraints [0.9694940903078658]
  We study the problem of designing online autobidding algorithms to optimize value subject to ROI and budget constraints. Our main result is an algorithm with full information feedback that guarantees a near-optimal $tilde O(sqrt T)$ regret with respect to the best Lipschitz function.
  arXiv  Detail & Related papers  (2024-04-15T14:31:53Z)
• An Online Learning Theory of Brokerage [3.8059763597999012]
  We investigate brokerage between traders from an online learning perspective. Unlike other bilateral trade problems already studied, we focus on the case where there are no designated buyer and seller roles. We show that the optimal rate degrades to $sqrtT$ in the first case, and the problem becomes unlearnable in the second.
  arXiv  Detail & Related papers  (2023-10-18T17:01:32Z)
• Online Learning in Contextual Second-Price Pay-Per-Click Auctions [47.06746975822902]
  We study online learning in contextual pay-per-click auctions where at each of the $T$ rounds, the learner receives some context along with a set of ads. The learner's goal is to minimize her regret, defined as the gap between her total revenue and that of an oracle strategy.
  arXiv  Detail & Related papers  (2023-10-08T07:04:22Z)
• Repeated Bilateral Trade Against a Smoothed Adversary [5.939280057673226]
  We study repeated bilateral trade where an adaptive $sigma$-smooth adversary generates the valuations of sellers and buyers. We provide a complete characterization of the regret regimes for fixed-price mechanisms under different feedback models.
  arXiv  Detail & Related papers  (2023-02-21T16:30:10Z)
• Leveraging Reviews: Learning to Price with Buyer and Seller Uncertainty [30.60994780724878]
  We study a pricing problem in an online setting where the seller interacts with a set of buyers of finitely many types. We provide a no-regret algorithm that the seller can use to obtain high revenue.
  arXiv  Detail & Related papers  (2023-02-20T00:15:45Z)
• A Reinforcement Learning Approach in Multi-Phase Second-Price Auction Design [158.0041488194202]
  We study reserve price optimization in multi-phase second price auctions. From the seller's perspective, we need to efficiently explore the environment in the presence of potentially nontruthful bidders. Third, the seller's per-step revenue is unknown, nonlinear, and cannot even be directly observed from the environment.
  arXiv  Detail & Related papers  (2022-10-19T03:49:05Z)
• Double Auctions with Two-sided Bandit Feedback [11.334374665364214]
  Double Auction enables decentralized transfer of goods between multiple buyers and sellers. We show with confidence bound based bidding, and Average Pricing' there is an efficient price discovery among the participants. Our paper is the first to provide decentralized learning algorithms in a two-sided market where emphboth sides have uncertain preference that need to be learned.
  arXiv  Detail & Related papers  (2022-08-13T01:03:34Z)
• No-Regret Learning in Partially-Informed Auctions [85.67897346422122]
  We study a machine learning formulation of auctions with partially-revealed information. In each round, a new item is drawn from an unknown distribution and the platform publishes a price together with incomplete, "masked" information about the item. We show that when the distribution over items is known to the buyer and the mask is a SimHash function mapping $mathbbRd$ to $0,1ell$, our algorithm has regret $tilde mathcalO((Tdell)frac12)$.
  arXiv  Detail & Related papers  (2022-02-22T01:15:51Z)
• Top $K$ Ranking for Multi-Armed Bandit with Noisy Evaluations [102.32996053572144]
  We consider a multi-armed bandit setting where, at the beginning of each round, the learner receives noisy independent evaluations of the true reward of each arm. We derive different algorithmic approaches and theoretical guarantees depending on how the evaluations are generated.
  arXiv  Detail & Related papers  (2021-12-13T09:48:54Z)
• Robust Learning of Optimal Auctions [84.13356290199603]
  We study the problem of learning revenue-optimal multi-bidder auctions from samples when the samples of bidders' valuations can be adversarially corrupted or drawn from distributions that are adversarially perturbed. We propose new algorithms that can learn a mechanism whose revenue is nearly optimal simultaneously for all true distributions'' that are $alpha$-close to the original distribution in Kolmogorov-Smirnov distance.
  arXiv  Detail & Related papers  (2021-07-13T17:37:21Z)
• Stochastic Bandits with Linear Constraints [69.757694218456]
  We study a constrained contextual linear bandit setting, where the goal of the agent is to produce a sequence of policies. We propose an upper-confidence bound algorithm for this problem, called optimistic pessimistic linear bandit (OPLB)
  arXiv  Detail & Related papers  (2020-06-17T22:32:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.