We consider the problem of a single seller repeatedly selling a single item to a single buyer (specifically, the buyer has a value drawn fresh from known distribution D in every round). Prior work assumes that the buyer is fully rational and will perfectly reason about how their bids today affect the seller's decisions tomorrow. In this work we initiate a different direction: the buyer simply runs a no-regret learning algorithm over possible bids. We provide a fairly complete characterization of optimal auctions for the seller in this domain. Specifically:• If the buyer bids according to EXP3 (or any "mean-based" learning algorithm), then the seller can extract expected revenue arbitrarily close to the expected welfare. This auction is independent of the buyer's valuation D, but somewhat unnatural as it is sometimes in the buyer's interest to overbid.• There exists a learning algorithm A such that if the buyer bids according to A then the optimal strategy for the seller is simply to post the Myerson reserve for D every round.• If the buyer bids according to EXP3 (or any "mean-based" learning algorithm), but the seller is restricted to "natural" auction formats where overbidding is dominated (e.g. Generalized First-Price or Generalized Second-Price), then the optimal strategy for the seller is a pay-your-bid format with decreasing reserves over time. Moreover, the seller's optimal achievable revenue is characterized by a linear program, and can be unboundedly better than the best truthful auction yet simultaneously unboundedly worse than the expected welfare.2. There exists a natural no-regret algorithm A such that when the buyer bids according to A, the seller's default strategy (charging the Myerson reserve every round) is optimal (Theorem 3.2).3. If the buyer uses a "mean-based" algorithm only over undominated strategies, the seller can extract revenue MBRev(D) using an auction where overbidding is dominated in every round. Moreover, we characterize MBRev(D) as the value of a linear program, and show it can be
In the classical principal-agent problem, a principal must design a contract to incentivize an agent to perform an action on behalf of the principal. We study the classical principal-agent problem in a setting where the agent can be of one of several types (affecting the outcome of actions they might take). This combines the contract theory phenomena of "moral hazard" (incomplete information about actions) with that of "adverse selection" (incomplete information about types).We examine this problem through the computational lens. We show that in this setting it is APX-hard to compute either the profit-maximizing single contract or the profit-maximizing menu of contracts (as opposed to in the absence of types, where one can efficiently compute the optimal contract). We then show that the performance of the best linear contract scales especially well in the number of types: if agent has available actions and possible types, the best linear contract achieves an ( log ) approximation of the best possible profit. Finally, we apply our framework to prove tight worst-case approximation bounds between a variety of benchmarks of mechanisms for the principal.CCS Concepts: • Theory of computation → Algorithmic game theory; Algorithmic mechanism design.
Motivated by applications in recommender systems, web search, social choice and crowdsourcing, we consider the problem of identifying the set of top K items from noisy pairwise comparisons. In our setting, we are non-actively given r pairwise comparisons between each pair of n items, where each comparison has noise constrained by a very general noise model called the strong stochastic transitivity (SST) model. We analyze the competitive ratio of algorithms for the top-K problem. In particular, we present a linear time algorithm for the top-K problem which has a competitive ratio ofÕ( √ n); i.e. to solve any instance of top-K, our algorithm needs at mostÕ( √ n) times as many samples needed as the best possible algorithm for that instance (in contrast, all previous known algorithms for the top-K problem have competitive ratios ofΩ(n) or worse). We further show that this is tight: any algorithm for the top-K problem has competitive ratio at leastΩ( √ n). * Full version of this paper can be found at https://arxiv.org/abs/1605.03933.
We study the problem of contextual search, a multidimensional generalization of binary search that captures many problems in contextual decision-making. In contextual search, a learner is trying to learn the value of a hidden vector v ∈ [0, 1] d . Every round the learner is provided an adversarially-chosen context u t ∈ R d , submits a guess p t for the value of u t , v , learns whether p t < u t , v , and incurs loss ℓ( u t , v , p t ) (for some loss function ℓ). The learner's goal is to minimize their total loss over the course of T rounds.We present an algorithm for the contextual search problem for the symmetric loss function ℓ(θ, p) = |θ − p| that achieves O d (1) total loss. We present a new algorithm for the dynamic pricing problem (which can be realized as a special case of the contextual search problem) that achieves O d (log log T ) total loss, improving on the previous best known upper bounds of O d (log T ) and matching the known lower bounds (up to a polynomial dependence on d). Both algorithms make significant use of ideas from the field of integral geometry, most notably the notion of intrinsic volumes of a convex set. To the best of our knowledge this is the first application of intrinsic volumes to algorithm design.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.