Periodic Reporting for period 3 - AMDROMA (Algorithmic and Mechanism Design Research in Online MArkets)
Período documentado: 2021-07-01 hasta 2022-12-31
Our contribution on the second project objective is about the design of efficient and truthful pricing mechanisms in the cloud market in presence of uncertainty on the future arrivals and on the type of the agents. A second contribution addresses the problems of designing budget feasible strategies for the stochastic exploration of networks. Finally, we provide a new set of optimal and near optimal strategies for the Pandora's Box Problem, originally formalized by Weitzman in 1979, that models, for example, the problem of hiring one skilled worker, where the evaluation of each candidate is an expensive procedure.
For the third project objective we provide near optimal online algorithms for matching tasks to hired and freelance online workers. We also study the fair version of the team formation problem and of other fundamental classification and clustering methods, where we seek for example for a solution with good balance between genders. Finally, a number of computational issues for large-scale data analysis in markets have been considered for approximating k-means, perhaps the most used clustering methods, and for the efficient updating over time of near optimal solutions to a clustering or a matching problem.
Incentive compatibility is a fundamental property of auction mechanisms. Recent methods show that many counterfactual runs of the auction with different bids can be used to determine whether an auction is truthful. In [Colini-Baldeschi et al. 2020] we show that a similar result can be obtained for the setting of position auctions for sponsored search with one single execution of the auction by looking at the advertisers' envy. We plan in the near future to study the Ad-type setting where different agents have different discount factors on the positions.
Project objective 2 is related to copying with uncertainty in mechanism design. We introduce in [Anagnostopoulos et al. 2019] the stochastic exploration of an undirected graph with stochastic edge costs drawn from a distribution, and rewards on vertices. The goal is to find a set of edges of total cost at most equal to a maximum budget, and maximizes the total reward. We show that logarithmic budget augmentation suffices to obtain constant approximation oblivious strategies that are competitive against the optimal adaptive strategy. A challenging problem is to devise strategies with constant approximation and constant budget augmentation. Finally, for the problem of information acquisition in markets, Weitzman in 1979 showed that the Pandora's Box problem admits an elegant and simple greedy solution. In [Boodaghians et al. 2020], we are able to design an optimal strategy for tree-like order constraints on the exploration of the alternatives. We plan to extend our study to the more general setting of dag-like order constraints.
For the large-scale optimization of online markets of project objective 3, we studied the problems of operating online marketplaces. In [Anagnostopoulos et al 2018] we provide algorithms for outsourcing and hiring workers, where workers form a team and contribute different skills to perform a task. We also extend our study to consider the fairness issues of overcoming the unintentional algorithmic discrimination that frequently arises in the job market on grounds of nationality or gender. For the future we plan to study the online problem with a hard limit on the maximum number of hired workers.
Fairness is also a natural requirement to impose for the fundamental machine learning primitives used for classification and recommendation in online markets. Previous work obtained a constant factor approximation for the fair version with 1 protected attribute (e.g. gender) of most center based k-clustering objectives. In [Böhm et al, 2020], we give the first constant factor approximations for all center based k-clustering objectives with any number of attributes. In the near future we plan to devise fair clustering methods based on coresets. For the issues related to computational efficient methods for large-scale data analysis, we study in [Becchetti et al. 2019] the problem of speeding up all k-means clusterings. We show that oblivious random projections onto a logarithmic number O(log k) of dimensions is sufficient to approximate the cost of all k-means clusterings up to a multiplicative (1±ε) factor. This closes a longstanding open problem. Finally, in [Grandoni et al. 2019] we study the maximum matching problem in the incremental setting with small update time. We present a deterministic algorithm that maintains an (1 + ε)-approximate matching with constant amortized update time per insertion. We plan in the near future to study the problem of improving the best known 2-approximation for matching in fully dynamic graphs.