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We consider a general non-stochastic online pricing bandit setting in a procurement scenario where a buyer with a budget wants to procure items from a fixed set of sellers to maximize the buyer's reward by dynamically offering purchasing prices to the sellers, where the sellers' costs and values at each time period can change arbitrarily and the sellers determine whether to accept the offered prices to sell the items. This setting models online pricing scenarios of procuring resources or services in multi-agent systems. We first consider the offline setting when sellers' costs and values are known in advance and investigate the best fixed-price policy in hindsight. We show that it has a tight approximation guarantee with respect to the offline optimal solutions. In the general online setting, we propose an online pricing policy, Granularity-based Pricing (GAP), which exploits underlying side-information from the feedback graph when the budget is given as the input. We show that GAP achieves an upper bound of O(n{v_{max}}{c_{min}}sqrt{B/c_{min}}ln B) on the alpha-regret where n, v_{max}, c_{min}, and B are the number, the maximum value, the minimum cost of sellers, and the budget, respectively. We then extend it to the unknown budget case by developing a variant of GAP, namely Doubling-GAP, and show its alpha-regret is at most O(n{v_{max}}{c_{min}}sqrt{B/c_{min}}ln2 B). We also provide an alpha-regret lower bound Omega(v_{max}sqrt{Bn/c_{min}}) of any online policy that is tight up to sub-linear terms. We conduct simulation experiments to show that the proposed policy outperforms the baseline algorithms. 

In recent decades, the design of budget feasible mechanisms for a wide range of procurement auction settings has received significant attention in the Artificial Intelligence (AI) community. These procurement auction settings have practical applications in various domains such as federated learning, crowdsensing, edge computing, and resource allocation. In a basic procurement auction setting of these domains, a buyer with a limited budget is tasked with procuring items (\eg, goods or services) from strategic sellers, who have private information on the true costs of their items and incentives to misrepresent their items' true costs. The primary goal of budget feasible mechanisms is to elicit the true costs from sellers and determine items to procure from sellers to maximize the buyer valuation function for the items and ensure that the total payment to the sellers is no more than the budget. In this survey, we provide a comprehensive overview of key procurement auction settings and results of budget feasible mechanisms. We provide several promising future research directions. 

Abstract Precise modulating the vertical structure of active layers to boost charge transfer is an effective way to achieve high power conversion efficiencies (PCEs) in organic solar cells (OSCs). Herein, efficient OSCs with a well‐controlled vertical structure are realized by a rapid film‐forming method combining low boiling point solvent and the sequential blade‐coating (SBC) technology. The results of grazing incident wide‐angle X‐ray scattering measurement show that the vertical component distribution is varied by changing the processing solvent. Novel characterization technique such as tilt resonant soft X‐ray scattering is used to test the vertical structure of the films, demonstrating the dichloromethane (DCM)‐processed film is truly planar heterojunction. The devices with chloroform (CF) processed upper layer show an increased mixed phase region compared to these devices with toluene (TL) or ‐DCM‐, which is beneficial for improving charge generation and achieving a superior PCE of 17.36%. Despite significant morphological varies, the DCM‐processed devices perform slightly lower PCE of 16.66%, which is the highest value in truly planar heterojunction devices, demonstrating higher morphological tolerance. This work proposes a solvent‐regulating method to optimize the vertical structure of active layers through SBC technology, and provides a practical guidance for the optimization of the active‐layer microstructure.