Today's online platforms rely heavily on algorithmic recommendations to bolster user engagement and drive revenue. However, such algorithmic recommendations can impact diverse stakeholders involved, namely the platform, items (seller), and users (customers), each with their unique objectives. In such multi-sided platforms, finding an appropriate middle ground becomes a complex operational challenge. Motivated by this, we formulate a novel fair recommendation framework, called Problem (FAIR), that not only maximizes the platform's revenue, but also accommodates varying fairness considerations from the perspectives of items and users. Our framework's distinguishing trait lies in its flexibility -- it allows the platform to specify any definitions of item/user fairness that are deemed appropriate, as well as decide the "price of fairness" it is willing to pay to ensure fairness for other stakeholders. We further examine Problem (FAIR) in a dynamic online setting, where the platform needs to learn user data and generate fair recommendations simultaneously in real time, which are two tasks that are often at odds. In face of this additional challenge, we devise a low-regret online recommendation algorithm, called FORM, that effectively balances the act of learning and performing fair recommendation. Our theoretical analysis confirms that FORM proficiently maintains the platform's revenue, while ensuring desired levels of fairness for both items and users. Finally, we demonstrate the efficacy of our framework and method via several case studies on real-world data.

Today's online advertisers procure digital ad impressions through interacting with autobidding platforms: advertisers convey high level procurement goals via setting levers such as budget, target return-on-investment, max cost per click, etc.. Then ads platforms subsequently procure impressions on advertisers' behalf, and report final procurement conversions (e.g. click) to advertisers. In practice, advertisers may receive minimal information on platforms' procurement details, and procurement outcomes are subject to non-stationary factors like seasonal patterns, occasional system corruptions, and market trends which make it difficult for advertisers to optimize lever decisions effectively. Motivated by this, we present an online learning framework that helps advertisers dynamically optimize ad platform lever decisions while subject to general long-term constraints in a realistic bandit feedback environment with non-stationary procurement outcomes. In particular, we introduce a primal-dual algorithm for online decision making with multi-dimension decision variables, bandit feedback and long-term uncertain constraints. We show that our algorithm achieves low regret in many worlds when procurement outcomes are generated through procedures that are stochastic, adversarial, adversarially corrupted, periodic, and ergodic, respectively, without having to know which procedure is the ground truth. Finally, we emphasize that our proposed algorithm and theoretical results extend beyond the applications of online advertising.

In digital online advertising, advertisers procure ad impressions simultaneously on multiple platforms, or so-called channels, such as Google Ads, Meta Ads Manager, etc., each of which consists of numerous ad auctions. We study how an advertiser maximizes total conversion (e.g. ad clicks) while satisfying aggregate return-on-investment (ROI) and budget constraints across all channels. In practice, an advertiser does not have control over, and thus cannot globally optimize, which individual ad auctions she participates in for each channel, and instead authorizes a channel to procure impressions on her behalf: the advertiser can only utilize two levers on each channel, namely setting a per-channel budget and per-channel target ROI. In this work, we first analyze the effectiveness of each of these levers for solving the advertiser's global multi-channel problem. We show that when an advertiser only optimizes over per-channel ROIs, her total conversion can be arbitrarily worse than what she could have obtained in the global problem. Further, we show that the advertiser can achieve the global optimal conversion when she only optimizes over per-channel budgets. In light of this finding, under a bandit feedback setting that mimics real-world scenarios where advertisers have limited information on ad auctions in each channels and how channels procure ads, we present an efficient learning algorithm that produces per-channel budgets whose resulting conversion approximates that of the global optimal problem. Finally, we argue that all our results hold for both single-item and multi-item auctions from which channels procure impressions on advertisers' behalf.