Doubly Optimal No-Regret Learning in Monotone Games

We consider online learning in multi-player smooth monotone games. Existing algorithms have limitations such as (1) being only applicable to strongly monotone games; (2) lacking the no-regret guarantee; (3) having only asymptotic or slow $O(\frac{1}{\sqrt{T}})$ last-iterate convergence rate to a Nash equilibrium. While the $O(\frac{1}{\sqrt{T}})$ rate is tight for a large class of algorithms including the well-studied extragradient algorithm and optimistic gradient algorithm, it is not optimal for all gradient-based algorithms. We propose the accelerated optimistic gradient (AOG) algorithm, the first doubly optimal no-regret learning algorithm for smooth monotone games. Namely, our algorithm achieves both (i) the optimal $O(\sqrt{T})$ regret in the adversarial setting under smooth and convex loss functions and (ii) the optimal $O(\frac{1}{T})$ last-iterate convergence rate to a Nash equilibrium in multi-player smooth monotone games. As a byproduct of the accelerated last-iterate convergence rate, we further show that each player suffers only an $O(\log T)$ individual worst-case dynamic regret, providing an exponential improvement over the previous state-of-the-art $O(\sqrt{T})$ bound.Comment: Published at ICML 2023. V2 incorporates reviewers' feedbac

Religiosity and cross‐country differences in trade credit use

Using the firm‐level data over 1989–2012 from 53 countries, we find religiosity in a country is positively associated with trade credit use by local firms. Specifically, after controlling for firm‐ and country‐level factors as well as industry and year effects, we show that trade credit use is higher in more religious countries. Moreover, both creditor rights and social trust in a country enhance the positive association between religiosity and trade credit use, while the quality of national‐level disclosure mitigates the aforementioned positive association. These results are robust to alternative measures of religiosity, alternative sampling requirements and potential endogeneity concerns

Learning Thresholds with Latent Values and Censored Feedback

In this paper, we investigate a problem of actively learning threshold in latent space, where the unknown reward $g(\gamma, v)$ depends on the proposed threshold $\gamma$ and latent value $v$ and it can be $only$ achieved if the threshold is lower than or equal to the unknown latent value. This problem has broad applications in practical scenarios, e.g., reserve price optimization in online auctions, online task assignments in crowdsourcing, setting recruiting bars in hiring, etc. We first characterize the query complexity of learning a threshold with the expected reward at most $\epsilon$ smaller than the optimum and prove that the number of queries needed can be infinitely large even when $g(\gamma, v)$ is monotone with respect to both $\gamma$ and $v$. On the positive side, we provide a tight query complexity $\tilde{\Theta}(1/\epsilon^3)$ when $g$ is monotone and the CDF of value distribution is Lipschitz. Moreover, we show a tight $\tilde{\Theta}(1/\epsilon^3)$ query complexity can be achieved as long as $g$ satisfies one-sided Lipschitzness, which provides a complete characterization for this problem. Finally, we extend this model to an online learning setting and demonstrate a tight $\Theta(T^{2/3})$ regret bound using continuous-arm bandit techniques and the aforementioned query complexity results.Comment: 18 page

Revenue and User Traffic Maximization in Mobile Short-Video Advertising

A new mobile attention economy has emerged with the explosive growth of short-video apps such as TikTok. In this internet market, three types of agents interact with each other: the platform, influencers, and advertisers. A short-video platform encourages its influencers to attract users by creating appealing content through short-form videos and allows advertisers to display their ads in short-form videos. There are two options for the advertisers: one is to bid for platform advert slots in a similar way to search engine auctions; the other is to pay an influencer to make engaging short videos and promote them through the influencer's channel. The second option will generate a higher conversion ratio if advertisers choose the right influencers whose followers match their target market. Although displaying influencer ads will generate less revenue, it is more engaging than platform ads, which is better for maintaining user traffic. Therefore, it is crucial for a platform to balance these factors by establishing a sustainable business agreement with its influencers and advertisers. In this paper, we develop a two-stage solution for a platform to maximize short-term revenue and long-term user traffic maintenance. In the first stage, we estimate the impact of user traffic generated by displaying influencer ads and characterize the user traffic the platform should allocate to influencers for overall revenue maximization. In the second stage, we devise an optimal (1 - 1/e)-competitive algorithm for ad slot allocation. To complement this analysis, we examine the ratio of the revenue generated by our online algorithm to the optimal offline revenue. Our simulation results show that this ratio is 0.94 on average, which is much higher than (1 - 1/e) and outperforms four baseline algorithms