Ji Liu

Mark Braverman, Jingyi Liu, Jieming Mao et al.

The adversarial Bandit with Knapsack problem is a multi-armed bandits problem with budget constraints and adversarial rewards and costs. In each round, a learner selects an action to take and observes the reward and cost of the selected action. The goal is to maximize the sum of rewards while satisfying the budget constraint. The classical benchmark to compare against is the best fixed distribution over actions that satisfies the budget constraint in expectation. Unlike its stochastic counterpart, where rewards and costs are drawn from some fixed distribution (Badanidiyuru et al., 2018), the adversarial BwK problem does not admit a no-regret algorithm for every problem instance due to the "spend-or-save" dilemma (Immorlica et al., 2022). A key problem left open by existing works is whether there exists a weaker but still meaningful benchmark to compare against such that no-regret learning is still possible. In this work, we present a new benchmark to compare against, motivated both by real-world applications such as autobidding and by its underlying mathematical structure. The benchmark is based on the Earth Mover's Distance (EMD), and we show that sublinear regret is attainable against any strategy whose spending pattern is within EMD $o(T^2)$ of any sub-pacing spending pattern. As a special case, we obtain results against the "pacing over windows" benchmark, where we partition time into disjoint windows of size $w$ and allow the benchmark strategies to choose a different distribution over actions for each window while satisfying a pacing budget constraint. Against this benchmark, our algorithm obtains a regret bound of $\tilde{O}(T/\sqrt{w}+\sqrt{wT})$. We also show a matching lower bound, proving the optimality of our algorithm in this important special case. In addition, we provide further evidence of the necessity of the EMD condition for obtaining a sublinear regret.

Hong Jun Jeon, Songbin Liu, Yuantong Li et al.

The exploding popularity of online content and its user base poses an evermore challenging matching problem for modern recommendation systems. Unlike other frontiers of machine learning such as natural language, recommendation systems are responsible for collecting their own data. Simply exploiting current knowledge can lead to pernicious feedback loops but naive exploration can detract from user experience and lead to reduced engagement. This exploration-exploitation trade-off is exemplified in the classic multi-armed bandit problem for which algorithms such as upper confidence bounds (UCB) and Thompson sampling (TS) demonstrate effective performance. However, there have been many challenges to scaling these approaches to settings which do not exhibit a conjugate prior structure. Recent scalable approaches to uncertainty quantification via epinets have enabled efficient approximations of Thompson sampling even when the learning model is a complex neural network. In this paper, we demonstrate the first application of epinets to an online recommendation system. Our experiments demonstrate improvements in both user traffic and engagement efficiency on the Facebook Reels online video platform.