Prediction-Augmented Mechanism Design for Weighted Facility Location

Facility location is fundamental in operations research, mechanism design, and algorithmic game theory, with applications ranging from urban infrastructure planning to distributed systems. Recent research in this area has focused on augmenting classic strategyproof mechanisms with predictions to achieve an improved performance guarantee against the uncertainty under the strategic environment. Previous work has been devoted to address the trade-off obstacle of balancing the consistency (near-optimality under accurate predictions) and robustness (bounded inefficiency under poor predictions) primarily in the unweighted setting, assuming that all agents have the same importance. However, this assumption may not be true in some practical scenarios, leading to research of weighted facility location problems. The major contribution of the current work is to provide a prediction augmented algorithmic framework for balancing the consistency and robustness over strategic agents with non-uniform weights. In particular, through a reduction technique that identifies a subset of \emph{representative} instances and maps the other given locations to the representative ones, we prove that there exists a \emph{strategyproof} mechanism achieving a bounded consistency guarantee of $\frac{\sqrt{(1+c)^2W^2_{\min}+(1-c)^2W^2_{\max}}}{(1+c)W_{\min}}$ and a bounded robustness guarantee of $\frac{\sqrt{(1-c)^2W^2_{\min}+(1+c)^2W^2_{\max}}}{(1-c)W_{\min}}$ in weighted settings, where $c$ can be viewed as a parameter to make a trade-off between the consistency and robustness and $W_{\min}$ and $W_{\max}$ denote the minimum and maximum agents' weight. We also proved that there is no strategyproof deterministic mechanism that reach $1$-consistency and $O\left( n \cdot \frac{W_{\max}}{W_{\min}} \right)$-robustness in weighted FLP, even with fully predictions of all agents.

Online Paging with a Vanishing Regret

This paper considers a variant of the online paging problem, where the online algorithm has access to multiple predictors, each producing a sequence of predictions for the page arrival times. The predictors may have occasional prediction errors and it is assumed that at least one of them makes a sublinear number of prediction errors in total. Our main result states that this assumption suffices for the design of a randomized online algorithm whose time-average regret with respect to the optimal offline algorithm tends to zero as the time tends to infinity. This holds (with different regret bounds) for both the full information access model, where in each round, the online algorithm gets the predictions of all predictors, and the bandit access model, where in each round, the online algorithm queries a single predictor. While online algorithms that exploit inaccurate predictions have been a topic of growing interest in the last few years, to the best of our knowledge, this is the first paper that studies this topic in the context of multiple predictors for an online problem with unbounded request sequences. Moreover, to the best of our knowledge, this is also the first paper that aims for (and achieves) online algorithms with a vanishing regret for a classic online problem under reasonable assumptions.