Shirley Zhang — Page 2

arXiv2023

Selling to Multiple No-Regret Buyers

We consider the problem of repeatedly auctioning a single item to multiple i.i.d buyers who each use a no-regret learning algorithm to bid over time. In particular, we study the seller's optimal revenue, if they know that the buyers are no-regret learners (but only that their behavior satisfies some no-regret property -- they do not know the precise algorithm/heuristic used). Our main result designs an auction that extracts revenue equal to the full expected welfare whenever the buyers are "mean-based" (a property satisfied by standard no-regret learning algorithms such as Multiplicative Weights, Follow-the-Perturbed-Leader, etc.). This extends a main result of [BMSW18] which held only for a single buyer. Our other results consider the case when buyers are mean-based but never overbid. On this front, [BMSW18] provides a simple LP formulation for the revenue-maximizing auction for a single-buyer. We identify several formal barriers to extending this approach to multiple buyers.

cs.GT↗

arXiv2022

Balancing Flow Time and Energy Consumption

In this paper, we study the following batch scheduling model: find a schedule that minimizes total flow time for $n$ uniform length jobs, with release times and deadlines, where the machine is only actively processing jobs in at most $k$ synchronized batches of size at most $B$. Prior work on such batch scheduling models has considered only feasibility with no regard to the flow time of the schedule. However, algorithms that minimize the cost from the scheduler's perspective -- such as ones that minimize the active time of the processor -- can result in schedules where the total flow time is arbitrarily high \cite{ChangGabowKhuller}. Such schedules are not valuable from the perspective of the client. In response, our work provides dynamic programs which minimize flow time subject to active time constraints. Our main contribution focuses on jobs with agreeable deadlines; for such job instances, we introduce dynamic programs that achieve runtimes of O$(B \cdot k \cdot n)$ for unit jobs and O$(B \cdot k \cdot n^5)$ for uniform length jobs. These results improve upon our modification of a different, classical dynamic programming approach by Baptiste. While the modified DP works when deadlines are non-agreeable, this solution is more expensive, with runtime $O(B \cdot k^2 \cdot n^7)$ \cite{Baptiste00}.

cs.DS↗