On Simultaneous Two-player Combinatorial Auctions

We consider the following communication problem: Alice and Bob each have some valuation functions $v_1(\cdot)$ and $v_2(\cdot)$ over subsets of $m$ items, and their goal is to partition the items into $S, \bar{S}$ in a way that maximizes the welfare, $v_1(S) + v_2(\bar{S})$. We study both the allocation problem, which asks for a welfare-maximizing partition and the decision problem, which asks whether or not there exists a partition guaranteeing certain welfare, for binary XOS valuations. For interactive protocols with $poly(m)$ communication, a tight 3/4-approximation is known for both [Fei06,DS06]. For interactive protocols, the allocation problem is provably harder than the decision problem: any solution to the allocation problem implies a solution to the decision problem with one additional round and $\log m$ additional bits of communication via a trivial reduction. Surprisingly, the allocation problem is provably easier for simultaneous protocols. Specifically, we show: 1) There exists a simultaneous, randomized protocol with polynomial communication that selects a partition whose expected welfare is at least $3/4$ of the optimum. This matches the guarantee of the best interactive, randomized protocol with polynomial communication. 2) For all $\varepsilon > 0$, any simultaneous, randomized protocol that decides whether the welfare of the optimal partition is $\geq 1$ or $\leq 3/4 - 1/108+\varepsilon$ correctly with probability $> 1/2 + 1/ poly(m)$ requires exponential communication. This provides a separation between the attainable approximation guarantees via interactive ($3/4$) versus simultaneous ($\leq 3/4-1/108$) protocols with polynomial communication. In other words, this trivial reduction from decision to allocation problems provably requires the extra round of communication

Learning a Partitioning Advisor with Deep Reinforcement Learning

Commercial data analytics products such as Microsoft Azure SQL Data Warehouse or Amazon Redshift provide ready-to-use scale-out database solutions for OLAP-style workloads in the cloud. While the provisioning of a database cluster is usually fully automated by cloud providers, customers typically still have to make important design decisions which were traditionally made by the database administrator such as selecting the partitioning schemes. In this paper we introduce a learned partitioning advisor for analytical OLAP-style workloads based on Deep Reinforcement Learning (DRL). The main idea is that a DRL agent learns its decisions based on experience by monitoring the rewards for different workloads and partitioning schemes. We evaluate our learned partitioning advisor in an experimental evaluation with different databases schemata and workloads of varying complexity. In the evaluation, we show that our advisor is not only able to find partitionings that outperform existing approaches for automated partitioning design but that it also can easily adjust to different deployments. This is especially important in cloud setups where customers can easily migrate their cluster to a new set of (virtual) machines

Envy Freedom and Prior-free Mechanism Design

We consider the provision of an abstract service to single-dimensional agents. Our model includes position auctions, single-minded combinatorial auctions, and constrained matching markets. When the agents' values are drawn from a distribution, the Bayesian optimal mechanism is given by Myerson (1981) as a virtual-surplus optimizer. We develop a framework for prior-free mechanism design and analysis. A good mechanism in our framework approximates the optimal mechanism for the distribution if there is a distribution; moreover, when there is no distribution this mechanism still performs well. We define and characterize optimal envy-free outcomes in symmetric single-dimensional environments. Our characterization mirrors Myerson's theory. Furthermore, unlike in mechanism design where there is no point-wise optimal mechanism, there is always a point-wise optimal envy-free outcome. Envy-free outcomes and incentive-compatible mechanisms are similar in structure and performance. We therefore use the optimal envy-free revenue as a benchmark for measuring the performance of a prior-free mechanism. A good mechanism is one that approximates the envy free benchmark on any profile of agent values. We show that good mechanisms exist, and in particular, a natural generalization of the random sampling auction of Goldberg et al. (2001) is a constant approximation