Mechanism Design via Correlation Gap

For revenue and welfare maximization in single-dimensional Bayesian settings, Chawla et al. (STOC10) recently showed that sequential posted-price mechanisms (SPMs), though simple in form, can perform surprisingly well compared to the optimal mechanisms. In this paper, we give a theoretical explanation of this fact, based on a connection to the notion of correlation gap. Loosely speaking, for auction environments with matroid constraints, we can relate the performance of a mechanism to the expectation of a monotone submodular function over a random set. This random set corresponds to the winner set for the optimal mechanism, which is highly correlated, and corresponds to certain demand set for SPMs, which is independent. The notion of correlation gap of Agrawal et al.\ (SODA10) quantifies how much we {}"lose" in the expectation of the function by ignoring correlation in the random set, and hence bounds our loss in using certain SPM instead of the optimal mechanism. Furthermore, the correlation gap of a monotone and submodular function is known to be small, and it follows that certain SPM can approximate the optimal mechanism by a good constant factor. Exploiting this connection, we give tight analysis of a greedy-based SPM of Chawla et al.\ for several environments. In particular, we show that it gives an $e/(e-1)$-approximation for matroid environments, gives asymptotically a $1/(1-1/\sqrt{2\pi k})$-approximation for the important sub-case of $k$-unit auctions, and gives a $(p+1)$-approximation for environments with $p$-independent set system constraints

Lower Bounds for Complementation of omega-Automata Via the Full Automata Technique

In this paper, we first introduce a lower bound technique for the state complexity of transformations of automata. Namely we suggest first considering the class of full automata in lower bound analysis, and later reducing the size of the large alphabet via alphabet substitutions. Then we apply such technique to the complementation of nondeterministic \omega-automata, and obtain several lower bound results. Particularly, we prove an \omega((0.76n)^n) lower bound for B\"uchi complementation, which also holds for almost every complementation or determinization transformation of nondeterministic omega-automata, and prove an optimal (\omega(nk))^n lower bound for the complementation of generalized B\"uchi automata, which holds for Streett automata as well

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

Corporate social responsibility, strategic style and enterprise innovation: evidence from China

We make contribution to the literature on corporate social responsibility (CSR) and innovation by studying how CSR affects corporate innovation activities. Using data from listed firms in China, we find that CSR derived from legitimacy has a significant positive effect on corporate innovation. Specifically, our evidence shows that firms’ internal responsibility and business partners’ responsibility can facilitate innovation activities, and the corporate strategy is the potential channel for this positive association. From the perspective of the impact of external environmental pressure, the environmental uncertainty and the shock of the industry prosperity weaken the positive effect of CSR on innovation, namely, in the case of fewer environmental uncertainties and less industry prosperity, CSR plays a stronger role in promoting corporate innovation. From the point of the influence of heterogeneity, for firms with high employee loyalty, low agency cost and few financing constraints, CSR have a stronger impact on innovation. Overall, our results suggest that CSR does have a measurable impact on corporate innovation and contributes to understanding the special role of "legitimacy" in corporate decision-making in emerging markets

A Secure Federated Data-Driven Evolutionary Multi-objective Optimization Algorithm

Data-driven evolutionary algorithms usually aim to exploit the information behind a limited amount of data to perform optimization, which have proved to be successful in solving many complex real-world optimization problems. However, most data-driven evolutionary algorithms are centralized, causing privacy and security concerns. Existing federated Bayesian algorithms and data-driven evolutionary algorithms mainly protect the raw data on each client. To address this issue, this paper proposes a secure federated data-driven evolutionary multi-objective optimization algorithm to protect both the raw data and the newly infilled solutions obtained by optimizing the acquisition function conducted on the server. We select the query points on a randomly selected client at each round of surrogate update by calculating the acquisition function values of the unobserved points on this client, thereby reducing the risk of leaking the information about the solution to be sampled. In addition, since the predicted objective values of each client may contain sensitive information, we mask the objective values with Diffie-Hellmann-based noise, and then send only the masked objective values of other clients to the selected client via the server. Since the calculation of the acquisition function also requires both the predicted objective value and the uncertainty of the prediction, the predicted mean objective and uncertainty are normalized to reduce the influence of noise. Experimental results on a set of widely used multi-objective optimization benchmarks show that the proposed algorithm can protect privacy and enhance security with only negligible sacrifice in the performance of federated data-driven evolutionary optimization.Comment: This paper has been accepted by IEEE Transactions on Emerging Topics in Computational Intelligence journa