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Mehta and Panigrahi (FOCS 2012) introduce the problem of online matching with stochastic rewards, where edges are associated with success probabilities and a match succeeds with the probability of the corresponding edge. It is one of the few online matching problems that have defied the randomized online primal dual framework by Devanur, Jain, and Kleinberg (SODA 2013) thus far. This paper unlocks the power of randomized online primal dual in online matching with stochastic rewards by employing the configuration linear program rather than the standard matching linear program used in previous works. Our main result is a 0.572 competitive algorithm for the case of vanishing and unequal probabilities, improving the best previous bound of 0.534 by Mehta, Waggoner, and Zadimoghaddam (SODA 2015) and, in fact, is even better than the best previous bound of 0.567 by Mehta and Panigrahi (FOCS 2012) for the more restricted case of vanishing and equal probabilities. For vanishing and equal probabilities, we get a better competitive ratio of 0.576. Our results further generalize to the vertex-weighted case due to the intrinsic robustness of the randomized online primal dual analysis.

Three decades ago, Karp, Vazirani, and Vazirani (STOC 1990) defined the online matching problem and gave an optimal 1-1/e-competitive algorithm. Fifteen years later, Mehta, Saberi, Vazirani, and Vazirani (FOCS 2005) introduced the first generalization called AdWords driven by online advertising and obtained the optimal 1-1/e competitive ratio in the special case of small bids. It has been open ever since whether there is an algorithm for general bids better than the 0.5-competitive greedy algorithm. This paper presents a 0.5016-competitive algorithm for AdWords, answering this open question on the positive end. The algorithm builds on several ingredients, including a combination of the online primal dual framework and the configuration linear program of matching problems recently explored by Huang and Zhang (STOC 2020), a novel formulation of AdWords which we call the panorama view, and a generalization of the online correlated selection by Fahrbach, Huang, Tao, and Zadimorghaddam (FOCS 2020) which we call the panoramic online correlated selection.

Mehta and Panigrahi (2012) proposed Online Matching with Stochastic Rewards, which generalizes the Online Bipartite Matching problem of Karp, Vazirani, and Vazirani (1990) by associating the edges with success probabilities. This new feature captures the pay-per-click model in online advertising. Recently, Huang and Zhang (2020) studied this problem under the online primal dual framework using the Configuration Linear Program (LP), and got the best known competitive ratios of the Stochastic Balance algorithm. Their work suggests that the more expressive Configuration LP is more suitable for this problem than the Matching LP. This paper advances the theory of Configuration LP in two directions. Our technical contribution includes a characterization of the joint matching outcome of an offline vertex and all its neighbors. This characterization may be of independent interest, and is aligned with the spirit of Configuration LP. By contrast, previous analyses of Ranking generally focus on only one neighbor. Second, we designed a Stochastic Configuration LP that captures a stochastic benchmark proposed by Goyal and Udwani (2020), who used a Path-based LP. The Stochastic Configuration LP is smaller and simpler than the Path-based LP. Moreover, using the new LP we improved the competitive ratio of Stochastic Balance from 0.596 to 0.611 when the success probabilities are infinitesimal, and to 0.613 when the success probabilities are further equal.

Software-defined Network (SDN), presented to be a novel architecture of network because of its separation of data plane and control plane, brings centralization and extensibility to network management as well as new attacks that exploit the flexibility of SDN. OpenFlow, which is the protocol that is applied by the majority of SDN, leads to the widely used definition of the communication between the controller and the switch resulting in similar implementations regardless of different vendors. In this paper, we focus on the mechanisms of packet processing and topology discovery and their fundamental weaknesses caused by general implementations or device limitations. Despite the common vulnerabilities, the universal standard mechanisms of basic function in SDN also enlighten us to present an automated attack discovery method based on the formal verification with a generic model of SDN system. We describe the abstraction of the SDN components, their key functions, and communications along with the malicious operations that could be executed by malicious hosts and malicious switches and translate them into a formal model of the SDN system. The formal verification carried on with the assertion representing the security properties derived from the common vulnerabilities of the SDN system reports the potential attack paths each of which shows an attack process. Our evaluation shows that our method can discover feasible attack paths efficiently and effectively, with 23 attacks being identified, among which 2 are new. We further demonstrate the practicality of the 2 new attacks.

Feature-only partition of large graph data in distributed Graph Neural Network (GNN) training offers advantages over commonly adopted graph structure partition, such as minimal graph preprocessing cost and elimination of cross-worker subgraph sampling burdens. Nonetheless, performance bottle-neck of GNN training with feature-only partitions still largely lies in the substantial communication overhead due to cross-worker feature fetching. To reduce the communication overhead and expedite distributed training, we first investigate and answer two key questions on convergence behaviors of GNN model in feature-partition based distribute GNN training: 1) As no worker holds a complete copy of each feature, can gradient exchange among workers compensate for the information loss due to incomplete local features? 2) If the answer to the first question is negative, is feature fetching in every training iteration of the GNN model necessary to ensure model convergence? Based on our theoretical findings on these questions, we derive an optimal communication plan that decides the frequency for feature fetching during the training process, taking into account bandwidth levels among workers and striking a balance between model loss and training time. Extensive evaluation demonstrates consistent results with our theoretical analysis, and the effectiveness of our proposed design.

For a specific online optimization problem, for example, online bipartite matching (OBM), research efforts could be made in two directions before it is finally closed, i.e., the optimal competitive online algorithm is found. One is to continuously design algorithms with better performance. To this end, reinforcement learning (RL) has demonstrated great success in literature. However, little is known on the other direction: whether RL helps explore how hard an online problem is. In this paper, we study a generalized model of OBM, named online matching with stochastic rewards (OMSR, FOCS 2012), for which the optimal competitive ratio is still unknown. We adopt an adversarial RL approach that trains two RL agents adversarially and iteratively: the algorithm agent learns for algorithms with larger competitive ratios, while the adversarial agent learns to produce a family of hard instances. Through such a framework, agents converge at the end with a robust algorithm, which empirically outperforms the state of the art (STOC 2020). Much more significantly, it allows to track how the hard instances are generated. We succeed in distilling two structural properties from the learned graph patterns, which remarkably reduce the action space, and further enable theoretical improvement on the best-known hardness result of OMSR, from 0.621 (FOCS 2012) to 0.597. To the best of our knowledge, this gives the first evidence that RL can help enhance the theoretical understanding of an online problem.