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  1. null (Ed.)
    In this work we consider the problem of online submodular maximization under a cardinality constraint with differential privacy (DP). A stream of T submodular functions over a common finite ground set U arrives online, and at each time-step the decision maker must choose at most k elements of U before observing the function. The decision maker obtains a profit equal to the function evaluated on the chosen set and aims to learn a sequence of sets that achieves low expected regret. In the full-information setting, we develop an (πœ€,𝛿)-DP algorithm with expected (1-1/e)-regret bound of 𝑂(π‘˜2log|π‘ˆ|𝑇logπ‘˜/π›Ώβˆšπœ€). This algorithm contains k ordered experts that learn the best marginal increments for each item over the whole time horizon while maintaining privacy of the functions. In the bandit setting, we provide an (πœ€,𝛿+𝑂(π‘’βˆ’π‘‡1/3))-DP algorithm with expected (1-1/e)-regret bound of 𝑂(logπ‘˜/π›Ώβˆšπœ€(π‘˜(|π‘ˆ|log|π‘ˆ|)1/3)2𝑇2/3). One challenge for privacy in this setting is that the payoff and feedback of expert i depends on the actions taken by her i-1 predecessors. This particular type of information leakage is not covered by post-processing, and new analysis is required. Our techniques for maintaining privacy with feedforward may be of independent interest. 
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  2. Cloud computing has motivated renewed interest in resource allocation problems with new consumption models. A common goal is to share a resource, such as CPU or I/O bandwidth, among distinct users with different demand patterns as well as different quality of service requirements. To ensure these service requirements, cloud offerings often come with a service level agreement (SLA) between the provider and the users. A SLA specifies the amount of a resource a user is entitled to utilize. In many cloud settings, providers would like to operate resources at high utilization while simultaneously respecting individual SLAs. There is typically a trade-off between these two objectives; for example, utilization can be increased by shifting away resources from idle users to β€œscavenger” workload, but with the risk of the former then becoming active again. We study this fundamental tradeoff by formulating a resource allocation model that captures basic properties of cloud computing systems, including SLAs, highly limited feedback about the state of the system, and variable and unpredictable input sequences. Our main result is a simple and practical algorithm that achieves near-optimal performance on the above two objectives. First, we guarantee nearly optimal utilization of the resource even if compared with the omniscient offline dynamic optimum. Second, we simultaneously satisfy all individual SLAs up to a small error. The main algorithmic tool is a multiplicative weight update algorithm and a primal-dual argument to obtain its guarantees. We also provide numerical validation on real data to demonstrate the performance of our algorithm in practical applications. 
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