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Sparse basis recovery is a classical and important statistical learning problem when the number of model dimensions p is much larger than the number of samples n. However, there has been little work that studies sparse basis recovery in the Federated Learning (FL) setting, where the client data’s differential privacy (DP) must also be simultaneously protected. In particular, the performance guarantees of existing DP-FL algorithms (such as DP-SGD) will degrade significantly when p >> n, and thus, they will fail to learn the true underlying sparse model accurately. In this work, we develop a new differentially private sparse basis recovery algorithm for the FL setting, called SPriFed-OMP. SPriFed-OMP converts OMP (Orthogonal Matching Pursuit) to the FL setting. Further, it combines SMPC (secure multi-party computation) and DP to ensure that only a small amount of noise needs to be added in order to achieve differential privacy. As a result, SPriFed-OMP can efficiently recover the true sparse basis for a linear model with only O(sqrt(p)) samples. We further present an enhanced version of our approach, SPriFed-OMP-GRAD based on gradient privatization, that improves the performance of SPriFed-OMP. Our theoretical analysis and empirical results demonstrate that both SPriFed-OMP and SPriFed-OMP-GRAD terminate in a small number of steps, and they significantly outperform the previous state-of-the-art DP-FL solutions in terms of the accuracy-privacy trade-off. 

We study a scheduling problem for a base-station transmitting status information to multiple user-equipments (UE) with the goal of minimizing the total expected Age-of-Information (AoI). Such a problem can be formulated as a Restless MultiArmed Bandit (RMAB) problem and solved asymptoticallyoptimally by a low-complexity Whittle index policy, if each UE’s sub-problem is Whittle indexable. However, proving Whittle indexability can be highly non-trivial, especially when the value function cannot be derived in closed-form. In particular, this is the case for the AoI minimization problem with stochastic arrivals and unreliable channels, whose Whittle indexability remains an open problem. To overcome this difficulty, we develop a sufficient condition for Whittle indexability based on the notion of active time (AT). Even though the AT condition shares considerable similarity to the Partial Conservation Law (PCL) condition, it is much easier to understand and verify. We then apply our AT condition to the stochastic-arrival unreliablechannel AoI minimization problem and, for the first time in the literature, prove its Whittle indexability. Our proof uses a novel coupling approach to verify the AT condition, which may also be of independent interest to other large-scale RMAB problems.