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We introduce the problem of optimal congestion control in cache networks, whereby both rate allocations and content placements are optimized jointly. We formulate this as a maximization problem with non-convex constraints, and propose solving this problem via (a) a Lagrangian barrier algorithm and (b) a convex relaxation. We prove different optimality guarantees for each of these two algorithms; our proofs exploit the fact that the non-convex constraints of our problem involve DR-submodular functions. 

The mean squared error loss is widely used in many applications, including auto-encoders, multi-target regression, and matrix factorization, to name a few. Despite computational advantages due to its differentiability, it is not robust to outliers. In contrast, ℓ𝑝 norms are known to be robust, but cannot be optimized via, e.g., stochastic gradient descent, as they are non-differentiable. We propose an algorithm inspired by so-called model-based optimization (MBO), which replaces a non-convex objective with a convex model function and alternates between optimizing the model function and updating the solution. We apply this to robust regression, proposing SADM, a stochastic variant of the Online Alternating Direction Method of Multipliers (OADM) to solve the inner optimization in MBO. We show that SADM converges with the rate 𝑂(log𝑇/𝑇) . Finally, we demonstrate experimentally (a) the robustness of ℓ𝑝 norms to outliers and (b) the efficiency of our proposed model-based algorithms in comparison with gradient methods on autoencoders and multi-target regression. 

Complex systems such as smart cities and smart power grids rely heavily on their interdependent components. The failure of a component in one network may lead to the failure of the supported component in another network. Components which support a large number of interdependent components may be more vulnerable to attacks and failures. In this paper, we study the robustness of two interdependent networks under node failures. By modeling each network using a random geometric graph (RGG), we study conditions for the percolation of two interdependent RGGs after in-homogeneous node failures. We derive analytical bounds on the interdependent degree thresholds (k 1 ,k 2 ), such that the interdependent RGGs percolate after removing nodes in G i that support more than k j nodes in G j (∀i, j ∈ {1, 2}, i ≠ j). We verify the bounds using numerical simulation, and show that there is a tradeoff between k 1 and k 2 for maintaining percolation after the failures.