arXiv subjects

Armin Moharrer

Publications and source records attributed to Armin Moharrer.

4 recordsLinked to original sources

arXiv2021

Robust Regression via Model Based Methods

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, l_p 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) [35, 36], 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) [50] to solve the inner optimization in MBO. We show that SADM converges with the rate O(log T/T). Finally, we demonstrate experimentally (a) the robustness of l_p norms to outliers and (b) the efficiency of our proposed model-based algorithms in comparison with gradient methods on autoencoders and multi-target regression.

cs.LG↗

arXiv2021

Rate Allocation and Content Placement in Cache Networks

We introduce the problem of optimal congestion control in cache networks, whereby \emph{both} rate allocations and content placements are optimized \emph{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.

cs.NI↗

arXiv2021

Submodular Maximization via Taylor Series Approximation

We study submodular maximization problems with matroid constraints, in particular, problems where the objective can be expressed via compositions of analytic and multilinear functions. We show that for functions of this form, the so-called continuous greedy algorithm attains a ratio arbitrarily close to $(1-1/e) \approx 0.63$ using a deterministic estimation via Taylor series approximation. This drastically reduces execution time over prior art that uses sampling.

cs.LG↗

arXiv2019

Kelly Cache Networks

We study networks of M/M/1 queues in which nodes act as caches that store objects. Exogenous requests for objects are routed towards nodes that store them; as a result, object traffic in the network is determined not only by demand but, crucially, by where objects are cached. We determine how to place objects in caches to attain a certain design objective, such as, e.g., minimizing network congestion or retrieval delays. We show that for a broad class of objectives, including minimizing both the expected network delay and the sum of network queue lengths, this optimization problem can be cast as an NP- hard submodular maximization problem. We show that so-called continuous greedy algorithm attains a ratio arbitrarily close to $1 - 1/e \approx 0.63$ using a deterministic estimation via a power series; this drastically reduces execution time over prior art, which resorts to sampling. Finally, we show that our results generalize, beyond M/M/1 queues, to networks of M/M/k and symmetric M/D/1 queues.

cs.NI↗