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This work studies multi-agent sharing optimization problems with the objective function being the sum of smooth local functions plus a convex (possibly non-smooth) function coupling all agents. This scenario arises in many machine learning and engineering ...
In this thesis, we explore techniques for addressing the communication bottleneck in data-parallel distributed training of deep learning models. We investigate algorithms that either reduce the size of the messages that are exchanged between workers, or th ...
We consider the problem of finding a saddle point for the convex-concave objective minxmaxyf(x)+⟨Ax,y⟩−g∗(y), where f is a convex function with locally Lipschitz gradient and g is convex and possibly non-smooth. We propose an ...
The ordering of communication channels was first introduced by Shannon. In this paper, we aim to find a characterization of the Shannon ordering. We show that W' contains W if and only if W is the skew-composition of W' with a convex-product channel. This ...
We consider finite-energy equivariant solutions for the wave map problem from ℝ2+1 to S2 which are close to the soliton family. We prove asymptotic orbital stability for a codimension-two class of initial data which is small with respect to a stronger topo ...
A general feature of particle transport in the core of tokamak plasmas is that when core particle sources are small, a stationary peaked density profile is provided by a balance of outward diffusion and inward convection, driven by either neoclassical or t ...
Two channels are said to be equivalent if they are degraded from each other. The space of equivalent channels with input alphabet X and output alphabet Y can be naturally endowed with the quotient of the Euclidean topology by the equivalence relation. We s ...
We address adaptive multivariate polynomial approximation by means of the discrete least-squares method with random evaluations, to approximate in the L2 probability sense a smooth function depending on a random variable distributed according to a given pr ...
