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However, all known theoretical rates are worse than the rate of gradient descent, which synchronizes after every gradient step.

A common approach to this problem is to use a linear approximationVπ(s)=ϕ(s) x,whereϕ(s)isafeaturevectorofastate s.

More than twenty years after its introduction, Annealed Importance Sampling (AIS) remains oneofthemost effectivemethods formarginal likelihood estimation.

We also establish new convergence complexities to achieve an approximate KKT solution when the objective can be smooth/nonsmooth, deterministic/stochastic and convex/nonconvex with complexity that is on a par with gradient descent for unconstrained optimization problems in respective cases. To the best of our knowledge, this is the first study of the first-order methods with complexity guarantee for nonconvex sparse-constrained problems.

We experimentally show higher accuracy in gradient estimation and demonstrate a more stable and better performing training in deep convolutional modelswithbothproposedmethods.

Thecentral nodeisthe busiest node since it needs to communicate with each worker concurrently.

ProofofObservation4. Figure 2 (middle) depicts the plane of iteration of TMM. Now, we complete the proof by showing that{Uk}Kk=0 is nonincreasing. Optimality condition for strongly convex function implies that there existu g(x) such that f(x)+u+L(x x)=0. Linear coupling [4] interprets acceleration as a unification of gradient descent and mirror descent. The auxiliary iterates ofour setup are referred toasthe mirror descent iterates inthe linear coupling viewpoint.

Wherein, the first step, i.e. gradient estimation, is critical since it provides the essential direction to update variables, which have been explored by many recent works[5,30].