15 problems

Gradient accumulation uses large-batch samples for gradient evaluation. Gradient-accumulation generalization conjecture. Although gradient accumulation can help during optimization…

Oracle-call optimality conjecture. For the class of methods that require an optimal number of communication rounds, these bounds are also optimal, up to polylogarithmic factors, in…

In decentralized optimization over time-varying networks, let $\chi$ denote the network condition number, and consider the communication complexity of solving non-smooth convex opt…

Consider the upper bounds on time complexity obtained in the paper for the stated classes of convex functions and stochastic optimization problems, including the homogeneous and he…

Let $T_{\textnormal{star}}$ denote the time-complexity bound for decentralized stochastic optimization on the star graph described above, with heterogeneous worker computation time…

In decentralized optimization over directed networks with column-stochastic, row-stochastic, or alternating column- and row-stochastic mixing matrices, let the equilibrium skewness…

Non-tight-analysis conjecture. The worse result is caused by the possibly non-tight analysis.

Global convergence conjecture. Global convergence results with inexact subproblem solutions may be derived using merit functions.

Consider the Acc-DNGD algorithm with diminishing step-size … and let $f(\bar{x}^K)-f(x^*)$ denote its average functional error, where $f(x)=\frac{1}{N}\sum_{i=1}^N f_i(x)$ and…

The Acc-DNGD algorithm uses a diminishing step-size … where $\eta$ and $k_0$ are parameters, and its average functional error is measured by $f(\bar{x}^k)-f(x^*)$, with…

Decentralized stochastic gradient descent (D-SGD) is an optimization method in which agents communicate over a network and use stochastic gradients; data heterogeneity refers to di…

Let $\kappa_g$ denote the global condition number, and let $\bar{y}_t$, $x^*$, and $V_t$ be the quantities defined in the algorithm and its analysis, with $V_t$ defined in the proo…

Optimality conjecture. Under these assumptions, the obtained bound for zeroth-order oracle calculations per node is optimal up to polylogarithmic factors among methods with an opti…

Let the synchronous distributed optimization algorithm use a parameter $Delta$ that may change during an execution. Convergence conjecture. The algorithm will work as intended even…

Distributed convergence-rate conjecture. For a broad range of centralized algorithms, the distributed algorithm obtained in this way should have a similar convergence rate to the c…