40 problems

Fixed-step-size convergence conjecture. The algorithm should converge with rate

Inflection-point conjecture. The convergence performance of NIDS should also have an inflection point.

Let $F_m$ denote the objective of client $m$, let $F$ be the global objective, and let $H$, $B$, and $\sigma$ denote the smoothness, initial-distance, and noise parameters, respect…

Maximum-eigenvalue slowdown conjecture. For more general data distributions, a weaker version of this theorem holds, perhaps only for the maximum eigenvalue of

General-distribution conjecture. Similar results hold for other data distributions.

Consider decentralized learning on a directed graph in which communication edge weights are optimized using the agents' data distributions. An optimized topology is the resulting w…

In directed distributed learning, let the communication graph topology be refined dynamically by adjusting its edge weights during training. Dynamic topology refinement conjecture.…

Let the global objective function be the sum of the agents' local objective functions, and suppose that it satisfies the Polyak–Łojasiewicz (PL) inequality, without necessarily bei…

Unbiased-compressor lower-bound conjecture. The lower bounds proved in the paper should also hold for the entire family of unbiased compressors.

Let $\calA^t$ denote the set of active clients, let $p_i^t=\mathbb{E}[\Indc_{\{i\in\calA^t\}}]$ be client $i$'s availability probability in round $t$, and consider federated learni…

Geometric interpolation conjecture. For all $\mathcal{K}>0$, $\kappa_1,\kappa_2>0$, and $\theta\in[0,1]$, the mixed-conditioning performance satisfies

Stability-extension conjecture. Due to the q-linear optimizer convergence of Algorithm1 of Hours et al., Theorem should also hold under suitable assumptions if dSQP is replaced wit…

The linear-speedup conjecture. Such linear speedup cannot be obtained for sIAG under these realistic conditions in which $\bm{w}^t$ is not independent of $\bm{g}^t$.

In federated learning with inter-agent communication, let the agents' communication network become sufficiently dense. Dense-network conjecture. Server communication rounds might h…

The algorithm operates on local gradients computed on each GPU, without averaging those gradients across all machines before clipping. Conjecture. The more frequent clipping observ…

In the scalable compressed gossip setting, let $gamma$ denote the algorithm's step-size parameter, let $omega$ denote its compression parameter, and let the convergence rate refer…

In decentralized training, computing nodes may be organized using different communication topologies, including a ring topology. The batch size is the number of training examples p…

DecentLaM uses partial averaging, which can cause the models maintained by different nodes to be inconsistent. Model-inconsistency hypothesis. This model inconsistency helps the al…

Periodic-communication lower-bound conjecture. Unless restrictive assumptions are imposed on the level of statistical or objective heterogeneity, a lower bound of this type should…

Local-step utility conjecture. The phenomenon that increasing $H$ does not improve the convergence rate may be an artifact of a conservative analysis of $\texttt{FedLin}$; a more r…

Let $M$ be the number of machines, and consider the lower bound for the optimization error in the massively parallel regime described above. Logarithmic-factor conjecture. We conje…

Consider the distributed empirical risk minimization (ERM) setting, in which a fixed finite collection of objectives is optimized, and let FedAc denote the federated accelerated st…

Let $f$ be $bc$-strongly convex and $L$-smooth. Consider the same penalized optimization setting and technique as in the preceding convex, $L$-smooth case, where $A^\top A x$ calcu…

The experiments compare hierarchical federated learning (HFL) and federated learning (FL) on CIFAR-10, including sparse variants, and observe a small degradation in the accuracy of…

Let $(\alpha,\beta,\gamma,\delta)$ denote the parameters of the SVL algorithm, and consider algorithms in the form of Algorithm whose convergence can be certified using Theorem. SV…