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In recent years, federated minimax optimization has attracted growing interest due to its extensive applications in various machine learning tasks. While Smoothed Alternative Gradient Descent Ascent (Smoothed-AGDA) has proved successful in centralized nonconvex minimax optimization, how and whether smoothing techniques could be helpful in a federated setting remains unexplored. In this paper, we propose a new algorithm termed Federated Stochastic Smoothed Gradient Descent Ascent (FESS-GDA), which utilizes the smoothing technique for federated minimax optimization. We prove that FESS-GDA can be uniformly applied to solve several classes of federated minimax problems and prove new or better analytical convergence results for these settings. We showcase the practical efficiency of FESS-GDA in practical federated learning tasks of training generative adversarial networks (GANs) and fair classification. 

Federated bilevel learning has received increasing attention in various emerging machine learning and communication applications. Recently, several Hessian-vector-based algorithms have been proposed to solve the federated bilevel optimization problem. However, several important properties in federated learning such as the partial client participation and the linear speedup for convergence (i.e., the convergence rate and complexity are improved linearly with respect to the number of sampled clients) in the presence of non-i.i.d.~datasets, still remain open. In this paper, we fill these gaps by proposing a new federated bilevel algorithm named FedMBO with a novel client sampling scheme in the federated hypergradient estimation. We show that FedMBO achieves a convergence rate of $$\mathcal{O}\big(\frac{1}{\sqrt{nK}}+\frac{1}{K}+\frac{\sqrt{n}}{K^{3/2}}\big)$$ on non-i.i.d.~datasets, where $$n$$ is the number of participating clients in each round, and $$K$$ is the total number of iteration. This is the first theoretical linear speedup result for non-i.i.d.~federated bilevel optimization. Extensive experiments validate our theoretical results and demonstrate the effectiveness of our proposed method. 

Abstract The structure of the critical zone (CZ) is a product of feedbacks among hydrologic, climatic, biotic, and chemical processes. Past research within snow‐dominated systems has shown that aspect‐dependent solar radiation inputs can produce striking differences in vegetation composition, topography, and soil depth between opposing hillslopes. However, far fewer studies have evaluated the role of microclimates on CZ development within rain‐dominated systems, especially below the soil and into weathered bedrock. To address this need, we characterized the CZ of a north‐facing and south‐facing slope within a first‐order headwater catchment located in central coast California. We combined terrain analysis of vegetation distribution and topography with soil pit characterization, geophysical surveys and hydrologic measurements between slope‐aspects. We documented denser vegetation and higher shallow soil moisture on north facing slopes, which matched previously documented observations in snow‐dominated sites. However, average topographic gradients were 24° and saprolite thickness was approximately 6 m across both hillslopes, which did not match common observations from the literature that showed widespread asymmetry in snow‐dominated systems. These results suggest that dominant processes for CZ evolution are not necessarily transferable across regions. Thus, there is a continued need to expand CZ research, especially in rain‐dominated and water‐limited systems. Here, we present two non‐exclusive mechanistic hypotheses that may explain these unexpected similarities in slope and saprolite thickness between hillslopes with opposing aspects. 

Bedrock weathering regulates nutrient mobilization, water storage, and soil production. Relative to the mobile soil layer, little is known about the relationship between topography and bedrock weathering. Here, we identify a common pattern of weathering and water storage across a sequence of three ridges and valleys in the sedimentary Great Valley Sequence in Northern California that share a tectonic and climate history. Deep drilling, downhole logging, and characterization of chemistry and porosity reveal two weathering fronts. The shallower front is ∼7 m deep at the ridge of all three hillslopes, and marks the extent of pervasive fracturing and oxidation of pyrite and organic carbon. A deeper weathering front marks the extent of open fractures and discoloration. This front is 11 m deep under two ridges of similar ridge-valley spacing, but 17.5 m deep under a ridge with nearly twice the ridge-valley spacing. Hence, at ridge tops, the fraction of the hillslope relief that is weathered scales with hillslope length. In all three hillslopes, below this second weathering front, closed fractures and unweathered bedrock extend about one-half the hilltop elevation above the adjacent channels. Neutron probe surveys reveal that seasonally dynamic moisture is stored to approximately the same depth as the shallow weathering front. Under the channels that bound our study hillslopes, the two weathering fronts coincide and occur within centimeters of the ground surface. Our findings provide evidence for feedbacks between erosion and weathering in mountainous landscapes that result in systematic subsurface structuring and water routing.