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Rapid federated bilevel optimization (FBO) developments have attracted much attention in various emerging machine learning and communication applications. Existing work on FBO often assumes that clients participate in the learning process with some particular pattern (such as balanced participation), and/or in a synchronous manner, and/or with homogeneous local iteration numbers, which might be hard to hold in practice. This paper proposes a novel Anarchic Federated Bilevel Optimization (AFBO) algorithm, which allows clients to 1) participate in any inner or outer rounds; 2) participate asynchronously; and 3) participate with any number of local iterations. The AFBO algorithm enables clients to participate in FBO training flexibly. We provide a theoretical analysis of the learning loss of AFBO for both cases of non-convex and strongly convex loss functions. The convergence results of the AFBO algorithm match that of the existing benchmarks. Numerical studies are conducted to verify the effectiveness of AFBO. 

Abstract The design of high‐entropy single‐atom catalysts (HESAC) with 5.2 times higher entropy compared to single‐atom catalysts (SAC) is proposed, by using four different metals (FeCoNiRu‐HESAC) for oxygen reduction reaction (ORR). Fe active sites with intermetallic distances of 6.1 Å exhibit a low ORR overpotential of 0.44 V, which originates from weakening the adsorption of OH intermediates. Based on density functional theory (DFT) findings, the FeCoNiRu‐HESAC with a nitrogen‐doped sample were synthesized. The atomic structures are confirmed with X‐ray photoelectron spectroscopy (XPS), X‐ray absorption (XAS), and scanning transmission electron microscopy (STEM). The predicted high catalytic activity is experimentally verified, finding that FeCoNiRu‐HESAC has overpotentials of 0.41 and 0.37 V with Tafel slopes of 101 and 210 mVdec⁻¹at the current density of 1 mA cm⁻²and the kinetic current densities of 8.2 and 5.3 mA cm⁻², respectively, in acidic and alkaline electrolytes. These results are comparable with Pt/C. The FeCoNiRu‐HESAC is used for Zinc–air battery applications with an open circuit potential of 1.39 V and power density of 0.16 W cm⁻². Therefore, a strategy guided by DFT is provided for the rational design of HESAC which can be replaced with high‐cost Pt catalysts toward ORR and beyond.