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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. 

The popularization of Text-to-Image (T2I) diffusion mod- els enables the generation of high-quality images from text descriptions. However, generating diverse customized im- ages with reference visual attributes remains challenging. This work focuses on personalizing T2I diffusion models at a more abstract concept or category level, adapting com- monalities from a set of reference images while creating new instances with sufficient variations. We introduce a solution that allows a pretrained T2I diffusion model to learn a set of soft prompts, enabling the generation of novel images by sampling prompts from the learned distri- bution. These prompts offer text-guided editing capabilities and additional flexibility in controlling variation and mix- ing between multiple distributions. We also show the adapt- ability of the learned prompt distribution to other tasks, such as text-to-3D. Finally we demonstrate effectiveness of our approach through quantitative analysis including auto- matic evaluation and human assessment.