Long Luo

Luo Long, Coralia Cartis, Paz Fink Shustin

Bayesian optimisation (BO) is a standard approach for sample-efficient global optimisation of expensive black-box functions, yet its scalability to high dimensions remains challenging. Here, we investigate nonlinear dimensionality reduction techniques that reduce the problem to a sequence of low-dimensional Latent-Space BO (LSBO). While early LSBO methods used (linear) random projections (Wang et al., 2013), building on Grosnit et al. (2021), we employ Variational Autoencoders (VAEs) for LSBO, focusing on deep metric loss for structured latent manifolds and VAE retraining to adapt the encoder-decoder to newly sampled regions. We propose some changes in their implementation, originally designed for tasks such as molecule generation, and reformulate the algorithm for broader optimisation purposes. We then couple LSBO with Sequential Domain Reduction (SDR) directly in the latent space (SDR-LSBO), yielding an algorithm that narrows the latent search domains as evidence accumulates. Implemented in a GPU-accelerated BoTorch stack with Matern-5/2 Gaussian process surrogates, our numerical results show improved optimisation quality across benchmark tasks and that structured latent manifolds improve BO performance. Additionally, we compare random embeddings and VAEs as two mechanisms for dimensionality reduction, showing that the latter outperforms the former. To the best of our knowledge, this is the first study to combine SDR with VAE-based LSBO, and our analysis clarifies design choices for metric shaping and retraining that are critical for scalable latent space BO. For reproducibility, our source code is available at https://github.com/L-Lok/Nonlinear-Dimensionality-Reduction-Techniques-for-Bayesian-Optimization.git.

Luo Long, Coralia Cartis, Paz Fink Shustin

Bayesian Optimisation (BO) is a state-of-the-art global optimisation technique for black-box problems where derivative information is unavailable, and sample efficiency is crucial. However, improving the general scalability of BO has proved challenging. Here, we explore Latent Space Bayesian Optimisation (LSBO), that applies dimensionality reduction to perform BO in a reduced-dimensional subspace. While early LSBO methods used (linear) random projections (Wang et al., 2013), we employ Variational Autoencoders (VAEs) to manage more complex data structures and general DR tasks. Building on Grosnit et. al. (2021), we analyse the VAE-based LSBO framework, focusing on VAE retraining and deep metric loss. We suggest a few key corrections in their implementation, originally designed for tasks such as molecule generation, and reformulate the algorithm for broader optimisation purposes. Our numerical results show that structured latent manifolds improve BO performance. Additionally, we examine the use of the Matérn-$\frac{5}{2}$ kernel for Gaussian Processes in this LSBO context. We also integrate Sequential Domain Reduction (SDR), a standard global optimization efficiency strategy, into BO. SDR is included in a GPU-based environment using \textit{BoTorch}, both in the original and VAE-generated latent spaces, marking the first application of SDR within LSBO.

Wenjiao Feng, Rongxing Xiao, Zonghang Li et al.

Node and link churn in multi-party, cross-region clusters over wide-area networks (WANs) often disrupts distributed training. However, checkpoint-based recovery and cloud-centric autoscaling react slowly and assume centralized control, which is misaligned with the self-governed setup where institutions can freely join and leave. This paper proposes Chaos, a multi-party distributed training system with self-healing and autoscaling, enabling robust and elastic training under churn. It speeds up autoscaling via multi-neighbor state replication and model sharding. We formalize the sharding and assignment as a MINLP that captures WAN heterogeneity, and reduce it to a tractable MILP by analyzing its monotonicity on a divisibility chain. By establishing an equivalence, we derive a greedy algorithm that follows optimality rules and yields the optimal solution in polynomial time. Chaos uses a cluster monitor to track resource and topology changes, and handles scaling events through peer negotiation protocols, enabling fully self-governed autoscaling among institutions. Experiments show that Chaos has substantially lower scale-out delay than Pollux, Elan, and Autoscaling, and handles scale-in, connect-link, and disconnect-link events within 20ms. It also delivers the lowest idle time, showing superior resource use and scalability as the cluster grows.