Alexandre Maraval

Alexandre Maraval, Matthieu Zimmer, Antoine Grosnit et al.

Faced with problems of increasing complexity, recent research in Bayesian Optimisation (BO) has focused on adapting deep probabilistic models as flexible alternatives to Gaussian Processes (GPs). In a similar vein, this paper investigates the feasibility of employing state-of-the-art probabilistic transformers in BO. Upon further investigation, we observe two drawbacks stemming from their training procedure and loss definition, hindering their direct deployment as proxies in black-box optimisation. First, we notice that these models are trained on uniformly distributed inputs, which impairs predictive accuracy on non-uniform data - a setting arising from any typical BO loop due to exploration-exploitation trade-offs. Second, we realise that training losses (e.g., cross-entropy) only asymptotically guarantee accurate posterior approximations, i.e., after arriving at the global optimum, which generally cannot be ensured. At the stationary points of the loss function, however, we observe a degradation in predictive performance especially in exploratory regions of the input space. To tackle these shortcomings we introduce two components: 1) a BO-tailored training prior supporting non-uniformly distributed points, and 2) a novel approximate posterior regulariser trading-off accuracy and input sensitivity to filter favourable stationary points for improved predictive performance. In a large panel of experiments, we demonstrate, for the first time, that one transformer pre-trained on data sampled from random GP priors produces competitive results on 16 benchmark black-boxes compared to GP-based BO. Since our model is only pre-trained once and used in all tasks without any retraining and/or fine-tuning, we report an order of magnitude time-reduction, while matching and sometimes outperforming GPs.

Rasul Tutunov, Alexandre Maraval, Antoine Grosnit et al.

Sphere packing, Hilbert's eighteenth problem, asks for the densest arrangement of congruent spheres in n-dimensional Euclidean space. Although relevant to areas such as cryptography, crystallography, and medical imaging, the problem remains unresolved: beyond a few special dimensions, neither optimal packings nor tight upper bounds are known. Even a major breakthrough in dimension $n=8$, later recognised with a Fields Medal, underscores its difficulty. A leading technique for upper bounds, the three-point method, reduces the problem to solving large, high-precision semidefinite programs (SDPs). Because each candidate SDP may take days to evaluate, standard data-intensive AI approaches are infeasible. We address this challenge by formulating SDP construction as a sequential decision process, the SDP game, in which a policy assembles SDP formulations from a set of admissible components. Using a sample-efficient model-based framework that combines Bayesian optimisation with Monte Carlo Tree Search, we obtain new state-of-the-art upper bounds in dimensions $4-16$, showing that model-based search can advance computational progress in longstanding geometric problems. Together, these results demonstrate that sample-efficient, model-based search can make tangible progress on mathematically rigid, evaluation limited problems, pointing towards a complementary direction for AI-assisted discovery beyond large-scale LLM-driven exploration.

Zhongwei Yu, Rasul Tutunov, Alexandre Max Maraval et al.

Traditional scientific discovery relies on an iterative hypothesise-experiment-refine cycle that has driven progress for centuries, but its intuitive, ad-hoc implementation often wastes resources, yields inefficient designs, and misses critical insights. This tutorial presents Bayesian Optimisation (BO), a principled probability-driven framework that formalises and automates this core scientific cycle. BO uses surrogate models (e.g., Gaussian processes) to model empirical observations as evolving hypotheses, and acquisition functions to guide experiment selection, balancing exploitation of known knowledge and exploration of uncharted domains to eliminate guesswork and manual trial-and-error. We first frame scientific discovery as an optimisation problem, then unpack BO's core components, end-to-end workflows, and real-world efficacy via case studies in catalysis, materials science, organic synthesis, and molecule discovery. We also cover critical technical extensions for scientific applications, including batched experimentation, heteroscedasticity, contextual optimisation, and human-in-the-loop integration. Tailored for a broad audience, this tutorial bridges AI advances in BO with practical natural science applications, offering tiered content to empower cross-disciplinary researchers to design more efficient experiments and accelerate principled scientific discovery.

Alexander I. Cowen-Rivers, Wenlong Lyu, Rasul Tutunov et al.

In this work we rigorously analyse assumptions inherent to black-box optimisation hyper-parameter tuning tasks. Our results on the Bayesmark benchmark indicate that heteroscedasticity and non-stationarity pose significant challenges for black-box optimisers. Based on these findings, we propose a Heteroscedastic and Evolutionary Bayesian Optimisation solver (HEBO). HEBO performs non-linear input and output warping, admits exact marginal log-likelihood optimisation and is robust to the values of learned parameters. We demonstrate HEBO's empirical efficacy on the NeurIPS 2020 Black-Box Optimisation challenge, where HEBO placed first. Upon further analysis, we observe that HEBO significantly outperforms existing black-box optimisers on 108 machine learning hyperparameter tuning tasks comprising the Bayesmark benchmark. Our findings indicate that the majority of hyper-parameter tuning tasks exhibit heteroscedasticity and non-stationarity, multi-objective acquisition ensembles with Pareto front solutions improve queried configurations, and robust acquisition maximisers afford empirical advantages relative to their non-robust counterparts. We hope these findings may serve as guiding principles for practitioners of Bayesian optimisation. All code is made available at https://github.com/huawei-noah/HEBO.

Antoine Grosnit, Alexandre Maraval, Refinath S N et al.

Human expertise emerges through iterative cycles of interaction, reflection, and internal model updating, which are central to cognitive theories such as Kolb's experiential learning and Vygotsky's zone of proximal development. In contrast, current AI systems, particularly LLM agents, rely on static pre-training or rigid workflows, lacking mechanisms for continual adaptation. Recent studies identified early cognitive traits in LLM agents (reflection, revision, and self-correction) suggesting foundational elements of human-like experiential learning. Thus the key question: Can we design LLM agents capable of structured, cognitively grounded learning similar to human processes? In response, we propose a computational framework of Kolb's learning cycle with Vygotsky's ZPD for autonomous agents. Our architecture separates extrinsic (environment interaction) and intrinsic (internal reflection/abstraction) functions, enabling cognitively grounded scaffolded learning, where the agent initially learns within structured environments, followed by open-ended generalisation. This approach empowers agents to master complex tasks ; domains that traditional fine-tuning or simple reflective methods could not tackle effectively. Its potential is powerfully demonstrated via direct comparison with humans in real-world Kaggle data science competitions. Learning fully automated data science code generation across 81 tasks, our system, Agent K, demonstrated the ability to perform the entire workflow autonomously, achieving an Elo-MMR score of 1694, beyond median score of the Kaggle Masters (the top 2% among 200,000 users) of our study. With 9 gold, 8 silver, and 12 bronze medals level performance - including 4 gold and 4 silver on prize-awarding competitions - Agent K is the 1st AI system to successfully integrate Kolb- and Vygotsky-inspired human cognitive learning, marking a major step toward generalist AI.

Alexandre Maraval, Matthieu Zimmer, Antoine Grosnit et al.

Meta-Bayesian optimisation (meta-BO) aims to improve the sample efficiency of Bayesian optimisation by leveraging data from related tasks. While previous methods successfully meta-learn either a surrogate model or an acquisition function independently, joint training of both components remains an open challenge. This paper proposes the first end-to-end differentiable meta-BO framework that generalises neural processes to learn acquisition functions via transformer architectures. We enable this end-to-end framework with reinforcement learning (RL) to tackle the lack of labelled acquisition data. Early on, we notice that training transformer-based neural processes from scratch with RL is challenging due to insufficient supervision, especially when rewards are sparse. We formalise this claim with a combinatorial analysis showing that the widely used notion of regret as a reward signal exhibits a logarithmic sparsity pattern in trajectory lengths. To tackle this problem, we augment the RL objective with an auxiliary task that guides part of the architecture to learn a valid probabilistic model as an inductive bias. We demonstrate that our method achieves state-of-the-art regret results against various baselines in experiments on standard hyperparameter optimisation tasks and also outperforms others in the real-world problems of mixed-integer programming tuning, antibody design, and logic synthesis for electronic design automation.

Antoine Grosnit, Rasul Tutunov, Alexandre Max Maraval et al.

We introduce a method combining variational autoencoders (VAEs) and deep metric learning to perform Bayesian optimisation (BO) over high-dimensional and structured input spaces. By adapting ideas from deep metric learning, we use label guidance from the blackbox function to structure the VAE latent space, facilitating the Gaussian process fit and yielding improved BO performance. Importantly for BO problem settings, our method operates in semi-supervised regimes where only few labelled data points are available. We run experiments on three real-world tasks, achieving state-of-the-art results on the penalised logP molecule generation benchmark using just 3% of the labelled data required by previous approaches. As a theoretical contribution, we present a proof of vanishing regret for VAE BO.

Vincent Moens, Hang Ren, Alexandre Maraval et al.

In this paper, we propose CI-VI an efficient and scalable solver for semi-implicit variational inference (SIVI). Our method, first, maps SIVI's evidence lower bound (ELBO) to a form involving a nonlinear functional nesting of expected values and then develops a rigorous optimiser capable of correctly handling bias inherent to nonlinear nested expectations using an extrapolation-smoothing mechanism coupled with gradient sketching. Our theoretical results demonstrate convergence to a stationary point of the ELBO in general non-convex settings typically arising when using deep network models and an order of $O(t^{-\frac{4}{5}})$ gradient-bias-vanishing rate. We believe these results generalise beyond the specific nesting arising from SIVI to other forms. Finally, in a set of experiments, we demonstrate the effectiveness of our algorithm in approximating complex posteriors on various data-sets including those from natural language processing.