Neural Information Processing Systems http://nips.cc/

Bayesian Optimization (BO) is widely used for optimising black-box functions but requires us to specify the length scale hyperparameter, which defines the smoothness of the functions the optimizer will consider. Most current BO algorithms choose this hyperparameter by maximizing the marginal likelihood of the observed data, albeit risking misspecification if the objective function is less smooth in regions we have not yet explored. The only prior solution addressing this problem with theoretical guarantees was A-GP-UCB, proposed by Berkenkamp et al. (2019). This algorithm progressively decreases the length scale, expanding the class of functions considered by the optimizer. However, A-GP-UCB lacks a stopping mechanism, leading to over-exploration and slow convergence.

Leveraging this flexibility, we implement 47 novel MCBO algorithms and benchmark them against seven existing MCBO solvers and five standard black-box optimization algorithms on ten tasks, conducting over 4000 experiments.

Neural Information Processing Systems http://nips.cc/

The popularity of bi-level optimization (BO) in deep learning has spurred a growing interest in studying gradient-based BO algorithms.However, existing algorithms involve two coupled learning rates that can be affected by approximation errors when computing hypergradients, making careful fine-tuning necessary to ensure fast convergence. To alleviate this issue, we investigate the use of recently proposed adaptive step-size methods, namely stochastic line search (SLS) and stochastic Polyak step size (SPS), for computing both the upper and lower-level learning rates. First, we revisit the use of SLS and SPS in single-level optimization without the additional interpolation condition that is typically assumed in prior works. For such settings, we investigate new variants of SLS and SPS that improve upon existing suggestions in the literature and are simpler to implement. Importantly, these two variants can be seen as special instances of general family of methods with an envelope-type step-size. This unified envelope strategy allows for the extension of the algorithms and their convergence guarantees to BO settings. Finally, our extensive experiments demonstrate that the new algorithms, which are available in both SGD and Adam versions, can find large learning rates with minimal tuning and converge faster than corresponding vanilla SGD or Adam BO algorithms that require fine-tuning.

Kernelized bandits, also known as Bayesian optimization (BO), has been a prevalent method for optimizing complicated black-box reward functions. Various BO algorithms have been theoretically shown to enjoy upper bounds on their cumulative regret which are sub-linear in the number $T$ of iterations, and a regret lower bound of $\Omega(\sqrt{T})$ has been derived which represents the unavoidable regrets for any classical BO algorithm. Recent works on quantum bandits have shown that with the aid of quantum computing, it is possible to achieve tighter regret upper bounds better than their corresponding classical lower bounds. However, these works are restricted to either multi-armed or linear bandits, and are hence not able to solve sophisticated real-world problems with non-linear reward functions. To this end, we introduce the quantum-Gaussian process-upper confidence bound (Q-GP-UCB) algorithm. To the best of our knowledge, our Q-GP-UCB is the first BO algorithm able to achieve a regret upper bound of $\mathcal{O}(\text{poly}\log T)$, which is significantly smaller than its regret lower bound of $\Omega(\sqrt{T})$ in the classical setting. Moreover, thanks to our novel analysis of the confidence ellipsoid, our Q-GP-UCB with the linear kernel achieves a smaller regret than the quantum linear UCB algorithm from the previous work. We use simulations, as well as an experiment using a real quantum computer, to verify that the theoretical quantum speedup achieved by our Q-GP-UCB is also potentially relevant in practice.

For example, in hardware design optimization, we need to find the designs that trade-off performance, energy, and area overhead using expensive computational simulations.

Many safety-critical real-world problems, such as autonomous driving and collaborative robots, are of a distributed multi-agent nature. To optimize the performance of these systems while ensuring safety, we can cast them as distributed optimization problems, where each agent aims to optimize their parameters to maximize a coupled reward function subject to coupled constraints. Prior work either studies a centralized setting, does not consider safety, or struggles with sample efficiency. Since we require sample efficiency and work with unknown and nonconvex rewards and constraints, we solve this optimization problem using safe Bayesian optimization with Gaussian process regression. Moreover, we consider nearest-neighbor communication between the agents. To capture the behavior of non-neighboring agents, we reformulate the static global optimization problem as a time-varying local optimization problem for each agent, essentially introducing time as a latent variable. To this end, we propose a custom spatio-temporal kernel to integrate prior knowledge. We show the successful deployment of our algorithm in simulations.

Bayesian optimization (BO) is a powerful class of algorithms for optimizing expensive black-box functions, but designing effective BO algorithms remains a manual, expertise-driven task. Recent advancements in Large Language Models (LLMs) have opened new avenues for automating scientific discovery, including the automatic design of optimization algorithms. While prior work has used LLMs within optimization loops or to generate non-BO algorithms, we tackle a new challenge: Using LLMs to automatically generate full BO algorithm code. Our framework uses an evolution strategy to guide an LLM in generating Python code that preserves the key components of BO algorithms: An initial design, a surrogate model, and an acquisition function. The LLM is prompted to produce multiple candidate algorithms, which are evaluated on the established Black-Box Optimization Benchmarking (BBOB) test suite from the COmparing Continuous Optimizers (COCO) platform. Based on their performance, top candidates are selected, combined, and mutated via controlled prompt variations, enabling iterative refinement. Despite no additional fine-tuning, the LLM-generated algorithms outperform state-of-the-art BO baselines in 19 (out of 24) BBOB functions in dimension 5 and generalize well to higher dimensions, and different tasks (from the Bayesmark framework). This work demonstrates that LLMs can serve as algorithmic co-designers, offering a new paradigm for automating BO development and accelerating the discovery of novel algorithmic combinations. The source code is provided at https://github.com/Ewendawi/LLaMEA-BO.