Bayesian Optimization over Permutation Spaces

Abstract

Optimizing expensive to evaluate black-box functions over an input space consisting of all permutations of d objects is an important problem with many real-world applications. For example, placement of functional blocks in hardware design to optimize performance via simulations. The overall goal is to minimize the number of function evaluations to find high-performing permutations. The key challenge in solving this problem using the Bayesian optimization (BO) framework is to trade-off the complexity of statistical model and tractability of acquisition function optimization. In this paper, we propose and evaluate two algorithms for BO over Permutation Spaces (BOPS). First, BOPS-T employs Gaussian process (GP) surrogate model with Kendall kernels and a Tractable acquisition function optimization approach to select the sequence of permutations for evaluation. Second, BOPS-H employs GP surrogate model with Mallow kernels and a Heuristic search approach to optimize the acquisition function. We theoretically analyze the performance of BOPS-T to show that their regret grows sub-linearly. Our experiments on multiple synthetic and real-world benchmarks show that both BOPS-T and BOPS-H perform better than the state-of-the-art BO algorithm for combinatorial spaces. To drive future research on this important problem, we make new resources and real-world benchmarks available to the community.

Grey-Box Bayesian Optimization for Sensor Placement in Assisted Living Environments

“…Sample-efficient optimization of black-box functions. In recent work, Deshwal et al (2023) proposed a surrogate modeling approach for high-dimensional combinatorial spaces. They used a dictionary-based embedding to map discrete structures from the input space into an ordinal feature space, allowing the use of continuous surrogate models, such as the Gaussian process.…”

“…When this model represents f (x) accurately, the optimizer can perform more effective exploration/exploitation. A wide range of problems have been recently solved using BO, from optimization over permutation spaces (Deshwal et al 2022) and combinatorial spaces (Deshwal et al 2020(Deshwal et al , 2023 to setting up sensor networks for air quality monitoring (Hellan, Lucas, and Goddard 2022). However, the application of BO to optimize the sensor placement for indoor activity recognition has not been explored in previous work.…”

Bayesian Optimization for Macro Placement

“…Recently, BO was tested on similar but much smaller cases in (Deshwal et al, 2022). Their focus is on proposing a new kernel on permutations and it is orthogonal to our focus on the batch acquisition to tackle super-exponential growth.…”

“…Their focus is on proposing a new kernel on permutations and it is orthogonal to our focus on the batch acquisition to tackle super-exponential growth. In contrast to (Deshwal et al, 2022), our experiments were conducted on much larger spaces i.e., 3∼4 times more macros -in terms of the size of search space, this makes huge difference due to super-exponential growth of permutation spaces -and demonstrated the effectiveness of the batch acquisition. We leave the search for the optimal combination of the kernel and the batch acquisition for macro placement as a future work.…”

“…Especially when it is desirable to perform optimization close to the real objective, not a proxy, inevitable evaluation cost leaves only BO as a viable option. For the application to macro placement, more relevant is BO on combinatorial structures (Baptista and Poloczek, 2018;Oh et al, 2019;Oh et al, 2021;Deshwal et al, 2022). For the details on BO on combinatorial structures, please refer to the references.…”