Context

Black-box optimization (also called derivative-free optimization or 0th-order optimization) refers to the optimization of an objective function without any knowledge about its closed form. One of the most popular subdomains of black-box optimization is Bayesian optimization (BO), which is performed by exploiting a Gaussian process (GP) as a surrogate model, based on the pioneering work [1]. BO is used in numerous applications where the objective function is too complex to be analytically modeled (e.g. hyperparameters tuning of deep neural networks [2], wireless communications [3] or computational biology [4]).

In such applications, the objective function often varies with time. Used in this particular context, BO is called dynamic Bayesian optimization (DBO). Although GPs can be naturally extended in space-time (e.g. see [5]), data staleness remains a fundamental problem to be addressed. In fact, since GP inference is in $O(n^3)$ for a dataset comprising $n$ observations, a criterion able to identify stale data is much needed for DBO to be fully effective in dynamic environments.

Subject

Such a criterion is currently researched at INDY lab. The student will handle the experimental side of the research, producing an efficient, friendly and well-documented implementation of the criterion and running numerous experiments to assess its performance.

The student will also be encouraged to get familiar with DBO in order to contribute to the design and improvement of the existing criterion. Exploring other applications of the criterion can also be considered.

Skills

• Excellent coding skills (Python, C++).
• Familiarity with stochastic processes.
• An experience in building Python libraries with a C++ backend would be a plus.
• Excellent calculus (mostly integration) and algebra skills would be a plus.
• Familiarity with Bayesian optimization would be a plus.

References

[1] Williams, C., & Rasmussen, C. (1995). Gaussian processes for regression. Advances in neural information processing systems, 8.

[2] Bergstra, J., Yamins, D., & Cox, D. (2013, February). Making a science of model search: Hyperparameter optimization in hundreds of dimensions for vision architectures. In International conference on machine learning (pp. 115-123). PMLR.

[3] Bardou, A., & Begin, T. (2022, October). Inspire: Distributed bayesian optimization for improving spatial reuse in dense wlans. In Proceedings of the 25th International ACM Conference on Modeling Analysis and Simulation of Wireless and Mobile Systems (pp. 133-142).

[4] González, J., Dai, Z., Hennig, P., & Lawrence, N. (2016, May). Batch Bayesian optimization via local penalization. In Artificial intelligence and statistics (pp. 648-657). PMLR.

[5] Nyikosa, F. M., Osborne, M. A., & Roberts, S. J. (2018). Bayesian optimization for dynamic problems. arXiv preprint arXiv:1803.03432.