Solving a sequence of high-dimensional, nonconvex, but potentially similar optimization problems poses a significant computational challenge in various engineering applications. This thesis presents the first meta-learning framework that leverages the shared structure among sequential tasks to improve the computational efficiency and sample complexity of derivative-free optimization. Based on the observation that most practical high-dimensional functions lie on a latent low-dimensional manifold, which can be further shared among problem instances, the proposed method jointly learns the meta-initialization of a search point and a meta-manifold. This novel approach enables the efficient adaptation of the optimization process to new tasks by exploiting the learned meta-knowledge. Theoretically, the benefit of meta-learning in this challenging setting is established by proving that the proposed method achieves improved convergence rates and reduced sample complexity compared to traditional derivative-free optimization techniques. Empirically, the effectiveness of the proposed algorithm is demonstrated in two high-dimensional reinforcement learning tasks, showcasing its ability to accelerate learning and improve performance across multiple domains. Furthermore, the robustness and generalization capabilities of the meta-learning framework are explored through extensive ablation studies and sensitivity analyses. The thesis highlights the potential of meta-learning in tackling complex optimization problems and opens up new avenues for future research in this area. / Master of Science / Optimization problems are ubiquitous in various fields, from engineering to finance, where the goal is to find the best solution among a vast number of possibilities. However, solving these problems can be computationally challenging, especially when the search space is high-dimensional and the problem is nonconvex, meaning that there may be multiple locally optimal solutions. This thesis introduces a novel approach to tackle these challenges by leveraging the power of meta-learning, a technique that allows algorithms to learn from previous experiences and adapt to new tasks more efficiently.
The proposed framework is based on the observation that many real-world optimization problems share similar underlying structures, even though they may appear different on the surface. By exploiting this shared structure, the meta-learning algorithm can learn a low-dimensional representation of the problem space, which serves as a guide for efficiently searching for optimal solutions in new, unseen problems. This approach is particularly useful when dealing with a sequence of related optimization tasks, as it allows the algorithm to transfer knowledge from one task to another, thereby reducing the computational burden and improving the overall performance.
The effectiveness of the proposed meta-learning framework is demonstrated through rigorous theoretical analysis and empirical evaluations on challenging reinforcement learning tasks. These tasks involve high-dimensional search spaces and require the algorithm to adapt to changing environments. The results show that the meta-learning approach can significantly accelerate the learning process and improve the quality of the solutions compared to traditional optimization methods.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/119325 |
| Date | 06 1900 |
| Creators | Sel, Bilgehan |
| Contributors | Electrical and Computer Engineering, Jin, Ming, Jia, Ruoxi, Ramakrishnan, Naren |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis, Text |
| Format | ETD, application/pdf, application/pdf |
| Rights | Creative Commons Attribution-NonCommercial 4.0 International, http://creativecommons.org/licenses/by-nc/4.0/ |
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