BOFormer: Learning to Solve Multi-Objective Bayesian Optimization via Non-Markovian RL
This addresses a key bottleneck in MOBO for applications like hyperparameter optimization, offering a novel solution to improve efficiency.
The paper tackles the hypervolume identifiability issue in multi-objective Bayesian optimization (MOBO) by proposing BOFormer, a non-Markovian reinforcement learning framework using Transformers, which consistently outperforms benchmark algorithms in synthetic and real-world problems.
Bayesian optimization (BO) offers an efficient pipeline for optimizing black-box functions with the help of a Gaussian process prior and an acquisition function (AF). Recently, in the context of single-objective BO, learning-based AFs witnessed promising empirical results given its favorable non-myopic nature. Despite this, the direct extension of these approaches to multi-objective Bayesian optimization (MOBO) suffer from the \textit{hypervolume identifiability issue}, which results from the non-Markovian nature of MOBO problems. To tackle this, inspired by the non-Markovian RL literature and the success of Transformers in language modeling, we present a generalized deep Q-learning framework and propose \textit{BOFormer}, which substantiates this framework for MOBO via sequence modeling. Through extensive evaluation, we demonstrate that BOFormer constantly outperforms the benchmark rule-based and learning-based algorithms in various synthetic MOBO and real-world multi-objective hyperparameter optimization problems. We have made the source code publicly available to encourage further research in this direction.