Batch Multi-Fidelity Bayesian Optimization with Deep Auto-Regressive Networks
This work addresses the challenge of reducing optimization costs in multi-fidelity Bayesian optimization for applications like hyperparameter tuning, though it appears incremental by building on existing methods like Max-value Entropy Search.
The paper tackles the problem of optimizing expensive black-box functions with multiple fidelity levels by proposing BMBO-DARN, which uses deep auto-regressive networks and a batch querying method to improve surrogate learning and query diversity, achieving better performance on four real-world hyperparameter optimization applications.
Bayesian optimization (BO) is a powerful approach for optimizing black-box, expensive-to-evaluate functions. To enable a flexible trade-off between the cost and accuracy, many applications allow the function to be evaluated at different fidelities. In order to reduce the optimization cost while maximizing the benefit-cost ratio, in this paper, we propose Batch Multi-fidelity Bayesian Optimization with Deep Auto-Regressive Networks (BMBO-DARN). We use a set of Bayesian neural networks to construct a fully auto-regressive model, which is expressive enough to capture strong yet complex relationships across all the fidelities, so as to improve the surrogate learning and optimization performance. Furthermore, to enhance the quality and diversity of queries, we develop a simple yet efficient batch querying method, without any combinatorial search over the fidelities. We propose a batch acquisition function based on Max-value Entropy Search (MES) principle, which penalizes highly correlated queries and encourages diversity. We use posterior samples and moment matching to fulfill efficient computation of the acquisition function and conduct alternating optimization over every fidelity-input pair, which guarantees an improvement at each step. We demonstrate the advantage of our approach on four real-world hyperparameter optimization applications.