  Bayesian optimization (BO) conventionally relies on handcrafted acquisition
functions (AFs) to sequentially determine the sample points. However, it has
been widely observed in practice that the best-performing AF in terms of regret
can vary significantly under different types of black-box functions. It has
remained a challenge to design one AF that can attain the best performance over
a wide variety of black-box functions. This paper aims to attack this challenge
through the perspective of reinforced few-shot AF learning (FSAF).
Specifically, we first connect the notion of AFs with Q-functions and view a
deep Q-network (DQN) as a surrogate differentiable AF. While it serves as a
natural idea to combine DQN and an existing few-shot learning method, we
identify that such a direct combination does not perform well due to severe
overfitting, which is particularly critical in BO due to the need of a
versatile sampling policy. To address this, we present a Bayesian variant of
DQN with the following three features: (i) It learns a distribution of
Q-networks as AFs based on the Kullback-Leibler regularization framework. This
inherently provides the uncertainty required in sampling for BO and mitigates
overfitting. (ii) For the prior of the Bayesian DQN, we propose to use a demo
policy induced by an off-the-shelf AF for better training stability. (iii) On
the meta-level, we leverage the meta-loss of Bayesian model-agnostic
meta-learning, which serves as a natural companion to the proposed FSAF.
Moreover, with the proper design of the Q-networks, FSAF is general-purpose in
that it is agnostic to the dimension and the cardinality of the input domain.
Through extensive experiments, we demonstrate that the FSAF achieves comparable
or better regrets than the state-of-the-art benchmarks on a wide variety of
synthetic and real-world test functions.
