SPQR: Controlling Q-ensemble Independence with Spiked Random Model for
  Reinforcement Learning
Dohyeok Lee Seungyub Han Taehyun Cho Jungwoo Lee
Alleviating overestimation bias is a critical challenge for deep
reinforcement learning to achieve successful performance on more complex tasks
or offline datasets containing out-of-distribution data. In order to overcome
overestimation bias, ensemble methods for Q-learning have been investigated to
exploit the diversity of multiple Q-functions. Since network initialization has
been the predominant approach to promote diversity in Q-functions,
heuristically designed diversity injection methods have been studied in the
literature. However, previous studies have not attempted to approach guaranteed
independence over an ensemble from a theoretical perspective. By introducing a
novel regularization loss for Q-ensemble independence based on random matrix
theory, we propose spiked Wishart Q-ensemble independence regularization (SPQR)
for reinforcement learning. Specifically, we modify the intractable hypothesis
testing criterion for the Q-ensemble independence into a tractable KL
divergence between the spectral distribution of the Q-ensemble and the target
Wigner's semicircle distribution. We implement SPQR in several online and
offline ensemble Q-learning algorithms. In the experiments, SPQR outperforms
the baseline algorithms in both online and offline RL benchmarks.