  Statistical inference methods are fundamentally important in machine
learning. Most state-of-the-art inference algorithms are variants of Markov
chain Monte Carlo (MCMC) or variational inference (VI). However, both methods
struggle with limitations in practice: MCMC methods can be computationally
demanding; VI methods may have large bias. In this work, we aim to improve upon
MCMC and VI by a novel hybrid method based on the idea of reducing simulation
bias of finite-length MCMC chains using gradient-based optimisation. The
proposed method can generate low-biased samples by increasing the length of
MCMC simulation and optimising the MCMC hyper-parameters, which offers
attractive balance between approximation bias and computational efficiency. We
show that our method produces promising results on popular benchmarks when
compared to recent hybrid methods of MCMC and VI.
