Loaded DiCE: Trading off Bias and Variance in Any-Order Score Function Estimators for Reinforcement Learning
This addresses gradient estimation challenges in reinforcement learning, particularly for higher-order derivatives, though it appears incremental as an extension of existing score function estimators.
The paper tackles the problem of optimizing objectives in stochastic settings with unknown dynamics by developing an objective that produces low-variance unbiased estimators for derivatives of any order, compatible with arbitrary advantage estimators to control bias and variance. They demonstrate correctness in analytically tractable MDPs and achieve utility in meta-reinforcement-learning for continuous control.
Gradient-based methods for optimisation of objectives in stochastic settings with unknown or intractable dynamics require estimators of derivatives. We derive an objective that, under automatic differentiation, produces low-variance unbiased estimators of derivatives at any order. Our objective is compatible with arbitrary advantage estimators, which allows the control of the bias and variance of any-order derivatives when using function approximation. Furthermore, we propose a method to trade off bias and variance of higher order derivatives by discounting the impact of more distant causal dependencies. We demonstrate the correctness and utility of our objective in analytically tractable MDPs and in meta-reinforcement-learning for continuous control.