Sigmoidally Preconditioned Off-policy Learning:a new exploration method for reinforcement learning

One of the major difficulties of reinforcement learning is learning from {\em off-policy} samples, which are collected by a different policy (behavior policy) from what the algorithm evaluates (the target policy). Off-policy learning needs to correct the distribution of the samples from the behavior policy towards that of the target policy. Unfortunately, important sampling has an inherent high variance issue which leads to poor gradient estimation in policy gradient methods. We focus on an off-policy Actor-Critic architecture, and propose a novel method, called Preconditioned Proximal Policy Optimization (P3O), which can control the high variance of importance sampling by applying a preconditioner to the Conservative Policy Iteration (CPI) objective. {\em This preconditioning uses the sigmoid function in a special way that when there is no policy change, the gradient is maximal and hence policy gradient will drive a big parameter update for an efficient exploration of the parameter space}. This is a novel exploration method that has not been studied before given that existing exploration methods are based on the novelty of states and actions. We compare with several best-performing algorithms on both discrete and continuous tasks and the results confirmed that {\em P3O is more off-policy than PPO} according to the "off-policyness" measured by the DEON metric, and P3O explores in a larger policy space than PPO. Results also show that our P3O maximizes the CPI objective better than PPO during the training process.