Expected Policy Gradients

We propose expected policy gradients (EPG), which unify stochastic policy gradients (SPG) and deterministic policy gradients (DPG) for reinforcement learning. Inspired by expected sarsa, EPG integrates across the action when estimating the gradient, instead of relying only on the action in the sampled trajectory. We establish a new general policy gradient theorem, of which the stochastic and deterministic policy gradient theorems are special cases. We also prove that EPG reduces the variance of the gradient estimates without requiring deterministic policies and, for the Gaussian case, with no computational overhead. Finally, we show that it is optimal in a certain sense to explore with a Gaussian policy such that the covariance is proportional to the exponential of the scaled Hessian of the critic with respect to the actions. We present empirical results confirming that this new form of exploration substantially outperforms DPG with the Ornstein-Uhlenbeck heuristic in four challenging MuJoCo domains.Comment: Conference paper, AAAI-18, 12 pages including supplemen

Fourier Policy Gradients

We propose a new way of deriving policy gradient updates for reinforcement learning. Our technique, based on Fourier analysis, recasts integrals that arise with expected policy gradients as convolutions and turns them into multiplications. The obtained analytical solutions allow us to capture the low variance benefits of EPG in a broad range of settings. For the critic, we treat trigonometric and radial basis functions, two function families with the universal approximation property. The choice of policy can be almost arbitrary, including mixtures or hybrid continuous-discrete probability distributions. Moreover, we derive a general family of sample-based estimators for stochastic policy gradients, which unifies existing results on sample-based approximation. We believe that this technique has the potential to shape the next generation of policy gradient approaches, powered by analytical results

Better Exploration with Optimistic Actor-Critic

Actor-critic methods, a type of model-free Reinforcement Learning, have been successfully applied to challenging tasks in continuous control, often achieving state-of-the art performance. However, wide-scale adoption of these methods in real-world domains is made difficult by their poor sample efficiency. We address this problem both theoretically and empirically. On the theoretical side, we identify two phenomena preventing efficient exploration in existing state-of-the-art algorithms such as Soft Actor Critic. First, combining a greedy actor update with a pessimistic estimate of the critic leads to the avoidance of actions that the agent does not know about, a phenomenon we call pessimistic underexploration. Second, current algorithms are directionally uninformed, sampling actions with equal probability in opposite directions from the current mean. This is wasteful, since we typically need actions taken along certain directions much more than others. To address both of these phenomena, we introduce a new algorithm, Optimistic Actor Critic, which approximates a lower and upper confidence bound on the state-action value function. This allows us to apply the principle of optimism in the face of uncertainty to perform directed exploration using the upper bound while still using the lower bound to avoid overestimation. We evaluate OAC in several challenging continuous control tasks, achieving state-of the art sample efficiency.Comment: 20 pages (including supplement