Multi-step Reinforcement Learning: A Unifying Algorithm

Unifying seemingly disparate algorithmic ideas to produce better performing algorithms has been a longstanding goal in reinforcement learning. As a primary example, TD($\lambda$) elegantly unifies one-step TD prediction with Monte Carlo methods through the use of eligibility traces and the trace-decay parameter $\lambda$. Currently, there are a multitude of algorithms that can be used to perform TD control, including Sarsa, $Q$-learning, and Expected Sarsa. These methods are often studied in the one-step case, but they can be extended across multiple time steps to achieve better performance. Each of these algorithms is seemingly distinct, and no one dominates the others for all problems. In this paper, we study a new multi-step action-value algorithm called $Q(\sigma)$ which unifies and generalizes these existing algorithms, while subsuming them as special cases. A new parameter, $\sigma$, is introduced to allow the degree of sampling performed by the algorithm at each step during its backup to be continuously varied, with Sarsa existing at one extreme (full sampling), and Expected Sarsa existing at the other (pure expectation). $Q(\sigma)$ is generally applicable to both on- and off-policy learning, but in this work we focus on experiments in the on-policy case. Our results show that an intermediate value of $\sigma$, which results in a mixture of the existing algorithms, performs better than either extreme. The mixture can also be varied dynamically which can result in even greater performance.Comment: Appeared at the Thirty-Second AAAI Conference on Artificial Intelligence (AAAI-18

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

Addressing Function Approximation Error in Actor-Critic Methods

In value-based reinforcement learning methods such as deep Q-learning, function approximation errors are known to lead to overestimated value estimates and suboptimal policies. We show that this problem persists in an actor-critic setting and propose novel mechanisms to minimize its effects on both the actor and the critic. Our algorithm builds on Double Q-learning, by taking the minimum value between a pair of critics to limit overestimation. We draw the connection between target networks and overestimation bias, and suggest delaying policy updates to reduce per-update error and further improve performance. We evaluate our method on the suite of OpenAI gym tasks, outperforming the state of the art in every environment tested.Comment: Accepted at ICML 201

Learning with Options that Terminate Off-Policy

A temporally abstract action, or an option, is specified by a policy and a termination condition: the policy guides option behavior, and the termination condition roughly determines its length. Generally, learning with longer options (like learning with multi-step returns) is known to be more efficient. However, if the option set for the task is not ideal, and cannot express the primitive optimal policy exactly, shorter options offer more flexibility and can yield a better solution. Thus, the termination condition puts learning efficiency at odds with solution quality. We propose to resolve this dilemma by decoupling the behavior and target terminations, just like it is done with policies in off-policy learning. To this end, we give a new algorithm, Q(\beta), that learns the solution with respect to any termination condition, regardless of how the options actually terminate. We derive Q(\beta) by casting learning with options into a common framework with well-studied multi-step off-policy learning. We validate our algorithm empirically, and show that it holds up to its motivating claims.Comment: AAAI 201