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

Deep Conservative Policy Iteration

Conservative Policy Iteration (CPI) is a founding algorithm of Approximate Dynamic Programming (ADP). Its core principle is to stabilize greediness through stochastic mixtures of consecutive policies. It comes with strong theoretical guarantees, and inspired approaches in deep Reinforcement Learning (RL). However, CPI itself has rarely been implemented, never with neural networks, and only experimented on toy problems. In this paper, we show how CPI can be practically combined with deep RL with discrete actions. We also introduce adaptive mixture rates inspired by the theory. We experiment thoroughly the resulting algorithm on the simple Cartpole problem, and validate the proposed method on a representative subset of Atari games. Overall, this work suggests that revisiting classic ADP may lead to improved and more stable deep RL algorithms.Comment: AAAI 2020 (long version

IOB: Integrating Optimization Transfer and Behavior Transfer for Multi-Policy Reuse

Humans have the ability to reuse previously learned policies to solve new tasks quickly, and reinforcement learning (RL) agents can do the same by transferring knowledge from source policies to a related target task. Transfer RL methods can reshape the policy optimization objective (optimization transfer) or influence the behavior policy (behavior transfer) using source policies. However, selecting the appropriate source policy with limited samples to guide target policy learning has been a challenge. Previous methods introduce additional components, such as hierarchical policies or estimations of source policies' value functions, which can lead to non-stationary policy optimization or heavy sampling costs, diminishing transfer effectiveness. To address this challenge, we propose a novel transfer RL method that selects the source policy without training extra components. Our method utilizes the Q function in the actor-critic framework to guide policy selection, choosing the source policy with the largest one-step improvement over the current target policy. We integrate optimization transfer and behavior transfer (IOB) by regularizing the learned policy to mimic the guidance policy and combining them as the behavior policy. This integration significantly enhances transfer effectiveness, surpasses state-of-the-art transfer RL baselines in benchmark tasks, and improves final performance and knowledge transferability in continual learning scenarios. Additionally, we show that our optimization transfer technique is guaranteed to improve target policy learning.Comment: 26 pages, 9 figure

Lexicographic Multi-Objective Reinforcement Learning

In this work we introduce reinforcement learning techniques for solving lexicographic multi-objective problems. These are problems that involve multiple reward signals, and where the goal is to learn a policy that maximises the first reward signal, and subject to this constraint also maximises the second reward signal, and so on. We present a family of both action-value and policy gradient algorithms that can be used to solve such problems, and prove that they converge to policies that are lexicographically optimal. We evaluate the scalability and performance of these algorithms empirically, demonstrating their practical applicability. As a more specific application, we show how our algorithms can be used to impose safety constraints on the behaviour of an agent, and compare their performance in this context with that of other constrained reinforcement learning algorithms