title: Reinforcement Learning Curricula as Interpolations between Task Distributions
Creators: name: Klink, Pascal
Publisher: name: UNSPECIFIED
Year: 2023

description: In the last decade, the increased availability of powerful computing machinery has led to an increasingly widespread application of machine learning methods. Machine learning has been particularly successful when large models, typically neural networks with an ever-increasing number of parameters, can leverage vast data to make predictions. While reinforcement learning (RL) has been no exception from this development, a distinguishing feature of RL is its well-known exploration-exploitation trade-off, whose optimal solution – while possible to model as a partially observable Markov decision process – evades computation in all but the simplest problems. Consequently, it seems unsurprising that notable demonstrations of reinforcement learning, such as an RL-based Go agent (AlphaGo) by Deepmind beating the professional Go player Lee Sedol, relied both on the availability of massive computing capabilities and specific forms of regularization that facilitate learning. In the case of AlphaGo, this regularization came in the form of self-play, enabling learning by interacting with gradually more proficient opponents. In this thesis, we develop techniques that, similarly to the concept of self-play of AlphaGo, improve the learning performance of RL agents by training on sequences of increasingly complex tasks. These task sequences are typically called curricula and are known to side-step problems such as slow learning or convergence to poor behavior that may occur when directly learning in complicated tasks. The algorithms we develop in this thesis create curricula by minimizing distances or divergences between probability distributions of learning tasks, generating interpolations between an initial distribution of easy learning tasks and a target task distribution. Apart from improving the learning performance of RL agents in experiments, developing methods that realize curricula as interpolations between task distributions results in a nuanced picture of key aspects of successful reinforcement learning curricula. In Chapter 1, we start this thesis by introducing required reinforcement learning notation and then motivating curriculum reinforcement learning from the perspective of continuation methods for non-linear optimization. Similar to curricula for reinforcement learning agents, continuation methods have been used in non-linear optimization to solve challenging optimization problems. This similarity provides an intuition about the effect of the curricula we aim to generate and their limits. In Chapter 2, we transfer the concept of self-paced learning, initially proposed in the supervised learning community, to the problem of RL, showing that an automated curriculum generation for RL agents can be motivated by a regularized RL objective. This regularized RL objective implies generating a curriculum as a sequence of task distributions that trade off the expected agent performance against similarity to a specified distribution of target tasks. This view on curriculum RL contrasts existing approaches, as it motivates curricula via a regularized RL objective instead of generating them from a set of assumptions about an optimal curriculum. In experiments, we show that an approximate implementation of the aforementioned curriculum – that restricts the interpolating task distribution to a Gaussian – results in improved learning performance compared to regular reinforcement learning, matching or surpassing the performance of existing curriculum-based methods. Subsequently, Chapter 3 builds up on the intuition of curricula as sequences of interpolating task distributions established in Chapter 2. Motivated by using more flexible task distribution representations, we show how parametric assumptions play a crucial role in the empirical success of the previous approach and subsequently uncover key ingredients that enable the generation of meaningful curricula without assuming a parametric model of the task distributions. One major ingredient is an explicit notion of task similarity via a distance function of two Markov Decision Processes. We turn towards optimal transport theory, allowing for flexible particle-based representations of the task distributions while properly considering the newly introduced metric structure of the task space. Combined with other improvements to our first method, such as a more aggressive restriction of the curriculum to tasks that are not too hard for the agent, the resulting approach delivers consistently high learning performance in multiple experiments. In the final Chapter 4, we apply the refined method of Chapter 3 to a trajectory-tracking task, in which we task an RL agent to follow a three-dimensional reference trajectory with the tip of an inverted pendulum mounted on a Barrett Whole Arm Manipulator. The access to only positional information results in a partially observable system that, paired with its inherent instability, underactuation, and non-trivial kinematic structure, presents a challenge for modern reinforcement learning algorithms, which we tackle via curricula. The technically infinite-dimensional task space of target trajectories allows us to probe the developed curriculum learning method for flaws that have not surfaced in the rather low-dimensional experiments of the previous chapters. Through an improved optimization scheme that better respects the non-Euclidean structure of target trajectories, we reliably generate curricula of trajectories to be tracked, resulting in faster and more robust learning compared to an RL baseline that does not exploit this form of structured learning. The learned policy matches the performance of an optimal control baseline on the real system, demonstrating the potential of curriculum RL to learn state estimation and control for non-linear tracking tasks jointly. In summary, this thesis introduces a perspective on reinforcement learning curricula as interpolations between task distributions. The methods developed under this perspective enjoy a precise formulation as optimization problems and deliver empirical benefits throughout experiments. Building upon this precise formulation may allow future work to advance the formal understanding of reinforcement learning curricula and, with that, enable the solution of challenging decision-making and control problems with reinforcement learning.