We provide an original theoretical study of Inverse Reinforcement Learning (IRL) through the lens of reward compatibility, a novel framework to quantify the compatibility of a reward with the given expert's demonstrations. Intuitively, a reward is more compatible with the demonstrations the closer the performance of the expert's policy computed with that reward is to the optimal performance for that reward. This generalizes the notion of feasible reward set, the most common framework in the theoretical IRL literature, for which a reward is either compatible or not compatible. The grayscale introduced by the reward compatibility is the key to extend the realm of provably efficient IRL far beyond what is attainable with the feasible reward set: from tabular to large-scale MDPs. We analyze the IRL problem across various settings, including optimal and suboptimal expert's demonstrations and both online and offline data collection. For all of these dimensions, we provide a tractable algorithm and corresponding sample complexity analysis, as well as various insights on reward compatibility and how the framework can pave the way to yet more general problem settings.

Reinforcement Learning (RL) requires a large amount of exploration especially in sparse-reward settings. Imitation Learning (IL) can learn from expert demonstrations without exploration, but it never exceeds the expert's performance and is also vulnerable to distributional shift between demonstration and execution. In this paper, we radically unify RL and IL based on Free Energy Principle (FEP). FEP is a unified Bayesian theory of the brain that explains perception, action and model learning by a common fundamental principle. We present a theoretical extension of FEP and derive an algorithm in which an agent learns the world model that internalizes expert demonstrations and at the same time uses the model to infer the current and future states and actions that maximize rewards. The algorithm thus reduces exploration costs by partially imitating experts as well as maximizing its return in a seamless way, resulting in a higher performance than the suboptimal expert. Our experimental results show that this approach is promising in visual control tasks especially in sparse-reward environments.

Learning dexterous manipulation in high-dimensional state-action spaces is an important open challenge with exploration presenting a major bottleneck. Although in many cases the learning process could be guided by demonstrations or other suboptimal experts, current RL algorithms for continuous action spaces often fail to effectively utilize combinations of highly off-policy expert data and on-policy exploration data. As a solution, we introduce Relative Entropy Q-Learning (REQ), a simple policy iteration algorithm that combines ideas from successful offline and conventional RL algorithms. It represents the optimal policy via importance sampling from a learned prior and is well-suited to take advantage of mixed data distributions. We demonstrate experimentally that REQ outperforms several strong baselines on robotic manipulation tasks for which suboptimal experts are available. We show how suboptimal experts can be constructed effectively by composing simple waypoint tracking controllers, and we also show how learned primitives can be combined with waypoint controllers to obtain reference behaviors to bootstrap a complex manipulation task on a simulated bimanual robot with human-like hands. Finally, we show that REQ is also effective for general off-policy RL, offline RL, and RL from demonstrations. Videos and further materials are available at sites.google.com/view/rlfse.