Inverse Reinforcement Learning in Contextual MDPs

We consider the task of Inverse Reinforcement Learning in Contextual Markov Decision Processes (MDPs). In this setting, contexts, which define the reward and transition kernel, are sampled from a distribution. In addition, although the reward is a function of the context, it is not provided to the agent. Instead, the agent observes demonstrations from an optimal policy. The goal is to learn the reward mapping, such that the agent will act optimally even when encountering previously unseen contexts, also known as zero-shot transfer. We formulate this problem as a non-differential convex optimization problem and propose a novel algorithm to compute its subgradients. Based on this scheme, we analyze several methods both theoretically, where we compare the sample complexity and scalability, and empirically. Most importantly, we show both theoretically and empirically that our algorithms perform zero-shot transfer (generalize to new and unseen contexts). Specifically, we present empirical experiments in a dynamic treatment regime, where the goal is to learn a reward function which explains the behavior of expert physicians based on recorded data of them treating patients diagnosed with sepsis

Reinforcement Learning in Feature Space: Matrix Bandit, Kernels, and Regret Bound

Exploration in reinforcement learning (RL) suffers from the curse of dimensionality when the state-action space is large. A common practice is to parameterize the high-dimensional value and policy functions using given features. However existing methods either have no theoretical guarantee or suffer a regret that is exponential in the planning horizon $H$. In this paper, we propose an online RL algorithm, namely the MatrixRL, that leverages ideas from linear bandit to learn a low-dimensional representation of the probability transition model while carefully balancing the exploitation-exploration tradeoff. We show that MatrixRL achieves a regret bound ${O}\big(H^2d\log T\sqrt{T}\big)$ where $d$ is the number of features. MatrixRL has an equivalent kernelized version, which is able to work with an arbitrary kernel Hilbert space without using explicit features. In this case, the kernelized MatrixRL satisfies a regret bound ${O}\big(H^2\widetilde{d}\log T\sqrt{T}\big)$, where $\widetilde{d}$ is the effective dimension of the kernel space. To our best knowledge, for RL using features or kernels, our results are the first regret bounds that are near-optimal in time $T$ and dimension $d$ (or $\widetilde{d}$) and polynomial in the planning horizon $H$

Sample Complexity of Reinforcement Learning using Linearly Combined Model Ensembles

Reinforcement learning (RL) methods have been shown to be capable of learning intelligent behavior in rich domains. However, this has largely been done in simulated domains without adequate focus on the process of building the simulator. In this paper, we consider a setting where we have access to an ensemble of pre-trained and possibly inaccurate simulators (models). We approximate the real environment using a state-dependent linear combination of the ensemble, where the coefficients are determined by the given state features and some unknown parameters. Our proposed algorithm provably learns a near-optimal policy with a sample complexity polynomial in the number of unknown parameters, and incurs no dependence on the size of the state (or action) space. As an extension, we also consider the more challenging problem of model selection, where the state features are unknown and can be chosen from a large candidate set. We provide exponential lower bounds that illustrate the fundamental hardness of this problem, and develop a provably efficient algorithm under additional natural assumptions

PAC Bounds for Imitation and Model-based Batch Learning of Contextual Markov Decision Processes

We consider the problem of batch multi-task reinforcement learning with observed context descriptors, motivated by its application to personalized medical treatment. In particular, we study two general classes of learning algorithms: direct policy learning (DPL), an imitation-learning based approach which learns from expert trajectories, and model-based learning. First, we derive sample complexity bounds for DPL, and then show that model-based learning from expert actions can, even with a finite model class, be impossible. After relaxing the conditions under which the model-based approach is expected to learn by allowing for greater coverage of state-action space, we provide sample complexity bounds for model-based learning with finite model classes, showing that there exist model classes with sample complexity exponential in their statistical complexity. We then derive a sample complexity upper bound for model-based learning based on a measure of concentration of the data distribution. Our results give formal justification for imitation learning over model-based learning in this setting