We present new policy mirror descent (PMD) methods for solving reinforcement learning (RL) problems with either strongly convex or general convex regularizers. By exploring the structural properties of these overall seemly highly nonconvex problems we show that the PMD methods exhibit fast linear rate of convergence to the global optimality. We develop stochastic counterparts of these methods, and establish an ${\cal O}(1/\epsilon)$ (resp., ${\cal O}(1/\epsilon^2)$) sampling complexity for solving these RL problems with strongly (resp., general) convex regularizers using different sampling schemes, where $\epsilon$ denote the target accuracy. We further show that the complexity for computing the gradients of these regularizers, if necessary, can be bounded by ${\cal O}\{(\log_\gamma \epsilon) [(1-\gamma)L/\mu]^{1/2}\log (1/\epsilon)\}$ (resp., ${\cal O} \{(\log_\gamma \epsilon ) (L/\epsilon)^{1/2}\}$)for problems with strongly (resp., general) convex regularizers. Here $\gamma$ denotes the discounting factor. To the best of our knowledge, these complexity bounds, along with our algorithmic developments, appear to be new in both optimization and RL literature. The introduction of these convex regularizers also greatly expands the flexibility and applicability of RL models.

There has been rapidly growing interest in meta-learning as a method for increasing the flexibility and sample efficiency of reinforcement learning. One problem in this area of research, however, has been a scarcity of adequate benchmark tasks. In general, the structure underlying past benchmarks has either been too simple to be inherently interesting, or too ill-defined to support principled analysis. In the present work, we introduce a new benchmark for meta-RL research, which combines structural richness with structural transparency. Alchemy is a 3D video game, implemented in Unity, which involves a latent causal structure that is resampled procedurally from episode to episode, affording structure learning, online inference, hypothesis testing and action sequencing based on abstract domain knowledge. We evaluate a pair of powerful RL agents on Alchemy and present an in-depth analysis of one of these agents. Results clearly indicate a frank and specific failure of meta-learning, providing validation for Alchemy as a challenging benchmark for meta-RL. Concurrent with this report, we are releasing Alchemy as public resource, together with a suite of analysis tools and sample agent trajectories.

In this paper, we investigate the problem of the inverse reinforcement learning (IRL), especially the beyond-demonstrator (BD) IRL. The BD-IRL aims to not only imitate the expert policy but also extrapolate BD policy based on finite demonstrations of the expert. Currently, most of the BD-IRL algorithms are two-stage, which first infer a reward function then learn the policy via reinforcement learning (RL). Because of the two separate procedures, the two-stage algorithms have high computation complexity and lack robustness. To overcome these flaw, we propose a BD-IRL framework entitled hybrid adversarial inverse reinforcement learning (HAIRL), which successfully integrates the imitation and exploration into one procedure. The simulation results show that the HAIRL is more efficient and robust when compared with other similar state-of-the-art (SOTA) algorithms.

The recent outbreak of COVID-19 poses a serious threat to people's lives. Epidemic control strategies have also caused damage to the economy by cutting off humans' daily commute. In this paper, we develop an Individual-based Reinforcement Learning Epidemic Control Agent (IDRLECA) to search for smart epidemic control strategies that can simultaneously minimize infections and the cost of mobility intervention. IDRLECA first hires an infection probability model to calculate the current infection probability of each individual. Then, the infection probabilities together with individuals' health status and movement information are fed to a novel GNN to estimate the spread of the virus through human contacts. The estimated risks are used to further support an RL agent to select individual-level epidemic-control actions. The training of IDRLECA is guided by a specially designed reward function considering both the cost of mobility intervention and the effectiveness of epidemic control. Moreover, we design a constraint for control-action selection that eases its difficulty and further improve exploring efficiency. Extensive experimental results demonstrate that IDRLECA can suppress infections at a very low level and retain more than 95% of human mobility.

Off-policy evaluation (OPE) is the problem of estimating the expected return in an unknown Markov decision process (MDP) of a given decision policy, known as the evaluation policy, using transition data generated by another policy, known as the behavior policy (Bibaut et al., 2019; Precup et al., 2000; Thomas et al., 2015). OPE is especially important in applications where experimentation is particularly costly, such as in medicine. Recently, the first-order efficiency bound for OPE was derived by Kallus and Uehara (2020) for time-varying MDPs and by Kallus and Uehara (2019) for time-homogeneous MDPs (which we focus on and simply call MDPs). That is, the smallest-possible coefficient of the leading 1/ n term C in the estimation error C/ n o(1/ n). In the time-varying tabular setting, the bounds coincides with that of Jiang and Li (2016), and Yin and Wang (2020) showed that the model-based estimator achieves it. However, the achievability of the lower bound in general settings is unclear. Among the approaches to OPE, many of them rely on estimating the q-function (representing long-term value) or the w-function (representing density ratios), under the so-called realizability (a.k.a well-specification) and/or completeness (a.k.a hypothesis class closed under Bellman operators; Antos et al., 2008; Chen and Jiang, 2019) assumptions. For example, the q-function can be estimated via Fitted-Q Iteration (FQI; Ernst et al., 2005), and the w-function is central to recent methods based on the idea of marginalized importance sampling (Gelada and Bellemare, 2019; Liu et al., 2018). In this paper, we study minimax estimators of q-and w-functions and its implications for OPE.

Purpose: Image classification may be the fundamental task in imaging artificial intelligence. We have recently shown that reinforcement learning can achieve high accuracy for lesion localization and segmentation even with minuscule training sets. Here, we introduce reinforcement learning for image classification. In particular, we apply the approach to normal vs. tumor-containing 2D MRI brain images. Materials and Methods: We applied multi-step image classification to allow for combined Deep Q learning and TD(0) Q learning. We trained on a set of 30 images (15 normal and 15 tumor-containing). We tested on a separate set of 30 images (15 normal and 15 tumor-containing). For comparison, we also trained and tested a supervised deep-learning classification network on the same set of training and testing images. Results: Whereas the supervised approach quickly overfit the training data and as expected performed poorly on the testing set (57% accuracy, just over random guessing), the reinforcement learning approach achieved an accuracy of 100%. Conclusion: We have shown a proof-of-principle application of reinforcement learning to the classification of brain tumors. We achieved perfect testing set accuracy with a training set of merely 30 images.

Interactive reinforcement learning has allowed speeding up the learning process in autonomous agents by including a human trainer providing extra information to the agent in real-time. Current interactive reinforcement learning research has been limited to interactions that offer relevant advice to the current state only. Additionally, the information provided by each interaction is not retained and instead discarded by the agent after a single-use. In this work, we propose a persistent rule-based interactive reinforcement learning approach, i.e., a method for retaining and reusing provided knowledge, allowing trainers to give general advice relevant to more than just the current state. Our experimental results show persistent advice substantially improves the performance of the agent while reducing the number of interactions required for the trainer. Moreover, rule-based advice shows similar performance impact as state-based advice, but with a substantially reduced interaction count.

We consider the problem of local planning in fixed-horizon Markov Decision Processes (MDPs) with a generative model under the assumption that the optimal value function lies in the span of a feature map that is accessible through the generative model. As opposed to previous work where linear realizability of all policies was assumed, we consider the significantly relaxed assumption of a single linearly realizable (deterministic) policy. A recent lower bound established that the related problem when the action-value function of the optimal policy is linearly realizable requires an exponential number of queries, either in H (the horizon of the MDP) or d (the dimension of the feature mapping). Their construction crucially relies on having an exponentially large action set. In contrast, in this work, we establish that poly$(H, d)$ learning is possible (with state value function realizability) whenever the action set is small (i.e. O(1)). In particular, we present the TensorPlan algorithm which uses poly$((dH/\delta)^A)$ queries to find a $\delta$-optimal policy relative to any deterministic policy for which the value function is linearly realizable with a parameter from a fixed radius ball around zero. This is the first algorithm to give a polynomial query complexity guarantee using only linear-realizability of a single competing value function. Whether the computation cost is similarly bounded remains an interesting open question. The upper bound is complemented by a lower bound which proves that in the infinite-horizon episodic setting, planners that achieve constant suboptimality need exponentially many queries, either in the dimension or the number of actions.

Finding the minimal structural assumptions that empower sample-efficient learning is one of the most important research directions in Reinforcement Learning (RL). This paper advances our understanding of this fundamental question by introducing a new complexity measure -- Bellman Eluder (BE) dimension. We show that the family of RL problems of low BE dimension is remarkably rich, which subsumes a vast majority of existing tractable RL problems including but not limited to tabular MDPs, linear MDPs, reactive POMDPs, low Bellman rank problems as well as low Eluder dimension problems. This paper further designs a new optimization-based algorithm -- GOLF, and reanalyzes a hypothesis elimination-based algorithm -- OLIVE (proposed in Jiang et al. (2017)). We prove that both algorithms learn the near-optimal policies of low BE dimension problems in a number of samples that is polynomial in all relevant parameters, but independent of the size of state-action space. Our regret and sample complexity results match or improve the best existing results for several well-known subclasses of low BE dimension problems.

In multi-agent reinforcement learning, the problem of learning to act is particularly difficult because the policies of co-players may be heavily conditioned on information only observed by them. On the other hand, humans readily form beliefs about the knowledge possessed by their peers and leverage beliefs to inform decision-making. Such abilities underlie individual success in a wide range of Markov games, from bluffing in Poker to conditional cooperation in the Prisoner's Dilemma, to convention-building in Bridge. Classical methods are usually not applicable to complex domains due to the intractable nature of hierarchical beliefs (i.e. beliefs of other agents' beliefs). We propose a scalable method to approximate these belief structures using recursive deep generative models, and to use the belief models to obtain representations useful to acting in complex tasks. Our agents trained with belief models outperform model-free baselines with equivalent representational capacity using common training paradigms. We also show that higher-order belief models outperform agents with lower-order models.