The convergence of many reinforcement learning (RL) algorithms with linear function approximation has been investigated extensively but most proofs assume that these methods converge to a unique solution. In this paper, we provide a complete characterization of non-uniqueness issues for a large class of reinforcement learning algorithms, simultaneously unifying many counter-examples to convergence in a theoretical framework. We achieve this by proving a new condition on features that can determine whether the convergence assumptions are valid or non-uniqueness holds. We consider a general class of RL methods, which we call natural algorithms, whose solutions are characterized as the fixed point of a projected Bellman equation (when it exists); notably, bootstrapped temporal difference-based methods such as $TD(\lambda)$ and $GTD(\lambda)$ are natural algorithms. Our main result proves that natural algorithms converge to the correct solution if and only if all the value functions in the approximation space satisfy a certain shape. This implies that natural algorithms are, in general, inherently prone to converge to the wrong solution for most feature choices even if the value function can be represented exactly. Given our results, we show that state aggregation based features are a safe choice for natural algorithms and we also provide a condition for finding convergent algorithms under other feature constructions.

We consider a new family of operators for reinforcement learning with the goal of alleviating the negative effects and becoming more robust to approximation or estimation errors. Various theoretical results are established, which include showing on a sample path basis that our family of operators preserve optimality and increase the action gap. Our empirical results illustrate the strong benefits of our family of operators, significantly outperforming the classical Bellman operator and recently proposed operators.

In Multi-Goal Reinforcement Learning, an agent learns to achieve multiple goals with a goal-conditioned policy. During learning, the agent first collects the trajectories into a replay buffer, and later these trajectories are selected randomly for replay. However, the achieved goals in the replay buffer are often biased towards the behavior policies. From a Bayesian perspective, when there is no prior knowledge about the target goal distribution, the agent should learn uniformly from diverse achieved goals. Therefore, we first propose a novel multi-goal RL objective based on weighted entropy. This objective encourages the agent to maximize the expected return, as well as to achieve more diverse goals. Secondly, we developed a maximum entropy-based prioritization framework to optimize the proposed objective. For evaluation of this framework, we combine it with Deep Deterministic Policy Gradient, both with or without Hindsight Experience Replay. On a set of multi-goal robotic tasks of OpenAI Gym, we compare our method with other baselines and show promising improvements in both performance and sample-efficiency.

The linear quadratic regulator (LQR) problem has reemerged as an important theoretical benchmark for reinforcement learning-based control of complex dynamical systems with continuous state and action spaces. In contrast with nearly all recent work in this area, we consider multiplicative noise models, which are increasingly relevant because they explicitly incorporate inherent uncertainty and variation in the system dynamics and thereby improve robustness properties of the controller. Robustness is a critical and poorly understood issue in reinforcement learning; existing methods which do not account for uncertainty can converge to fragile policies or fail to converge at all. Additionally, intentional injection of multiplicative noise into learning algorithms can enhance robustness of policies, as observed in ad hoc work on domain randomization. Although policy gradient algorithms require optimization of a non-convex cost function, we show that the multiplicative noise LQR cost has a special property called gradient domination, which is exploited to prove global convergence of policy gradient algorithms to the globally optimum control policy with polynomial dependence on problem parameters. Results are provided both in the model-known and model-unknown settings where samples of system trajectories are used to estimate policy gradients.

While there are convergence guarantees for temporal difference (TD) learning when using linear function approximators, the situation for nonlinear models is far less understood, and divergent examples are known. Here we take a first step towards extending theoretical convergence guarantees to TD learning with nonlinear function approximation. More precisely, we consider the expected dynamics of the TD(0) algorithm. We prove that this ODE is attracted to a compact set for smooth homogeneous functions including some ReLU networks. For over-parametrized and well-conditioned functions in sufficiently reversible environments we prove convergence to the global optimum. This result improves when using $k$-step or $ \lambda$ returns. Finally, we generalize a divergent counterexample to a family of divergent problems to motivate the assumptions needed to prove convergence.

Adversarial attacks have exposed a significant security vulnerability in state-of-the-art machine learning models. Among these models include deep reinforcement learning agents. The existing methods for attacking reinforcement learning agents assume the adversary either has access to the target agent's learned parameters or the environment that the agent interacts with. In this work, we propose a new class of threat models, called snooping threat models, that are unique to reinforcement learning. In these snooping threat models, the adversary does not have the ability to personally interact with the environment, and can only eavesdrop on the action and reward signals being exchanged between agent and environment. We show that adversaries operating in these highly constrained threat models can still launch devastating attacks against the target agent by training proxy models on related tasks and leveraging the transferability of adversarial examples.

We propose an algorithm based on reinforcement learning for solving NP-hard problems on graphs. We combine Graph Isomorphism Networks and the Monte-Carlo Tree Search, which was originally used for game searches, for solving combinatorial optimization on graphs. Similarly to AlphaGo Zero, our method does not require any problem-specific knowledge or labeled datasets (exact solutions), which are difficult to calculate in principle. We show that our method, which is trained by generated random graphs, successfully finds near-optimal solutions for the Maximum Independent Set problem on citation networks. Experiments illustrate that the performance of our method is comparable to SOTA solvers, but we do not require any problem-specific reduction rules, which is highly desirable in practice since collecting hand-crafted reduction rules is costly and not adaptive for a wide range of problems.

Though reinforcement learning has greatly benefited from the incorporation of neural networks, the inability to verify the correctness of such systems limits their use. Current work in explainable deep learning focuses on explaining only a single decision in terms of input features, making it unsuitable for explaining a sequence of decisions. To address this need, we introduce Abstracted Policy Graphs, which are Markov chains of abstract states. This representation concisely summarizes a policy so that individual decisions can be explained in the context of expected future transitions. Additionally, we propose a method to generate these Abstracted Policy Graphs for deterministic policies given a learned value function and a set of observed transitions, potentially off-policy transitions used during training. Since no restrictions are placed on how the value function is generated, our method is compatible with many existing reinforcement learning methods. We prove that the worst-case time complexity of our method is quadratic in the number of features and linear in the number of provided transitions, $O(|F|^2 |tr\_samples|)$. By applying our method to a family of domains, we show that our method scales well in practice and produces Abstracted Policy Graphs which reliably capture relationships within these domains.

Imagine a robot trying to learn how to stack blocks and push objects using visual inputs from a camera feed. In order to minimize cost and safety concerns, we want our robot to learn these skills with minimal interaction time, but efficient learning from complex sensory inputs such as images is difficult. This work introduces SOLAR, a new model-based reinforcement learning (RL) method that can learn skills – including manipulation tasks on a real Sawyer robot arm – directly from visual inputs with under an hour of interaction. To our knowledge, SOLAR is the most efficient RL method for solving real world image-based robotics tasks. Our robot learns to stack a Lego block and push a mug onto a coaster with only inputs from a camera pointed at the robot.

Automatic machine learning is an important problem in the forefront of machine learning. The strongest AutoML systems are based on neural networks, evolutionary algorithms, and Bayesian optimization. Recently AlphaD3M reached state-of-the-art results with an order of magnitude speedup using reinforcement learning with self-play. In this work we extend AlphaD3M by using a pipeline grammar and a pre-trained model which generalizes from many different datasets and similar tasks. Our results demonstrate improved performance compared with our earlier work and existing methods on AutoML benchmark datasets for classification and regression tasks.