Empirical design in reinforcement learning is no small task. Running good experiments requires attention to detail and at times significant computational resources. While compute resources available per dollar have continued to grow rapidly, so have the scale of typical experiments in reinforcement learning. It is now common to benchmark agents with millions of parameters against dozens of tasks, each using the equivalent of 30 days of experience. The scale of these experiments often conflict with the need for statistical evidence, especially when comparing algorithms. Recent studies have highlighted how popular algorithms are sensitive to hyperparameter settings and implementation details, and that common empirical practice leads to weak statistical evidence (Machado et al., 2018; Henderson et al., 2018). This manuscript represents both a call to action, and a comprehensive resource for how to do good experiments in reinforcement learning. In particular, we cover: the statistical assumptions underlying common performance measures, how to properly characterize performance variation and stability, hypothesis testing, special considerations for comparing multiple agents, baseline and illustrative example construction, and how to deal with hyperparameters and experimenter bias. Throughout we highlight common mistakes found in the literature and the statistical consequences of those in example experiments. The objective of this document is to provide answers on how we can use our unprecedented compute to do good science in reinforcement learning, as well as stay alert to potential pitfalls in our empirical design.

Most value function learning algorithms in reinforcement learning are based on the mean squared (projected) Bellman error. However, squared errors are known to be sensitive to outliers, both skewing the solution of the objective and resulting in high-magnitude and high-variance gradients. To control these high-magnitude updates, typical strategies in RL involve clipping gradients, clipping rewards, rescaling rewards, or clipping errors. While these strategies appear to be related to robust losses-like the Huber loss-they are built on semi-gradient update rules which do not minimize a known loss. In this work, we build on recent insights reformulating squared Bellman errors as a saddlepoint optimization problem and propose a saddlepoint reformulation for a Huber Bellman error and Absolute Bellman error. We start from a formalization of robust losses, then derive sound gradient-based approaches to minimize these losses in both the online off-policy prediction and control settings. We characterize the solutions of the robust losses, providing insight into the problem settings where the robust losses define notably better solutions than the mean squared Bellman error. Finally, we show that the resulting gradient-based algorithms are more stable, for both prediction and control, with less sensitivity to meta-parameters.

The policy gradient theorem (Sutton et al., 2000) prescribes the usage of a cumulative discounted state distribution under the target policy to approximate the gradient. Most algorithms based on this theorem, in practice, break this assumption, introducing a distribution shift that can cause the convergence to poor solutions. In this paper, we propose a new approach of reconstructing the policy gradient from the start state without requiring a particular sampling strategy. The policy gradient calculation in this form can be simplified in terms of a gradient critic, which can be recursively estimated due to a new Bellman equation of gradients. By using temporal-difference updates of the gradient critic from an off-policy data stream, we develop the first estimator that side-steps the distribution shift issue in a model-free way. We prove that, under certain realizability conditions, our estimator is unbiased regardless of the sampling strategy. We empirically show that our technique achieves a superior bias-variance trade-off and performance in presence of off-policy samples.

Many reinforcement learning algorithms rely on value estimation, however, the most widely used algorithms---namely temporal difference algorithms---can diverge under both off-policy sampling and nonlinear function approximation. Many algorithms have been developed for off-policy value estimation based on the linear mean squared projected Bellman error (MSPBE) and are sound under linear function approximation. Extending these methods to the nonlinear case has been largely unsuccessful. Recently, several methods have been introduced that approximate a different objective---the mean-squared Bellman error (MSBE)---which naturally facilitate nonlinear approximation. In this work, we build on these insights and introduce a new generalized MSPBE that extends the linear MSPBE to the nonlinear setting. We show how this generalized objective unifies previous work and obtain new bounds for the value error of the solutions of the generalized objective. We derive an easy-to-use, but sound, algorithm to minimize the generalized objective, and show that it is more stable across runs, is less sensitive to hyperparameters, and performs favorably across four control domains with neural network function approximation.

State construction is important for learning in partially observable environments. A general purpose strategy for state construction is to learn the state update using a Recurrent Neural Network (RNN), which updates the internal state using the current internal state and the most recent observation. This internal state provides a summary of the observed sequence, to facilitate accurate predictions and decision-making. At the same time, specifying and training RNNs is notoriously tricky, particularly as the common strategy to approximate gradients back in time, called truncated Back-prop Through Time (BPTT), can be sensitive to the truncation window. Further, domain-expertise—which can usually help constrain the function class and so improve trainability—can be difficult to incorporate into complex recurrent units used within RNNs. In this work, we explore how to use multi-step predictions to constrain the RNN and incorporate prior knowledge. In particular, we revisit the idea of using predictions to construct state and ask: does constraining (parts of) the state to consist of predictions about the future improve RNN trainability? We formulate a novel RNN architecture, called a General Value Function Network (GVFN), where each internal state component corresponds to a prediction about the future represented as a value function. We first provide an objective for optimizing GVFNs, and derive several algorithms to optimize this objective. We then show that GVFNs are more robust to the truncation level, in many cases only requiring one-step gradient updates.

It is still common to use Q-learning and temporal difference (TD) learning{—}even though they have divergence issues and sound Gradient TD alternatives exist{—}because divergence seems rare and they typically perform well. However, recent work with large neural network learning systems reveals that instability is more common than previously thought. Practitioners face a difficult dilemma: choose an easy to use and performant TD method, or a more complex algorithm that is more sound but harder to tune and all but unexplored with non-linear function approximation or control. In this paper, we introduce a new method called TD with Regularized Corrections (TDRC), that attempts to balance ease of use, soundness, and performance. It behaves as well as TD, when TD performs well, but is sound in cases where TD diverges. We empirically investigate TDRC across a range of problems, for both prediction and control, and for both linear and non-linear function approximation, and show, potentially for the first time, that Gradient TD methods could be a better alternative to TD and Q-learning.

Mapping structural brain connectomes for living human brains typically requires expert analysis and rule-based models on diffusion-weighted magnetic resonance imaging. A data-driven approach, however, could overcome limitations in such rule-based approaches and improve precision mappings for individuals. In this work, we explore a framework that facilitates applying learning algorithms to automatically extract brain connectomes. Using a tensor encoding, we design an objective with a group-regularizer that prefers biologically plausible fascicle structure. We show that the objective is convex and has unique solutions, ensuring identifiable connectomes for an individual. We develop an efficient optimization strategy for this extremely high-dimensional sparse problem, by reducing the number of parameters using a greedy algorithm designed specifically for the problem. We show that this greedy algorithm significantly improves on a standard greedy algorithm, called Orthogonal Matching Pursuit. We conclude with an analysis of the solutions found by our method, showing we can accurately reconstruct the diffusion information while maintaining contiguous fascicles with smooth direction changes.

Model-based strategies for control are critical to obtain sample efficient learning. Dyna is a planning paradigm that naturally interleaves learning and planning, by simulating one-step experience to update the action-value function. This elegant planning strategy has been mostly explored in the tabular setting. The aim of this paper is to revisit sample-based planning, in stochastic and continuous domains with learned models. We first highlight the flexibility afforded by a model over Experience Replay (ER). Replay-based methods can be seen as stochastic planning methods that repeatedly sample from a buffer of recent agent-environment interactions and perform updates to improve data efficiency. We show that a model, as opposed to a replay buffer, is particularly useful for specifying which states to sample from during planning, such as predecessor states that propagate information in reverse from a state more quickly. We introduce a semi-parametric model learning approach, called Reweighted Experience Models (REMs), that makes it simple to sample next states or predecessors. We demonstrate that REM-Dyna exhibits similar advantages over replay-based methods in learning in continuous state problems, and that the performance gap grows when moving to stochastic domains, of increasing size.

Generalization performance is a central goal in machine learning, particularly when learning representations with large neural networks. A common strategy to improve generalization has been through the use of regularizers, typically as a norm constraining the parameters. Regularizing hidden layers in a neural network architecture, however, is not straightforward. There have been a few effective layer-wise suggestions, but without theoretical guarantees for improved performance. In this work, we theoretically and empirically analyze one such model, called a supervised auto-encoder: a neural network that predicts both inputs (reconstruction error) and targets jointly. We provide a novel generalization result for linear auto-encoders, proving uniform stability based on the inclusion of the reconstruction error---particularly as an improvement on simplistic regularization such as norms or even on more advanced regularizations such as the use of auxiliary tasks. Empirically, we then demonstrate that, across an array of architectures with a different number of hidden units and activation functions, the supervised auto-encoder compared to the corresponding standard neural network never harms performance and can significantly improve generalization.

In recent years, social media has become one of the most popular tools for discovering and following breaking news and ongoing events. However tools and interfaces have lagged behind users' expectations, with current tools making it difficult to discover new events and failing to provide a solution to the problem of information overload. We have developed an interactive interface for visualizing events, backed by a state-of-the-art event detection approach, which is able to detect, track and summarize events in real-time. Our interface provides up-to-the-second information about ongoing events in an easy to understand manner, including category information, temporal distribution, and location information -- all of which was previously unobtainable in real-time.

The teaching of testing has never been easy. The introduction of object orientation into first year courses has made it even more difficult, since more and smaller units need to be tested more often. In professional contexts this is addressed by the use of testing support software. Unfortunately, no adequate software to support testing for introductory students is widely available, leaving teachers and students of first year courses struggling.In this paper we describe an attempt to address this problem by combining two existing systems that partly address our needs. We describe an integration of JUnit into BlueJ, which creates a testing tool that exhibits the flexibility and ease-of-use of the BlueJ system combined with the structured unit test approach provided by JUnit.