Andrew Patterson

Andrew Patterson, Samuel Neumann, Martha White et al. · deepmind

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 proper statistical evidence, especially when comparing algorithms. Recent studies have highlighted how popular algorithms are sensitive to hyper-parameter settings and implementation details, and that common empirical practice leads to weak statistical evidence (Machado et al., 2018; Henderson et al., 2018). Here we take this one step further. 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 hyper-parameters 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.

Andrew Patterson, Victor Liao, Martha White

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.

Steven Tang, Xinze Xiong, Anna Hakhverdyan et al.

In continual reinforcement learning (CRL), good performance requires never-ending learning, acting, and exploration in a big, partially observable world. Most CRL experiments have focused on loss of plasticity -- the inability to keep learning -- in one-off experiments where some unobservable non-stationarity is added to classic fully observable MDPs. Further, these experiments rarely consider the role of partial observability and the importance of CRL agents that use memory or recurrence. One potential reason for this focus on mitigating loss of plasticity without considering partial observability is that many partially-observable CRL environments are prohibitively expensive. In this paper, we introduce Forager, a light-weight partially-observable CRL environment with a constant memory footprint. We provide a set of experiments and sample tasks demonstrating that Forager is challenging for current CRL agents and yet also allows for in-depth study of those agents. We demonstrate that agents exhibit loss of plasticity, proposed mitigations can help, but that most useful is to leverage state construction. We conclude with a variant of Forager that generates an unending stream of new tasks to learn that clearly highlights the limitations of current CRL agents.

Andrew Patterson, Samuel Neumann, Raksha Kumaraswamy et al.

This paper introduces a new empirical methodology, the Cross-environment Hyperparameter Setting Benchmark, that compares RL algorithms across environments using a single hyperparameter setting, encouraging algorithmic development which is insensitive to hyperparameters. We demonstrate that this benchmark is robust to statistical noise and obtains qualitatively similar results across repeated applications, even when using few samples. This robustness makes the benchmark computationally cheap to apply, allowing statistically sound insights at low cost. We demonstrate two example instantiations of the CHS, on a set of six small control environments (SC-CHS) and on the entire DM Control suite of 28 environments (DMC-CHS). Finally, to illustrate the applicability of the CHS to modern RL algorithms on challenging environments, we conduct a novel empirical study of an open question in the continuous control literature. We show, with high confidence, that there is no meaningful difference in performance between Ornstein-Uhlenbeck noise and uncorrelated Gaussian noise for exploration with the DDPG algorithm on the DMC-CHS.

Parham Mohammad Panahi, Andrew Patterson, Martha White et al.

Experience replay, the reuse of past data to improve sample efficiency, is ubiquitous in reinforcement learning. Though a variety of smart sampling schemes have been introduced to improve performance, uniform sampling by far remains the most common approach. One exception is Prioritized Experience Replay (PER), where sampling is done proportionally to TD errors, inspired by the success of prioritized sweeping in dynamic programming. The original work on PER showed improvements in Atari, but follow-up results were mixed. In this paper, we investigate several variations on PER, to attempt to understand where and when PER may be useful. Our findings in prediction tasks reveal that while PER can improve value propagation in tabular settings, behavior is significantly different when combined with neural networks. Certain mitigations $-$ like delaying target network updates to control generalization and using estimates of expected TD errors in PER to avoid chasing stochasticity $-$ can avoid large spikes in error with PER and neural networks but generally do not outperform uniform replay. In control tasks, none of the prioritized variants consistently outperform uniform replay. We present new insight into the interaction between prioritization, bootstrapping, and neural networks and propose several improvements for PER in tabular settings and noisy domains.

Esraa Elelimy, Brett Daley, Andrew Patterson et al.

Achieving fast and stable off-policy learning in deep reinforcement learning (RL) is challenging. Most existing methods rely on semi-gradient temporal-difference (TD) methods for their simplicity and efficiency, but are consequently susceptible to divergence. While more principled approaches like Gradient TD (GTD) methods have strong convergence guarantees, they have rarely been used in deep RL. Recent work introduced the generalized Projected Bellman Error ($\overline{\text{PBE}}$), enabling GTD methods to work efficiently with nonlinear function approximation. However, this work is limited to one-step methods, which are slow at credit assignment and require a large number of samples. In this paper, we extend the generalized $\overline{\text{PBE}}$ objective to support multistep credit assignment based on the $λ$-return and derive three gradient-based methods that optimize this new objective. We provide both a forward-view formulation compatible with experience replay and a backward-view formulation compatible with streaming algorithms. Finally, we evaluate the proposed algorithms and show that they outperform both PPO and StreamQ in MuJoCo and MinAtar environments, respectively. Code available at https://github.com/esraaelelimy/gtd\_algos

Vincent Liu, Prabhat Nagarajan, Andrew Patterson et al.

Offline reinforcement learning algorithms often require careful hyperparameter tuning. Consequently, before deployment, we need to select amongst a set of candidate policies. As yet, however, there is little understanding about the fundamental limits of this offline policy selection (OPS) problem. In this work we aim to provide clarity on when sample efficient OPS is possible, primarily by connecting OPS to off-policy policy evaluation (OPE) and Bellman error (BE) estimation. We first show a hardness result, that in the worst case, OPS is just as hard as OPE, by proving a reduction of OPE to OPS. As a result, no OPS method can be more sample efficient than OPE in the worst case. We then propose a BE method for OPS, called Identifiable BE Selection (IBES), that has a straightforward method for selecting its own hyperparameters. We highlight that using IBES for OPS generally has more requirements than OPE methods, but if satisfied, can be more sample efficient. We conclude with an empirical study comparing OPE and IBES, and by showing the difficulty of OPS on an offline Atari benchmark dataset.

Mohamed A. Mohamed, Kateryna Nekhomiazh, Vedant Vyas et al.

Continual reinforcement learning (RL) concerns agents that are expected to learn continually, rather than converge to a policy that is then fixed for evaluation. Such an approach is well suited to environments the agent perceives as changing, which renders any static policy ineffective over time. The few simulators explicitly designed for empirical research in continual RL are often limited in scope or complexity, and it is now common for researchers to modify episodic RL environments by artificially incorporating abrupt task changes during interaction. In this paper, we introduce AgarCL, a research platform for continual RL that allows for a progression of increasingly sophisticated behaviour. AgarCL is based on the game Agar.io, a non-episodic, high-dimensional problem featuring stochastic, ever-evolving dynamics, continuous actions, and partial observability. Additionally, we provide benchmark results reporting the performance of DQN, PPO, and SAC in both the primary, challenging continual RL problem, and across a suite of smaller tasks within AgarCL, each of which isolates aspects of the full environment and allow us to characterize the challenges posed by different aspects of the game.

Samuele Tosatto, Andrew Patterson, Martha White et al.

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 sidesteps 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.

Andrew Patterson, Adam White, Martha White

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.

Aditya Gahlawat, Arun Lakshmanan, Lin Song et al.

We present $\mathcal{CL}_1$-$\mathcal{GP}$, a control framework that enables safe simultaneous learning and control for systems subject to uncertainties. The two main constituents are contraction theory-based $\mathcal{L}_1$ ($\mathcal{CL}_1$) control and Bayesian learning in the form of Gaussian process (GP) regression. The $\mathcal{CL}_1$ controller ensures that control objectives are met while providing safety certificates. Furthermore, $\mathcal{CL}_1$-$\mathcal{GP}$ incorporates any available data into a GP model of uncertainties, which improves performance and enables the motion planner to achieve optimality safely. This way, the safe operation of the system is always guaranteed, even during the learning transients. We provide a few illustrative examples for the safe learning and control of planar quadrotor systems in a variety of environments.

Sina Ghiassian, Andrew Patterson, Shivam Garg et al.

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.

Andrew Patterson, Aditya Gahlawat, Naira Hovakimyan

Autonomous agents must be able to safely interact with other vehicles to integrate into urban environments. The safety of these agents is dependent on their ability to predict collisions with other vehicles' future trajectories for replanning and collision avoidance. The information needed to predict collisions can be learned from previously observed vehicle trajectories in a specific environment, generating a traffic model. The learned traffic model can then be incorporated as prior knowledge into any trajectory estimation method being used in this environment. This work presents a Gaussian process based probabilistic traffic model that is used to quantify vehicle behaviors in an intersection. The Gaussian process model provides estimates for the average vehicle trajectory, while also capturing the variance between the different paths a vehicle may take in the intersection. The method is demonstrated on a set of time-series position trajectories. These trajectories are reconstructed by removing object recognition errors and missed frames that may occur due to data source processing. To create the intersection traffic model, the reconstructed trajectories are clustered based on their source and destination lanes. For each cluster, a Gaussian process model is created to capture the average behavior and the variance of the cluster. To show the applicability of the Gaussian model, the test trajectories are classified with only partial observations. Performance is quantified by the number of observations required to correctly classify the vehicle trajectory. Both the intersection traffic modeling computations and the classification procedure are timed. These times are presented as results and demonstrate that the model can be constructed in a reasonable amount of time and the classification procedure can be used for online applications.

Andrew Patterson, Arun Lakshmanan, Naira Hovakimyan

Collision prediction in a dynamic and unknown environment relies on knowledge of how the environment is changing. Many collision prediction methods rely on deterministic knowledge of how obstacles are moving in the environment. However, complete deterministic knowledge of the obstacles' motion is often unavailable. This work proposes a Gaussian process based prediction method that replaces the assumption of deterministic knowledge of each obstacle's future behavior with probabilistic knowledge, to allow a larger class of obstacles to be considered. The method solely relies on position and velocity measurements to predict collisions with dynamic obstacles. We show that the uncertainty region for obstacle positions can be expressed in terms of a combination of polynomials generated with Gaussian process regression. To control the growth of uncertainty over arbitrary time horizons, a probabilistic obstacle intention is assumed as a distribution over obstacle positions and velocities, which can be naturally included in the Gaussian process framework. Our approach is demonstrated in two case studies in which (i), an obstacle overtakes the agent and (ii), an obstacle crosses the agent's path perpendicularly. In these simulations we show that the collision can be predicted despite having limited knowledge of the obstacle's behavior.

Arun Lakshmanan, Andrew Patterson, Venanzio Cichella et al.

In motion planning problems for autonomous robots, such as self-driving cars, the robot must ensure that its planned path is not in close proximity to obstacles in the environment. However, the problem of evaluating the proximity is generally non-convex and serves as a significant computational bottleneck for motion planning algorithms. In this paper, we present methods for a general class of absolutely continuous parametric curves to compute: (i) the minimum separating distance, (ii) tolerance verification, and (iii) collision detection. Our methods efficiently compute bounds on obstacle proximity by bounding the curve in a convex region. This bound is based on an upper bound on the curve arc length that can be expressed in closed form for a useful class of parametric curves including curves with trigonometric or polynomial bases. We demonstrate the computational efficiency and accuracy of our approach through numerical simulations of several proximity problems.

Sina Ghiassian, Andrew Patterson, Martha White et al.

This paper investigates the problem of online prediction learning, where learning proceeds continuously as the agent interacts with an environment. The predictions made by the agent are contingent on a particular way of behaving, represented as a value function. However, the behavior used to select actions and generate the behavior data might be different from the one used to define the predictions, and thus the samples are generated off-policy. The ability to learn behavior-contingent predictions online and off-policy has long been advocated as a key capability of predictive-knowledge learning systems but remained an open algorithmic challenge for decades. The issue lies with the temporal difference (TD) learning update at the heart of most prediction algorithms: combining bootstrapping, off-policy sampling and function approximation may cause the value estimate to diverge. A breakthrough came with the development of a new objective function that admitted stochastic gradient descent variants of TD. Since then, many sound online off-policy prediction algorithms have been developed, but there has been limited empirical work investigating the relative merits of all the variants. This paper aims to fill these empirical gaps and provide clarity on the key ideas behind each method. We summarize the large body of literature on off-policy learning, focusing on 1- methods that use computation linear in the number of features and are convergent under off-policy sampling, and 2- other methods which have proven useful with non-fixed, nonlinear function approximation. We provide an empirical study of off-policy prediction methods in two challenging microworlds. We report each method's parameter sensitivity, empirical convergence rate, and final performance, providing new insights that should enable practitioners to successfully extend these new methods to large-scale applications.[Abridged abstract]

Matthew Schlegel, Andrew Jacobsen, Zaheer Abbas et al.

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.

Yangchen Pan, Muhammad Zaheer, Adam White et al.

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.