A. Rupam Mahmood

Amirmohammad Karimi, Jun Jin, Jun Luo et al. · eth-zurich

In classic reinforcement learning algorithms, agents make decisions at discrete and fixed time intervals. The duration between decisions becomes a crucial hyperparameter, as setting it too short may increase the problem's difficulty by requiring the agent to make numerous decisions to achieve its goal while setting it too long can result in the agent losing control over the system. However, physical systems do not necessarily require a constant control frequency, and for learning agents, it is often preferable to operate with a low frequency when possible and a high frequency when necessary. We propose a framework called Continuous-Time Continuous-Options (CTCO), where the agent chooses options as sub-policies of variable durations. These options are time-continuous and can interact with the system at any desired frequency providing a smooth change of actions. We demonstrate the effectiveness of CTCO by comparing its performance to classical RL and temporal-abstraction RL methods on simulated continuous control tasks with various action-cycle times. We show that our algorithm's performance is not affected by the choice of environment interaction frequency. Furthermore, we demonstrate the efficacy of CTCO in facilitating exploration in a real-world visual reaching task for a 7 DOF robotic arm with sparse rewards.

Qingfeng Lan, A. Rupam Mahmood, Shuicheng Yan et al.

In recent years, by leveraging more data, computation, and diverse tasks, learned optimizers have achieved remarkable success in supervised learning, outperforming classical hand-designed optimizers. Reinforcement learning (RL) is essentially different from supervised learning, and in practice, these learned optimizers do not work well even in simple RL tasks. We investigate this phenomenon and identify two issues. First, the agent-gradient distribution is non-independent and identically distributed, leading to inefficient meta-training. Moreover, due to highly stochastic agent-environment interactions, the agent-gradients have high bias and variance, which increases the difficulty of learning an optimizer for RL. We propose pipeline training and a novel optimizer structure with a good inductive bias to address these issues, making it possible to learn an optimizer for reinforcement learning from scratch. We show that, although only trained in toy tasks, our learned optimizer can generalize to unseen complex tasks in Brax.

Yan Wang, Gautham Vasan, A. Rupam Mahmood

Real-time learning is crucial for robotic agents adapting to ever-changing, non-stationary environments. A common setup for a robotic agent is to have two different computers simultaneously: a resource-limited local computer tethered to the robot and a powerful remote computer connected wirelessly. Given such a setup, it is unclear to what extent the performance of a learning system can be affected by resource limitations and how to efficiently use the wirelessly connected powerful computer to compensate for any performance loss. In this paper, we implement a real-time learning system called the Remote-Local Distributed (ReLoD) system to distribute computations of two deep reinforcement learning (RL) algorithms, Soft Actor-Critic (SAC) and Proximal Policy Optimization (PPO), between a local and a remote computer. The performance of the system is evaluated on two vision-based control tasks developed using a robotic arm and a mobile robot. Our results show that SAC's performance degrades heavily on a resource-limited local computer. Strikingly, when all computations of the learning system are deployed on a remote workstation, SAC fails to compensate for the performance loss, indicating that, without careful consideration, using a powerful remote computer may not result in performance improvement. However, a carefully chosen distribution of computations of SAC consistently and substantially improves its performance on both tasks. On the other hand, the performance of PPO remains largely unaffected by the distribution of computations. In addition, when all computations happen solely on a powerful tethered computer, the performance of our system remains on par with an existing system that is well-tuned for using a single machine. ReLoD is the only publicly available system for real-time RL that applies to multiple robots for vision-based tasks.

Fengdi Che, Gautham Vasan, A. Rupam Mahmood

The policy gradient theorem gives a convenient form of the policy gradient in terms of three factors: an action value, a gradient of the action likelihood, and a state distribution involving discounting called the \emph{discounted stationary distribution}. But commonly used on-policy methods based on the policy gradient theorem ignores the discount factor in the state distribution, which is technically incorrect and may even cause degenerate learning behavior in some environments. An existing solution corrects this discrepancy by using $γ^t$ as a factor in the gradient estimate. However, this solution is not widely adopted and does not work well in tasks where the later states are similar to earlier states. We introduce a novel distribution correction to account for the discounted stationary distribution that can be plugged into many existing gradient estimators. Our correction circumvents the performance degradation associated with the $γ^t$ correction with a lower variance. Importantly, compared to the uncorrected estimators, our algorithm provides improved state emphasis to evade suboptimal policies in certain environments and consistently matches or exceeds the original performance on several OpenAI gym and DeepMind suite benchmarks.

Mohamed Elsayed, A. Rupam Mahmood

Second-order optimization uses curvature information about the objective function, which can help in faster convergence. However, such methods typically require expensive computation of the Hessian matrix, preventing their usage in a scalable way. The absence of efficient ways of computation drove the most widely used methods to focus on first-order approximations that do not capture the curvature information. In this paper, we develop HesScale, a scalable approach to approximating the diagonal of the Hessian matrix, to incorporate second-order information in a computationally efficient manner. We show that HesScale has the same computational complexity as backpropagation. Our results on supervised classification show that HesScale achieves high approximation accuracy, allowing for scalable and efficient second-order optimization.

Qingfeng Lan, Yangchen Pan, Jun Luo et al.

Artificial neural networks are promising for general function approximation but challenging to train on non-independent or non-identically distributed data due to catastrophic forgetting. The experience replay buffer, a standard component in deep reinforcement learning, is often used to reduce forgetting and improve sample efficiency by storing experiences in a large buffer and using them for training later. However, a large replay buffer results in a heavy memory burden, especially for onboard and edge devices with limited memory capacities. We propose memory-efficient reinforcement learning algorithms based on the deep Q-network algorithm to alleviate this problem. Our algorithms reduce forgetting and maintain high sample efficiency by consolidating knowledge from the target Q-network to the current Q-network. Compared to baseline methods, our algorithms achieve comparable or better performance in both feature-based and image-based tasks while easing the burden of large experience replay buffers.

Mohamed Elsayed, A. Rupam Mahmood

Modern representation learning methods often struggle to adapt quickly under non-stationarity because they suffer from catastrophic forgetting and decaying plasticity. Such problems prevent learners from fast adaptation since they may forget useful features or have difficulty learning new ones. Hence, these methods are rendered ineffective for continual learning. This paper proposes Utility-based Perturbed Gradient Descent (UPGD), an online learning algorithm well-suited for continual learning agents. UPGD protects useful weights or features from forgetting and perturbs less useful ones based on their utilities. Our empirical results show that UPGD helps reduce forgetting and maintain plasticity, enabling modern representation learning methods to work effectively in continual learning.

Shibhansh Dohare, J. Fernando Hernandez-Garcia, Parash Rahman et al.

Modern deep-learning systems are specialized to problem settings in which training occurs once and then never again, as opposed to continual-learning settings in which training occurs continually. If deep-learning systems are applied in a continual learning setting, then it is well known that they may fail to remember earlier examples. More fundamental, but less well known, is that they may also lose their ability to learn on new examples, a phenomenon called loss of plasticity. We provide direct demonstrations of loss of plasticity using the MNIST and ImageNet datasets repurposed for continual learning as sequences of tasks. In ImageNet, binary classification performance dropped from 89% accuracy on an early task down to 77%, about the level of a linear network, on the 2000th task. Loss of plasticity occurred with a wide range of deep network architectures, optimizers, activation functions, batch normalization, dropout, but was substantially eased by L2-regularization, particularly when combined with weight perturbation. Further, we introduce a new algorithm -- continual backpropagation -- which slightly modifies conventional backpropagation to reinitialize a small fraction of less-used units after each example and appears to maintain plasticity indefinitely.

Mohamed Elsayed, Qingfeng Lan, Clare Lyle et al.

Many failures in deep continual and reinforcement learning are associated with increasing magnitudes of the weights, making them hard to change and potentially causing overfitting. While many methods address these learning failures, they often change the optimizer or the architecture, a complexity that hinders widespread adoption in various systems. In this paper, we focus on learning failures that are associated with increasing weight norm and we propose a simple technique that can be easily added on top of existing learning systems: clipping neural network weights to limit them to a specific range. We study the effectiveness of weight clipping in a series of supervised and reinforcement learning experiments. Our empirical results highlight the benefits of weight clipping for generalization, addressing loss of plasticity and policy collapse, and facilitating learning with a large replay ratio.

Qingfeng Lan, A. Rupam Mahmood

Catastrophic forgetting remains a significant challenge to continual learning for decades. While recent works have proposed effective methods to mitigate this problem, they mainly focus on the algorithmic side. Meanwhile, we do not fully understand what architectural properties of neural networks lead to catastrophic forgetting. This study aims to fill this gap by studying the role of activation functions in the training dynamics of neural networks and their impact on catastrophic forgetting. Our study reveals that, besides sparse representations, the gradient sparsity of activation functions also plays an important role in reducing forgetting. Based on this insight, we propose a new class of activation functions, elephant activation functions, that can generate both sparse representations and sparse gradients. We show that by simply replacing classical activation functions with elephant activation functions, we can significantly improve the resilience of neural networks to catastrophic forgetting. Our method has broad applicability and benefits for continual learning in regression, class incremental learning, and reinforcement learning tasks. Specifically, we achieves excellent performance on Split MNIST dataset in just one single pass, without using replay buffer, task boundary information, or pre-training.

Yufeng Yuan, A. Rupam Mahmood

An oft-ignored challenge of real-world reinforcement learning is that the real world does not pause when agents make learning updates. As standard simulated environments do not address this real-time aspect of learning, most available implementations of RL algorithms process environment interactions and learning updates sequentially. As a consequence, when such implementations are deployed in the real world, they may make decisions based on significantly delayed observations and not act responsively. Asynchronous learning has been proposed to solve this issue, but no systematic comparison between sequential and asynchronous reinforcement learning was conducted using real-world environments. In this work, we set up two vision-based tasks with a robotic arm, implement an asynchronous learning system that extends a previous architecture, and compare sequential and asynchronous reinforcement learning across different action cycle times, sensory data dimensions, and mini-batch sizes. Our experiments show that when the time cost of learning updates increases, the action cycle time in sequential implementation could grow excessively long, while the asynchronous implementation can always maintain an appropriate action cycle time. Consequently, when learning updates are expensive, the performance of sequential learning diminishes and is outperformed by asynchronous learning by a substantial margin. Our system learns in real-time to reach and track visual targets from pixels within two hours of experience and does so directly using real robots, learning completely from scratch.

Arsalan Sharifnassab, Mohamed Elsayed, Kris De Asis et al.

In gradient-based learning, a step size chosen in parameter units does not produce a predictable per-step change in function output. This often leads to instability in the streaming setting (i.e., batch size=1), where stochasticity is not averaged out and update magnitudes can momentarily become arbitrarily big or small. Instead, we propose intentional updates: first specify the intended outcome of an update and then solve for the step size that approximately achieves it. This strategy has precedent in online supervised linear regression via Normalized Least Mean Squares algorithm, which selects a step size to yield a specified change in the function output proportional to the current error. We extend this principle to streaming deep reinforcement learning by defining appropriate intended outcomes: Intentional TD aims for a fixed fractional reduction of the TD error, and Intentional Policy Gradient aims for a bounded per-step change in the policy, limiting local KL divergence. We propose practical algorithms combining eligibility traces and diagonal scaling. Empirically, these methods yield state-of-the-art streaming performance, frequently performing on par with batch and replay-buffer approaches.

A. Rupam Mahmood, Dmytro Korenkevych, Gautham Vasan et al.

Through many recent successes in simulation, model-free reinforcement learning has emerged as a promising approach to solving continuous control robotic tasks. The research community is now able to reproduce, analyze and build quickly on these results due to open source implementations of learning algorithms and simulated benchmark tasks. To carry forward these successes to real-world applications, it is crucial to withhold utilizing the unique advantages of simulations that do not transfer to the real world and experiment directly with physical robots. However, reinforcement learning research with physical robots faces substantial resistance due to the lack of benchmark tasks and supporting source code. In this work, we introduce several reinforcement learning tasks with multiple commercially available robots that present varying levels of learning difficulty, setup, and repeatability. On these tasks, we test the learning performance of off-the-shelf implementations of four reinforcement learning algorithms and analyze sensitivity to their hyper-parameters to determine their readiness for applications in various real-world tasks. Our results show that with a careful setup of the task interface and computations, some of these implementations can be readily applicable to physical robots. We find that state-of-the-art learning algorithms are highly sensitive to their hyper-parameters and their relative ordering does not transfer across tasks, indicating the necessity of re-tuning them for each task for best performance. On the other hand, the best hyper-parameter configuration from one task may often result in effective learning on held-out tasks even with different robots, providing a reasonable default. We make the benchmark tasks publicly available to enhance reproducibility in real-world reinforcement learning.

Mohamed Elsayed, A. Rupam Mahmood

Deep representation learning methods struggle with continual learning, suffering from both catastrophic forgetting of useful units and loss of plasticity, often due to rigid and unuseful units. While many methods address these two issues separately, only a few currently deal with both simultaneously. In this paper, we introduce Utility-based Perturbed Gradient Descent (UPGD) as a novel approach for the continual learning of representations. UPGD combines gradient updates with perturbations, where it applies smaller modifications to more useful units, protecting them from forgetting, and larger modifications to less useful units, rejuvenating their plasticity. We use a challenging streaming learning setup where continual learning problems have hundreds of non-stationarities and unknown task boundaries. We show that many existing methods suffer from at least one of the issues, predominantly manifested by their decreasing accuracy over tasks. On the other hand, UPGD continues to improve performance and surpasses or is competitive with all methods in all problems. Finally, in extended reinforcement learning experiments with PPO, we show that while Adam exhibits a performance drop after initial learning, UPGD avoids it by addressing both continual learning issues.

Mohamed Elsayed, Gautham Vasan, A. Rupam Mahmood

Natural intelligence processes experience as a continuous stream, sensing, acting, and learning moment-by-moment in real time. Streaming learning, the modus operandi of classic reinforcement learning (RL) algorithms like Q-learning and TD, mimics natural learning by using the most recent sample without storing it. This approach is also ideal for resource-constrained, communication-limited, and privacy-sensitive applications. However, in deep RL, learners almost always use batch updates and replay buffers, making them computationally expensive and incompatible with streaming learning. Although the prevalence of batch deep RL is often attributed to its sample efficiency, a more critical reason for the absence of streaming deep RL is its frequent instability and failure to learn, which we refer to as stream barrier. This paper introduces the stream-x algorithms, the first class of deep RL algorithms to overcome stream barrier for both prediction and control and match sample efficiency of batch RL. Through experiments in Mujoco Gym, DM Control Suite, and Atari Games, we demonstrate stream barrier in existing algorithms and successful stable learning with our stream-x algorithms: stream Q, stream AC, and stream TD, achieving the best model-free performance in DM Control Dog environments. A set of common techniques underlies the stream-x algorithms, enabling their success with a single set of hyperparameters and allowing for easy extension to other algorithms, thereby reviving streaming RL.

Gautham Vasan, Mohamed Elsayed, Alireza Azimi et al.

Modern deep policy gradient methods achieve effective performance on simulated robotic tasks, but they all require large replay buffers or expensive batch updates, or both, making them incompatible for real systems with resource-limited computers. We show that these methods fail catastrophically when limited to small replay buffers or during incremental learning, where updates only use the most recent sample without batch updates or a replay buffer. We propose a novel incremental deep policy gradient method -- Action Value Gradient (AVG) and a set of normalization and scaling techniques to address the challenges of instability in incremental learning. On robotic simulation benchmarks, we show that AVG is the only incremental method that learns effectively, often achieving final performance comparable to batch policy gradient methods. This advancement enabled us to show for the first time effective deep reinforcement learning with real robots using only incremental updates, employing a robotic manipulator and a mobile robot.

Fengdi Che, Bryan Chan, Chen Ma et al.

Off-policy policy evaluation (OPE), an essential component of reinforcement learning, has long suffered from stationary state distribution mismatch, undermining both stability and accuracy of OPE estimates. While existing methods correct distribution shifts by estimating density ratios, they often rely on expensive optimization or backward Bellman-based updates and struggle to outperform simpler baselines. We introduce AVG-DICE, a computationally simple Monte Carlo estimator for the density ratio that averages discounted importance sampling ratios, providing an unbiased and consistent correction. AVG-DICE extends naturally to nonlinear function approximation using regression, which we roughly tune and test on OPE tasks based on Mujoco Gym environments and compare with state-of-the-art density-ratio estimators using their reported hyperparameters. In our experiments, AVG-DICE is at least as accurate as state-of-the-art estimators and sometimes offers orders-of-magnitude improvements. However, a sensitivity analysis shows that best-performing hyperparameters may vary substantially across different discount factors, so a re-tuning is suggested.

Fahim Shahriar, Cheryl Wang, Alireza Azimi et al.

Goal-conditioned reinforcement learning (GCRL) allows agents to learn diverse objectives using a unified policy. The success of GCRL, however, is contingent on the choice of goal representation. In this work, we propose a mask-based goal representation system that provides object-agnostic visual cues to the agent, enabling efficient learning and superior generalization. In contrast, existing goal representation methods, such as target state images, 3D coordinates, and one-hot vectors, face issues of poor generalization to unseen objects, slow convergence, and the need for special cameras. Masks can be processed to generate dense rewards without requiring error-prone distance calculations. Learning with ground truth masks in simulation, we achieved 99.9% reaching accuracy on training and unseen test objects. Our proposed method can be utilized to perform pick-up tasks with high accuracy, without using any positional information of the target. Moreover, we demonstrate learning from scratch and sim-to-real transfer applications using two different physical robots, utilizing pretrained open vocabulary object detection models for mask generation.

Qingfeng Lan, Gautham Vasan, A. Rupam Mahmood

Catastrophic forgetting has remained a significant challenge for efficient reinforcement learning for decades (Ring 1994, Rivest and Precup 2003). While recent works have proposed effective methods to mitigate this issue, they mainly focus on the algorithmic side. Meanwhile, we do not fully understand what architectural properties of neural networks lead to catastrophic forgetting. This study aims to fill this gap by studying the role of activation functions in the training dynamics of neural networks and their impact on catastrophic forgetting in reinforcement learning setup. Our study reveals that, besides sparse representations, the gradient sparsity of activation functions also plays an important role in reducing forgetting. Based on this insight, we propose a new class of activation functions, elephant activation functions, that can generate both sparse outputs and sparse gradients. We show that by simply replacing classical activation functions with elephant activation functions in the neural networks of value-based algorithms, we can significantly improve the resilience of neural networks to catastrophic forgetting, thus making reinforcement learning more sample-efficient and memory-efficient.

Jiamin He, A. Rupam Mahmood, Martha White

We introduce a novel reinforcement learning (RL) framework that treats distribution parameters as actions, redefining the boundary between agent and environment. This reparameterization makes the new action space continuous, regardless of the original action type (discrete, continuous, mixed, etc.). Under this new parameterization, we develop a generalized deterministic policy gradient estimator, Distribution Parameter Policy Gradient (DPPG), which has lower variance than the gradient in the original action space. Although learning the critic over distribution parameters poses new challenges, we introduce interpolated critic learning (ICL), a simple yet effective strategy to enhance learning, supported by insights from bandit settings. Building on TD3, a strong baseline for continuous control, we propose a practical DPPG-based actor-critic algorithm, Distribution Parameter Actor-Critic (DPAC). Empirically, DPAC outperforms TD3 in MuJoCo continuous control tasks from OpenAI Gym and DeepMind Control Suite, and demonstrates competitive performance on the same environments with discretized action spaces.

Gautham Vasan, Yan Wang, Fahim Shahriar et al.

Many real-world robot learning problems, such as pick-and-place or arriving at a destination, can be seen as a problem of reaching a goal state as soon as possible. These problems, when formulated as episodic reinforcement learning tasks, can easily be specified to align well with our intended goal: -1 reward every time step with termination upon reaching the goal state, called minimum-time tasks. Despite this simplicity, such formulations are often overlooked in favor of dense rewards due to their perceived difficulty and lack of informativeness. Our studies contrast the two reward paradigms, revealing that the minimum-time task specification not only facilitates learning higher-quality policies but can also surpass dense-reward-based policies on their own performance metrics. Crucially, we also identify the goal-hit rate of the initial policy as a robust early indicator for learning success in such sparse feedback settings. Finally, using four distinct real-robotic platforms, we show that it is possible to learn pixel-based policies from scratch within two to three hours using constant negative rewards.

Haque Ishfaq, Yixin Tan, Yu Yang et al.

Thompson sampling (TS) is one of the most popular exploration techniques in reinforcement learning (RL). However, most TS algorithms with theoretical guarantees are difficult to implement and not generalizable to Deep RL. While the emerging approximate sampling-based exploration schemes are promising, most existing algorithms are specific to linear Markov Decision Processes (MDP) with suboptimal regret bounds, or only use the most basic samplers such as Langevin Monte Carlo. In this work, we propose an algorithmic framework that incorporates different approximate sampling methods with the recently proposed Feel-Good Thompson Sampling (FGTS) approach (Zhang, 2022; Dann et al., 2021), which was previously known to be computationally intractable in general. When applied to linear MDPs, our regret analysis yields the best known dependency of regret on dimensionality, surpassing existing randomized algorithms. Additionally, we provide explicit sampling complexity for each employed sampler. Empirically, we show that in tasks where deep exploration is necessary, our proposed algorithms that combine FGTS and approximate sampling perform significantly better compared to other strong baselines. On several challenging games from the Atari 57 suite, our algorithms achieve performance that is either better than or on par with other strong baselines from the deep RL literature.

Mohamed Elsayed, Homayoon Farrahi, Felix Dangel et al.

Second-order information is valuable for many applications but challenging to compute. Several works focus on computing or approximating Hessian diagonals, but even this simplification introduces significant additional costs compared to computing a gradient. In the absence of efficient exact computation schemes for Hessian diagonals, we revisit an early approximation scheme proposed by Becker and LeCun (1989, BL89), which has a cost similar to gradients and appears to have been overlooked by the community. We introduce HesScale, an improvement over BL89, which adds negligible extra computation. On small networks, we find that this improvement is of higher quality than all alternatives, even those with theoretical guarantees, such as unbiasedness, while being much cheaper to compute. We use this insight in reinforcement learning problems where small networks are used and demonstrate HesScale in second-order optimization and scaling the step-size parameter. In our experiments, HesScale optimizes faster than existing methods and improves stability through step-size scaling. These findings are promising for scaling second-order methods in larger models in the future.

Bram Grooten, Tristan Tomilin, Gautham Vasan et al.

The visual world provides an abundance of information, but many input pixels received by agents often contain distracting stimuli. Autonomous agents need the ability to distinguish useful information from task-irrelevant perceptions, enabling them to generalize to unseen environments with new distractions. Existing works approach this problem using data augmentation or large auxiliary networks with additional loss functions. We introduce MaDi, a novel algorithm that learns to mask distractions by the reward signal only. In MaDi, the conventional actor-critic structure of deep reinforcement learning agents is complemented by a small third sibling, the Masker. This lightweight neural network generates a mask to determine what the actor and critic will receive, such that they can focus on learning the task. The masks are created dynamically, depending on the current input. We run experiments on the DeepMind Control Generalization Benchmark, the Distracting Control Suite, and a real UR5 Robotic Arm. Our algorithm improves the agent's focus with useful masks, while its efficient Masker network only adds 0.2% more parameters to the original structure, in contrast to previous work. MaDi consistently achieves generalization results better than or competitive to state-of-the-art methods.

Haque Ishfaq, Qingfeng Lan, Pan Xu et al.

We present a scalable and effective exploration strategy based on Thompson sampling for reinforcement learning (RL). One of the key shortcomings of existing Thompson sampling algorithms is the need to perform a Gaussian approximation of the posterior distribution, which is not a good surrogate in most practical settings. We instead directly sample the Q function from its posterior distribution, by using Langevin Monte Carlo, an efficient type of Markov Chain Monte Carlo (MCMC) method. Our method only needs to perform noisy gradient descent updates to learn the exact posterior distribution of the Q function, which makes our approach easy to deploy in deep RL. We provide a rigorous theoretical analysis for the proposed method and demonstrate that, in the linear Markov decision process (linear MDP) setting, it has a regret bound of $\tilde{O}(d^{3/2}H^{3/2}\sqrt{T})$, where $d$ is the dimension of the feature mapping, $H$ is the planning horizon, and $T$ is the total number of steps. We apply this approach to deep RL, by using Adam optimizer to perform gradient updates. Our approach achieves better or similar results compared with state-of-the-art deep RL algorithms on several challenging exploration tasks from the Atari57 suite.

Homayoon Farrahi, A. Rupam Mahmood

Continuous-time reinforcement learning tasks commonly use discrete steps of fixed cycle times for actions. As practitioners need to choose the action-cycle time for a given task, a significant concern is whether the hyper-parameters of the learning algorithm need to be re-tuned for each choice of the cycle time, which is prohibitive for real-world robotics. In this work, we investigate the widely-used baseline hyper-parameter values of two policy gradient algorithms -- PPO and SAC -- across different cycle times. Using a benchmark task where the baseline hyper-parameters of both algorithms were shown to work well, we reveal that when a cycle time different than the task default is chosen, PPO with baseline hyper-parameters fails to learn. Moreover, both PPO and SAC with their baseline hyper-parameters perform substantially worse than their tuned values for each cycle time. We propose novel approaches for setting these hyper-parameters based on the cycle time. In our experiments on simulated and real-world robotic tasks, the proposed approaches performed at least as well as the baseline hyper-parameters, with significantly better performance for most choices of the cycle time, and did not result in learning failure for any cycle time. Hyper-parameter tuning still remains a significant barrier for real-world robotics, as our approaches require some initial tuning on a new task, even though it is negligible compared to an extensive tuning for each cycle time. Our approach requires no additional tuning after the cycle time is changed for a given task and is a step toward avoiding extensive and costly hyper-parameter tuning for real-world policy optimization.

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.

Shivam Garg, Samuele Tosatto, Yangchen Pan et al.

Policy gradient (PG) estimators are ineffective in dealing with softmax policies that are sub-optimally saturated, which refers to the situation when the policy concentrates its probability mass on sub-optimal actions. Sub-optimal policy saturation may arise from bad policy initialization or sudden changes in the environment that occur after the policy has already converged. Current softmax PG estimators require a large number of updates to overcome policy saturation, which causes low sample efficiency and poor adaptability to new situations. To mitigate this problem, we propose a novel PG estimator for softmax policies that utilizes the bias in the critic estimate and the noise present in the reward signal to escape the saturated regions of the policy parameter space. Our theoretical analysis and experiments, conducted on bandits and various reinforcement learning environments, show that this new estimator is significantly more robust to policy saturation.

Shibhansh Dohare, Richard S. Sutton, A. Rupam Mahmood

The Backprop algorithm for learning in neural networks utilizes two mechanisms: first, stochastic gradient descent and second, initialization with small random weights, where the latter is essential to the effectiveness of the former. We show that in continual learning setups, Backprop performs well initially, but over time its performance degrades. Stochastic gradient descent alone is insufficient to learn continually; the initial randomness enables only initial learning but not continual learning. To the best of our knowledge, ours is the first result showing this degradation in Backprop's ability to learn. To address this degradation in Backprop's plasticity, we propose an algorithm that continually injects random features alongside gradient descent using a new generate-and-test process. We call this the \textit{Continual Backprop} algorithm. We show that, unlike Backprop, Continual Backprop is able to continually adapt in both supervised and reinforcement learning (RL) problems. Continual Backprop has the same computational complexity as Backprop and can be seen as a natural extension of Backprop for continual learning.

Alan Chan, Hugo Silva, Sungsu Lim et al.

Approximate Policy Iteration (API) algorithms alternate between (approximate) policy evaluation and (approximate) greedification. Many different approaches have been explored for approximate policy evaluation, but less is understood about approximate greedification and what choices guarantee policy improvement. In this work, we investigate approximate greedification when reducing the KL divergence between the parameterized policy and the Boltzmann distribution over action values. In particular, we investigate the difference between the forward and reverse KL divergences, with varying degrees of entropy regularization. We show that the reverse KL has stronger policy improvement guarantees, but that reducing the forward KL can result in a worse policy. We also demonstrate, however, that a large enough reduction of the forward KL can induce improvement under additional assumptions. Empirically, we show on simple continuous-action environments that the forward KL can induce more exploration, but at the cost of a more suboptimal policy. No significant differences were observed in the discrete-action setting or on a suite of benchmark problems. Throughout, we highlight that many policy gradient methods can be seen as an instance of API, with either the forward or reverse KL for the policy update, and discuss next steps for understanding and improving our policy optimization algorithms.

Michael Przystupa, Masood Dehghan, Martin Jagersand et al.

Designing adaptable control laws that can transfer between different robots is a challenge because of kinematic and dynamic differences, as well as in scenarios where external sensors are used. In this work, we empirically investigate a neural networks ability to approximate the Jacobian matrix for an application in Cartesian control schemes. Specifically, we are interested in approximating the kinematic Jacobian, which arises from kinematic equations mapping a manipulator's joint angles to the end-effector's location. We propose two different approaches to learn the kinematic Jacobian. The first method arises from visual servoing where we learn the kinematic Jacobian as an approximate linear system of equations from the k-nearest neighbors for a desired joint configuration. The second, motivated by forward models in machine learning, learns the kinematic behavior directly and calculates the Jacobian by differentiating the learned neural kinematics model. Simulation experimental results show that both methods achieve better performance than alternative data-driven methods for control, provide closer approximations to the proper kinematics Jacobian matrix, and on average produce better-conditioned Jacobian matrices. Real-world experiments were conducted on a Kinova Gen-3 lightweight robotic manipulator, which includes an uncalibrated visual servoing experiment, a practical application of our methods, as well as a 7-DOF point-to-point task highlighting that our methods are applicable on real robotic manipulators.

Qingfeng Lan, Samuele Tosatto, Homayoon Farrahi et al.

Despite the increasing popularity of policy gradient methods, they are yet to be widely utilized in sample-scarce applications, such as robotics. The sample efficiency could be improved by making best usage of available information. As a key component in reinforcement learning, the reward function is usually devised carefully to guide the agent. Hence, the reward function is usually known, allowing access to not only scalar reward signals but also reward gradients. To benefit from reward gradients, previous works require the knowledge of environment dynamics, which are hard to obtain. In this work, we develop the \textit{Reward Policy Gradient} estimator, a novel approach that integrates reward gradients without learning a model. Bypassing the model dynamics allows our estimator to achieve a better bias-variance trade-off, which results in a higher sample efficiency, as shown in the empirical analysis. Our method also boosts the performance of Proximal Policy Optimization on different MuJoCo control tasks.

Dmytro Korenkevych, A. Rupam Mahmood, Gautham Vasan et al.

Reinforcement learning algorithms rely on exploration to discover new behaviors, which is typically achieved by following a stochastic policy. In continuous control tasks, policies with a Gaussian distribution have been widely adopted. Gaussian exploration however does not result in smooth trajectories that generally correspond to safe and rewarding behaviors in practical tasks. In addition, Gaussian policies do not result in an effective exploration of an environment and become increasingly inefficient as the action rate increases. This contributes to a low sample efficiency often observed in learning continuous control tasks. We introduce a family of stationary autoregressive (AR) stochastic processes to facilitate exploration in continuous control domains. We show that proposed processes possess two desirable features: subsequent process observations are temporally coherent with continuously adjustable degree of coherence, and the process stationary distribution is standard normal. We derive an autoregressive policy (ARP) that implements such processes maintaining the standard agent-environment interface. We show how ARPs can be easily used with the existing off-the-shelf learning algorithms. Empirically we demonstrate that using ARPs results in improved exploration and sample efficiency in both simulated and real world domains, and, furthermore, provides smooth exploration trajectories that enable safe operation of robotic hardware.

A. Rupam Mahmood, Dmytro Korenkevych, Brent J. Komer et al.

Reinforcement learning is a promising approach to developing hard-to-engineer adaptive solutions for complex and diverse robotic tasks. However, learning with real-world robots is often unreliable and difficult, which resulted in their low adoption in reinforcement learning research. This difficulty is worsened by the lack of guidelines for setting up learning tasks with robots. In this work, we develop a learning task with a UR5 robotic arm to bring to light some key elements of a task setup and study their contributions to the challenges with robots. We find that learning performance can be highly sensitive to the setup, and thus oversights and omissions in setup details can make effective learning, reproducibility, and fair comparison hard. Our study suggests some mitigating steps to help future experimenters avoid difficulties and pitfalls. We show that highly reliable and repeatable experiments can be performed in our setup, indicating the possibility of reinforcement learning research extensively based on real-world robots.

Huizhen Yu, A. Rupam Mahmood, Richard S. Sutton

We consider off-policy temporal-difference (TD) learning in discounted Markov decision processes, where the goal is to evaluate a policy in a model-free way by using observations of a state process generated without executing the policy. To curb the high variance issue in off-policy TD learning, we propose a new scheme of setting the $λ$-parameters of TD, based on generalized Bellman equations. Our scheme is to set $λ$ according to the eligibility trace iterates calculated in TD, thereby easily keeping these traces in a desired bounded range. Compared with prior work, this scheme is more direct and flexible, and allows much larger $λ$ values for off-policy TD learning with bounded traces. As to its soundness, using Markov chain theory, we prove the ergodicity of the joint state-trace process under nonrestrictive conditions, and we show that associated with our scheme is a generalized Bellman equation (for the policy to be evaluated) that depends on both the evolution of $λ$ and the unique invariant probability measure of the state-trace process. These results not only lead immediately to a characterization of the convergence behavior of least-squares based implementation of our scheme, but also prepare the ground for further analysis of gradient-based implementations.

Harm van Seijen, A. Rupam Mahmood, Patrick M. Pilarski et al.

The temporal-difference methods TD($λ$) and Sarsa($λ$) form a core part of modern reinforcement learning. Their appeal comes from their good performance, low computational cost, and their simple interpretation, given by their forward view. Recently, new versions of these methods were introduced, called true online TD($λ$) and true online Sarsa($λ$), respectively (van Seijen & Sutton, 2014). These new versions maintain an exact equivalence with the forward view at all times, whereas the traditional versions only approximate it for small step-sizes. We hypothesize that these true online methods not only have better theoretical properties, but also dominate the regular methods empirically. In this article, we put this hypothesis to the test by performing an extensive empirical comparison. Specifically, we compare the performance of true online TD($λ$)/Sarsa($λ$) with regular TD($λ$)/Sarsa($λ$) on random MRPs, a real-world myoelectric prosthetic arm, and a domain from the Arcade Learning Environment. We use linear function approximation with tabular, binary, and non-binary features. Our results suggest that the true online methods indeed dominate the regular methods. Across all domains/representations the learning speed of the true online methods are often better, but never worse than that of the regular methods. An additional advantage is that no choice between traces has to be made for the true online methods. Besides the empirical results, we provide an in-depth analysis of the theory behind true online temporal-difference learning. In addition, we show that new true online temporal-difference methods can be derived by making changes to the online forward view and then rewriting the update equations.

A. Rupam Mahmood, Huizhen Yu, Martha White et al.

Emphatic algorithms are temporal-difference learning algorithms that change their effective state distribution by selectively emphasizing and de-emphasizing their updates on different time steps. Recent works by Sutton, Mahmood and White (2015), and Yu (2015) show that by varying the emphasis in a particular way, these algorithms become stable and convergent under off-policy training with linear function approximation. This paper serves as a unified summary of the available results from both works. In addition, we demonstrate the empirical benefits from the flexibility of emphatic algorithms, including state-dependent discounting, state-dependent bootstrapping, and the user-specified allocation of function approximation resources.

Harm van Seijen, A. Rupam Mahmood, Patrick M. Pilarski et al.

The true online TD(λ) algorithm has recently been proposed (van Seijen and Sutton, 2014) as a universal replacement for the popular TD(λ) algorithm, in temporal-difference learning and reinforcement learning. True online TD(λ) has better theoretical properties than conventional TD(λ), and the expectation is that it also results in faster learning. In this paper, we put this hypothesis to the test. Specifically, we compare the performance of true online TD(λ) with that of TD(λ) on challenging examples, random Markov reward processes, and a real-world myoelectric prosthetic arm. We use linear function approximation with tabular, binary, and non-binary features. We assess the algorithms along three dimensions: computational cost, learning speed, and ease of use. Our results confirm the strength of true online TD(λ): 1) for sparse feature vectors, the computational overhead with respect to TD(λ) is minimal; for non-sparse features the computation time is at most twice that of TD(λ), 2) across all domains/representations the learning speed of true online TD(λ) is often better, but never worse than that of TD(λ), and 3) true online TD(λ) is easier to use, because it does not require choosing between trace types, and it is generally more stable with respect to the step-size. Overall, our results suggest that true online TD(λ) should be the first choice when looking for an efficient, general-purpose TD method.

Richard S. Sutton, A. Rupam Mahmood, Martha White

In this paper we introduce the idea of improving the performance of parametric temporal-difference (TD) learning algorithms by selectively emphasizing or de-emphasizing their updates on different time steps. In particular, we show that varying the emphasis of linear TD($λ$)'s updates in a particular way causes its expected update to become stable under off-policy training. The only prior model-free TD methods to achieve this with per-step computation linear in the number of function approximation parameters are the gradient-TD family of methods including TDC, GTD($λ$), and GQ($λ$). Compared to these methods, our _emphatic TD($λ$)_ is simpler and easier to use; it has only one learned parameter vector and one step-size parameter. Our treatment includes general state-dependent discounting and bootstrapping functions, and a way of specifying varying degrees of interest in accurately valuing different states.