Using a model of the environment, reinforcement learning agents can plan their future moves and achieve superhuman performance in board games like Chess, Shogi, and Go, while remaining relatively sample-efficient. As demonstrated by the MuZero Algorithm, the environment model can even be learned dynamically, generalizing the agent to many more tasks while at the same time achieving state-of-the-art performance. Notably, MuZero uses internal state representations derived from real environment states for its predictions. In this paper, we bind the model's predicted internal state representation to the environment state via two additional terms: a reconstruction model loss and a simpler consistency loss, both of which work independently and unsupervised, acting as constraints to stabilize the learning process. Our experiments show that this new integration of reconstruction model loss and simpler consistency loss provide a significant performance increase in OpenAI Gym environments. Our modifications also enable self-supervised pretraining for MuZero, so the algorithm can learn about environment dynamics before a goal is made available.
Model-based reinforcement learning (MBRL) approaches rely on discrete-time state transition models whereas physical systems and the vast majority of control tasks operate in continuous-time. To avoid time-discretization approximation of the underlying process, we propose a continuous-time MBRL framework based on a novel actor-critic method. Our approach also infers the unknown state evolution differentials with Bayesian neural ordinary differential equations (ODE) to account for epistemic uncertainty. We implement and test our method on a new ODE-RL suite that explicitly solves continuous-time control systems. Our experiments illustrate that the model is robust against irregular and noisy data, is sample-efficient, and can solve control problems which pose challenges to discrete-time MBRL methods.
In this paper, we present a Model-Based Reinforcement Learning (MBRL) algorithm named \emph{Monte Carlo Probabilistic Inference for Learning COntrol} (MC-PILCO). The algorithm relies on Gaussian Processes (GPs) to model the system dynamics and on a Monte Carlo approach to estimate the policy gradient. This defines a framework in which we ablate the choice of the following components: (i) the selection of the cost function, (ii) the optimization of policies using dropout, (iii) an improved data efficiency through the use of structured kernels in the GP models. The combination of the aforementioned aspects affects dramatically the performance of MC-PILCO. Numerical comparisons in a simulated cart-pole environment show that MC-PILCO exhibits better data efficiency and control performance w.r.t. state-of-the-art GP-based MBRL algorithms. Finally, we apply MC-PILCO to real systems, considering in particular systems with partially measurable states. We discuss the importance of modeling both the measurement system and the state estimators during policy optimization. The effectiveness of the proposed solutions has been tested in simulation and on two real systems, a Furuta pendulum and a ball-and-plate rig.
In this paper, we propose a Model-Based Reinforcement Learning (MBRL) algorithm for Partially Measurable Systems (PMS), i.e., systems where the state can not be directly measured, but must be estimated through proper state observers. The proposed algorithm, named Monte Carlo Probabilistic Inference for Learning COntrol for Partially Measurable Systems (MC-PILCO4PMS), relies on Gaussian Processes (GPs) to model the system dynamics, and on a Monte Carlo approach to update the policy parameters. W.r.t. previous GP-based MBRL algorithms, MC-PILCO4PMS models explicitly the presence of state observers during policy optimization, allowing to deal PMS. The effectiveness of the proposed algorithm has been tested both in simulation and in two real systems.
In this paper we study the problem of synthesizing optimal control policies for uncertain continuous-time nonlinear systems from syntactically co-safe linear temporal logic (scLTL) formulas. We formulate this problem as a sequence of reach-avoid optimal control sub-problems. We show that the resulting hybrid optimal control policy guarantees the satisfaction of a given scLTL formula by constructing a barrier certificate. Since solving each optimal control problem may be computationally intractable, we take a learning-based approach to approximately solve this sequence of optimal control problems online without requiring full knowledge of the system dynamics. Using Lyapunov-based tools, we develop sufficient conditions under which our approximate solution maintains correctness. Finally, we demonstrate the efficacy of the developed method with a numerical example.
In biopharmaceutical manufacturing, fermentation processes play a critical role in productivity and profit. A fermentation process uses living cells with complex biological mechanisms, leading to high variability in the process outputs, namely, the protein and impurity levels. By building on the biological mechanisms of protein and impurity growth, we introduce a stochastic model to characterize the accumulation of the protein and impurity levels in the fermentation process. However, a common challenge in the industry is the availability of only a very limited amount of data, especially in the development and early stages of production. This adds an additional layer of uncertainty, referred to as model risk, due to the difficulty of estimating the model parameters with limited data. In this paper, we study the harvesting decision for a fermentation process (i.e., when to stop the fermentation and collect the production reward) under model risk. We adopt a Bayesian approach to update the unknown parameters of the growth-rate distributions, and use the resulting posterior distributions to characterize the impact of model risk on fermentation output variability. The harvesting problem is formulated as a Markov decision process model with knowledge states that summarize the posterior distributions and hence incorporate the model risk in decision-making. Our case studies at MSD Animal Health demonstrate that the proposed model and solution approach improve the harvesting decisions in real life by achieving substantially higher average output from a fermentation batch along with lower batch-to-batch variability.
Balancing exploration and exploitation is crucial in reinforcement learning (RL). In this paper, we study model-based posterior sampling for reinforcement learning (PSRL) in continuous state-action spaces theoretically and empirically. First, we show the first regret bound of PSRL in continuous spaces which is polynomial in the episode length to the best of our knowledge. With the assumption that reward and transition functions can be modeled by Bayesian linear regression, we develop a regret bound of $\tilde{O}(H^{3/2}d\sqrt{T})$, where $H$ is the episode length, $d$ is the dimension of the state-action space, and $T$ indicates the total time steps. This result matches the best-known regret bound of non-PSRL methods in linear MDPs. Our bound can be extended to nonlinear cases as well with feature embedding: using linear kernels on the feature representation $\phi$, the regret bound becomes $\tilde{O}(H^{3/2}d_{\phi}\sqrt{T})$, where $d_\phi$ is the dimension of the representation space. Moreover, we present MPC-PSRL, a model-based posterior sampling algorithm with model predictive control for action selection. To capture the uncertainty in models, we use Bayesian linear regression on the penultimate layer (the feature representation layer $\phi$) of neural networks. Empirical results show that our algorithm achieves the state-of-the-art sample efficiency in benchmark continuous control tasks compared to prior model-based algorithms, and matches the asymptotic performance of model-free algorithms.
Accurately predicting the dynamics of robotic systems is crucial for model-based control and reinforcement learning. The most common way to estimate dynamics is by fitting a one-step ahead prediction model and using it to recursively propagate the predicted state distribution over long horizons. Unfortunately, this approach is known to compound even small prediction errors, making long-term predictions inaccurate. In this paper, we propose a new parametrization to supervised learning on state-action data to stably predict at longer horizons -- that we call a trajectory-based model. This trajectory-based model takes an initial state, a future time index, and control parameters as inputs, and directly predicts the state at the future time index. Experimental results in simulated and real-world robotic tasks show that trajectory-based models yield significantly more accurate long term predictions, improved sample efficiency, and the ability to predict task reward. With these improved prediction properties, we conclude with a demonstration of methods for using the trajectory-based model for control.
Model-based reinforcement learning (MBRL) methods have shown strong sample efficiency and performance across a variety of tasks, including when faced with high-dimensional visual observations. These methods learn to predict the environment dynamics and expected reward from interaction and use this predictive model to plan and perform the task. However, MBRL methods vary in their fundamental design choices, and there is no strong consensus in the literature on how these design decisions affect performance. In this paper, we study a number of design decisions for the predictive model in visual MBRL algorithms, focusing specifically on methods that use a predictive model for planning. We find that a range of design decisions that are often considered crucial, such as the use of latent spaces, have little effect on task performance. A big exception to this finding is that predicting future observations (i.e., images) leads to significant task performance improvement compared to only predicting rewards. We also empirically find that image prediction accuracy, somewhat surprisingly, correlates more strongly with downstream task performance than reward prediction accuracy. We show how this phenomenon is related to exploration and how some of the lower-scoring models on standard benchmarks (that require exploration) will perform the same as the best-performing models when trained on the same training data. Simultaneously, in the absence of exploration, models that fit the data better usually perform better on the downstream task as well, but surprisingly, these are often not the same models that perform the best when learning and exploring from scratch. These findings suggest that performance and exploration place important and potentially contradictory requirements on the model.
Reinforcement learning (RL) has shown great promise in optimizing long-term user interest in recommender systems. However, existing RL-based recommendation methods need a large number of interactions for each user to learn a robust recommendation policy. The challenge becomes more critical when recommending to new users who have a limited number of interactions. To that end, in this paper, we address the cold-start challenge in the RL-based recommender systems by proposing a meta-level model-based reinforcement learning approach for fast user adaptation. In our approach, we learn to infer each user's preference with a user context variable that enables recommendation systems to better adapt to new users with few interactions. To improve adaptation efficiency, we learn to recover the user policy and reward from only a few interactions via an inverse reinforcement learning method to assist a meta-level recommendation agent. Moreover, we model the interaction relationship between the user model and recommendation agent from an information-theoretic perspective. Empirical results show the effectiveness of the proposed method when adapting to new users with only a single interaction sequence. We further provide a theoretical analysis of the recommendation performance bound.
Reinforcement learning has been established over the past decade as an effective tool to find optimal control policies for dynamical systems, with recent focus on approaches that guarantee safety during the learning and/or execution phases. In general, safety guarantees are critical in reinforcement learning when the system is safety-critical and/or task restarts are not practically feasible. In optimal control theory, safety requirements are often expressed in terms of state and/or control constraints. In recent years, reinforcement learning approaches that rely on persistent excitation have been combined with a barrier transformation to learn the optimal control policies under state constraints. To soften the excitation requirements, model-based reinforcement learning methods that rely on exact model knowledge have also been integrated with the barrier transformation framework. The objective of this paper is to develop safe reinforcement learning method for deterministic nonlinear systems, with parametric uncertainties in the model, to learn approximate constrained optimal policies without relying on stringent excitation conditions. To that end, a model-based reinforcement learning technique that utilizes a novel filtered concurrent learning method, along with a barrier transformation, is developed in this paper to realize simultaneous learning of unknown model parameters and approximate optimal state-constrained control policies for safety-critical systems.
Buildings sector is one of the major consumers of energy in the United States. The buildings HVAC (Heating, Ventilation, and Air Conditioning) systems, whose functionality is to maintain thermal comfort and indoor air quality (IAQ), account for almost half of the energy consumed by the buildings. Thus, intelligent scheduling of the building HVAC system has the potential for tremendous energy and cost savings while ensuring that the control objectives (thermal comfort, air quality) are satisfied. Recently, several works have focused on model-free deep reinforcement learning based techniques such as Deep Q-Network (DQN). Such methods require extensive interactions with the environment. Thus, they are impractical to implement in real systems due to low sample efficiency. Safety-aware exploration is another challenge in real systems since certain actions at particular states may result in catastrophic outcomes. To address these issues and challenges, we propose a model-based reinforcement learning approach that learns the system dynamics using a neural network. Then, we adopt Model Predictive Control (MPC) using the learned system dynamics to perform control with random-sampling shooting method. To ensure safe exploration, we limit the actions within safe range and the maximum absolute change of actions according to prior knowledge. We evaluate our ideas through simulation using widely adopted EnergyPlus tool on a case study consisting of a two zone data-center. Experiments show that the average deviation of the trajectories sampled from the learned dynamics and the ground truth is below $20\%$. Compared with baseline approaches, we reduce the total energy consumption by $17.1\% \sim 21.8\%$. Compared with model-free reinforcement learning approach, we reduce the required number of training steps to converge by 10x.
Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local linear-quadratic approximations of system dynamics and reward, such methods can find both a target-optimal trajectory and time-variant optimal feedback controllers. However, the local linear-quadratic assumptions are a major source of optimization bias that leads to catastrophic greedy updates, raising the issue of proper regularization. Moreover, the approximate models' disregard for any physical state-action limits of the system causes further aggravation of the problem, as the optimization moves towards unreachable areas of the state-action space. In this paper, we address the issue of constrained systems in the scenario of online-fitted stochastic linear dynamics. We propose modeling state and action physical limits as probabilistic chance constraints linear in both state and action and introduce a new trajectory optimization technique that integrates these probabilistic constraints by optimizing a relaxed quadratic program. Our empirical evaluations show a significant improvement in learning robustness, which enables our approach to perform more effective updates and avoid premature convergence observed in state-of-the-art algorithms.
Generation of stroke-based non-photorealistic imagery, is an important problem in the computer vision community. As an endeavor in this direction, substantial recent research efforts have been focused on teaching machines "how to paint", in a manner similar to a human painter. However, the applicability of previous methods has been limited to datasets with little variation in position, scale and saliency of the foreground object. As a consequence, we find that these methods struggle to cover the granularity and diversity possessed by real world images. To this end, we propose a Semantic Guidance pipeline with 1) a bi-level painting procedure for learning the distinction between foreground and background brush strokes at training time. 2) We also introduce invariance to the position and scale of the foreground object through a neural alignment model, which combines object localization and spatial transformer networks in an end to end manner, to zoom into a particular semantic instance. 3) The distinguishing features of the in-focus object are then amplified by maximizing a novel guided backpropagation based focus reward. The proposed agent does not require any supervision on human stroke-data and successfully handles variations in foreground object attributes, thus, producing much higher quality canvases for the CUB-200 Birds and Stanford Cars-196 datasets. Finally, we demonstrate the further efficacy of our method on complex datasets with multiple foreground object instances by evaluating an extension of our method on the challenging Virtual-KITTI dataset. Source code and models are available at https://github.com/1jsingh/semantic-guidance.
Model-based reinforcement learning (MBRL) algorithms can attain significant sample efficiency but require an appropriate network structure to represent system dynamics. Current approaches include white-box modeling using analytic parameterizations and black-box modeling using deep neural networks. However, both can suffer from a bias-variance trade-off in the learning process, and neither provides a structured method for injecting domain knowledge into the network. As an alternative, gray-box modeling leverages prior knowledge in neural network training but only for simple systems. In this paper, we devise a nested mixture of experts (NMOE) for representing and learning hybrid dynamical systems. An NMOE combines both white-box and black-box models while optimizing bias-variance trade-off. Moreover, an NMOE provides a structured method for incorporating various types of prior knowledge by training the associative experts cooperatively or competitively. The prior knowledge includes information on robots' physical contacts with the environments as well as their kinematic and dynamic properties. In this paper, we demonstrate how to incorporate prior knowledge into our NMOE in various continuous control domains, including hybrid dynamical systems. We also show the effectiveness of our method in terms of data-efficiency, generalization to unseen data, and bias-variance trade-off. Finally, we evaluate our NMOE using an MBRL setup, where the model is integrated with a model-based controller and trained online.
In this work, we present a learning based approach to analog circuit design, where the goal is to optimize circuit performance subject to certain design constraints. One of the aspects that makes this problem challenging to optimize, is that measuring the performance of candidate configurations with simulation can be computationally expensive, particularly in the post-layout design. Additionally, the large number of design constraints and the interaction between the relevant quantities makes the problem complex. Therefore, to better facilitate supporting the human designers, it is desirable to gain knowledge about the whole space of feasible solutions. In order to tackle these challenges, we take inspiration from model-based reinforcement learning and propose a method with two key properties. First, it learns a reward model, i.e., surrogate model of the performance approximated by neural networks, to reduce the required number of simulation. Second, it uses a stochastic policy generator to explore the diverse solution space satisfying constraints. Together we combine these in a Dyna-style optimization framework, which we call DynaOpt, and empirically evaluate the performance on a circuit benchmark of a two-stage operational amplifier. The results show that, compared to the model-free method applied with 20,000 circuit simulations to train the policy, DynaOpt achieves even much better performance by learning from scratch with only 500 simulations.
With the rapid advance of information technology, network systems have become increasingly complex and hence the underlying system dynamics are often unknown or difficult to characterize. Finding a good network control policy is of significant importance to achieve desirable network performance (e.g., high throughput or low delay). In this work, we consider using model-based reinforcement learning (RL) to learn the optimal control policy for queueing networks so that the average job delay (or equivalently the average queue backlog) is minimized. Traditional approaches in RL, however, cannot handle the unbounded state spaces of the network control problem. To overcome this difficulty, we propose a new algorithm, called Reinforcement Learning for Queueing Networks (RL-QN), which applies model-based RL methods over a finite subset of the state space, while applying a known stabilizing policy for the rest of the states. We establish that the average queue backlog under RL-QN with an appropriately constructed subset can be arbitrarily close to the optimal result. We evaluate RL-QN in dynamic server allocation, routing and switching problems. Simulation results show that RL-QN minimizes the average queue backlog effectively.
Constructing agents with planning capabilities has long been one of the main challenges in the pursuit of artificial intelligence. Tree-based planning methods from AlphaGo to Muzero have enjoyed huge success in discrete domains, such as chess and Go. Unfortunately, in real-world applications like robot control and inverted pendulum, whose action space is normally continuous, those tree-based planning techniques will be struggling. To address those limitations, in this paper, we present a novel model-based reinforcement learning frameworks called Critic PI2, which combines the benefits from trajectory optimization, deep actor-critic learning, and model-based reinforcement learning. Our method is evaluated for inverted pendulum models with applicability to many continuous control systems. Extensive experiments demonstrate that Critic PI2 achieved a new state of the art in a range of challenging continuous domains. Furthermore, we show that planning with a critic significantly increases the sample efficiency and real-time performance. Our work opens a new direction toward learning the components of a model-based planning system and how to use them.
Techniques based on Reinforcement Learning (RL) are increasingly being used to design control policies for robotic systems. RL fundamentally relies on state-based reward functions to encode desired behavior of the robot and bad reward functions are prone to exploitation by the learning agent, leading to behavior that is undesirable in the best case and critically dangerous in the worst. On the other hand, designing good reward functions for complex tasks is a challenging problem. In this paper, we propose expressing desired high-level robot behavior using a formal specification language known as Signal Temporal Logic (STL) as an alternative to reward/cost functions. We use STL specifications in conjunction with model-based learning to design model predictive controllers that try to optimize the satisfaction of the STL specification over a finite time horizon. The proposed algorithm is empirically evaluated on simulations of robotic system such as a pick-and-place robotic arm, and adaptive cruise control for autonomous vehicles.
Model-based planning is often thought to be necessary for deep, careful reasoning and generalization in artificial agents. While recent successes of model-based reinforcement learning (MBRL) with deep function approximation have strengthened this hypothesis, the resulting diversity of model-based methods has also made it difficult to track which components drive success and why. In this paper, we seek to disentangle the contributions of recent methods by focusing on three questions: (1) How does planning benefit MBRL agents? (2) Within planning, what choices drive performance? (3) To what extent does planning improve generalization? To answer these questions, we study the performance of MuZero (Schrittwieser et al., 2019), a state-of-the-art MBRL algorithm with strong connections and overlapping components with many other MBRL algorithms. We perform a number of interventions and ablations of MuZero across a wide range of environments, including control tasks, Atari, and 9x9 Go. Our results suggest the following: (1) Planning is most useful in the learning process, both for policy updates and for providing a more useful data distribution. (2) Using shallow trees with simple Monte-Carlo rollouts is as performant as more complex methods, except in the most difficult reasoning tasks. (3) Planning alone is insufficient to drive strong generalization. These results indicate where and how to utilize planning in reinforcement learning settings, and highlight a number of open questions for future MBRL research.