Model-based reinforcement learning (MBRL) is a sample efficient technique to obtain control policies, yet unavoidable modeling errors often lead performance deterioration. The model in MBRL is often solely fitted to reconstruct dynamics, state observations in particular, while the impact of model error on the policy is not captured by the training objective. This leads to a mismatch between the intended goal of MBRL, enabling good policy and value learning, and the target of the loss function employed in practice, future state prediction. Naive intuition would suggest that value-aware model learning would fix this problem and, indeed, several solutions to this objective mismatch problem have been proposed based on theoretical analysis. However, they tend to be inferior in practice to commonly used maximum likelihood (MLE) based approaches. In this paper we propose the Value-gradient weighted Model Learning (VaGraM), a novel method for value-aware model learning which improves the performance of MBRL in challenging settings, such as small model capacity and the presence of distracting state dimensions. We analyze both MLE and value-aware approaches and demonstrate how they fail to account for exploration and the behavior of function approximation when learning value-aware models and highlight the additional goals that must be met to stabilize optimization in the deep learning setting. We verify our analysis by showing that our loss function is able to achieve high returns on the Mujoco benchmark suite while being more robust than maximum likelihood based approaches.
Model-based reinforcement learning algorithms are typically more sample efficient than their model-free counterparts, especially in sparse reward problems. Unfortunately, many interesting domains are too complex to specify the complete models required by traditional model-based approaches. Learning a model takes a large number of environment samples, and may not capture critical information if the environment is hard to explore. If we could specify an incomplete model and allow the agent to learn how best to use it, we could take advantage of our partial understanding of many domains. Existing hybrid planning and learning systems which address this problem often impose highly restrictive assumptions on the sorts of models which can be used, limiting their applicability to a wide range of domains. In this work we propose SAGE, an algorithm combining learning and planning to exploit a previously unusable class of incomplete models. This combines the strengths of symbolic planning and neural learning approaches in a novel way that outperforms competing methods on variations of taxi world and Minecraft.
Questions in causality, control, and reinforcement learning go beyond the classical machine learning task of prediction under i.i.d. observations. Instead, these fields consider the problem of learning how to actively perturb a system to achieve a certain effect on a response variable. Arguably, they have complementary views on the problem: In control, one usually aims to first identify the system by excitation strategies to then apply model-based design techniques to control the system. In (non-model-based) reinforcement learning, one directly optimizes a reward. In causality, one focus is on identifiability of causal structure. We believe that combining the different views might create synergies and this competition is meant as a first step toward such synergies. The participants had access to observational and (offline) interventional data generated by dynamical systems. Track CHEM considers an open-loop problem in which a single impulse at the beginning of the dynamics can be set, while Track ROBO considers a closed-loop problem in which control variables can be set at each time step. The goal in both tracks is to infer controls that drive the system to a desired state. Code is open-sourced ( https://github.com/LearningByDoingCompetition/learningbydoing-comp ) to reproduce the winning solutions of the competition and to facilitate trying out new methods on the competition tasks.
We consider a sequential decision making problem where the agent faces the environment characterized by the stochastic discrete events and seeks an optimal intervention policy such that its long-term reward is maximized. This problem exists ubiquitously in social media, finance and health informatics but is rarely investigated by the conventional research in reinforcement learning. To this end, we present a novel framework of the model-based reinforcement learning where the agent's actions and observations are asynchronous stochastic discrete events occurring in continuous-time. We model the dynamics of the environment by Hawkes process with external intervention control term and develop an algorithm to embed such process in the Bellman equation which guides the direction of the value gradient. We demonstrate the superiority of our method in both synthetic simulator and real-world problem.
We propose an optimistic model-based algorithm, dubbed SMRL, for finite-horizon episodic reinforcement learning (RL) when the transition model is specified by exponential family distributions with $d$ parameters and the reward is bounded and known. SMRL uses score matching, an unnormalized density estimation technique that enables efficient estimation of the model parameter by ridge regression. Under standard regularity assumptions, SMRL achieves $\tilde O(d\sqrt{H^3T})$ online regret, where $H$ is the length of each episode and $T$ is the total number of interactions (ignoring polynomial dependence on structural scale parameters).
Current state-of-the-art model-based reinforcement learning algorithms use trajectory sampling methods, such as the Cross-Entropy Method (CEM), for planning in continuous control settings. These zeroth-order optimizers require sampling a large number of trajectory rollouts to select an optimal action, which scales poorly for large prediction horizons or high dimensional action spaces. First-order methods that use the gradients of the rewards with respect to the actions as an update can mitigate this issue, but suffer from local optima due to the non-convex optimization landscape. To overcome these issues and achieve the best of both worlds, we propose a novel planner, Cross-Entropy Method with Gradient Descent (CEM-GD), that combines first-order methods with CEM. At the beginning of execution, CEM-GD uses CEM to sample a significant amount of trajectory rollouts to explore the optimization landscape and avoid poor local minima. It then uses the top trajectories as initialization for gradient descent and applies gradient updates to each of these trajectories to find the optimal action sequence. At each subsequent time step, however, CEM-GD samples much fewer trajectories from CEM before applying gradient updates. We show that as the dimensionality of the planning problem increases, CEM-GD maintains desirable performance with a constant small number of samples by using the gradient information, while avoiding local optima using initially well-sampled trajectories. Furthermore, CEM-GD achieves better performance than CEM on a variety of continuous control benchmarks in MuJoCo with 100x fewer samples per time step, resulting in around 25% less computation time and 10% less memory usage. The implementation of CEM-GD is available at $\href{https://github.com/KevinHuang8/CEM-GD}{\text{https://github.com/KevinHuang8/CEM-GD}}$.
Model-based reinforcement learning (MBRL) achieves significant sample efficiency in practice in comparison to model-free RL, but its performance is often limited by the existence of model prediction error. To reduce the model error, standard MBRL approaches train a single well-designed network to fit the entire environment dynamics, but this wastes rich information on multiple sub-dynamics which can be modeled separately, allowing us to construct the world model more accurately. In this paper, we propose the Environment Dynamics Decomposition (ED2), a novel world model construction framework that models the environment in a decomposing manner. ED2 contains two key components: sub-dynamics discovery (SD2) and dynamics decomposition prediction (D2P). SD2 discovers the sub-dynamics in an environment automatically and then D2P constructs the decomposed world model following the sub-dynamics. ED2 can be easily combined with existing MBRL algorithms and empirical results show that ED2 significantly reduces the model error, increases the sample efficiency, and achieves higher asymptotic performance when combined with the state-of-the-art MBRL algorithms on various continuous control tasks. Our code is open source and available at https://github.com/ED2-source-code/ED2.
The Robust Markov Decision Process (RMDP) framework focuses on designing control policies that are robust against the parameter uncertainties due to the mismatches between the simulator model and real-world settings. An RMDP problem is typically formulated as a max-min problem, where the objective is to find the policy that maximizes the value function for the worst possible model that lies in an uncertainty set around a nominal model. The standard robust dynamic programming approach requires the knowledge of the nominal model for computing the optimal robust policy. In this work, we propose a model-based reinforcement learning (RL) algorithm for learning an $\epsilon$-optimal robust policy when the nominal model is unknown. We consider three different forms of uncertainty sets, characterized by the total variation distance, chi-square divergence, and KL divergence. For each of these uncertainty sets, we give a precise characterization of the sample complexity of our proposed algorithm. In addition to the sample complexity results, we also present a formal analytical argument on the benefit of using robust policies. Finally, we demonstrate the performance of our algorithm on two benchmark problems.
We propose learning via retracing, a novel self-supervised approach for learning the state representation (and the associated dynamics model) for reinforcement learning tasks. In addition to the predictive (reconstruction) supervision in the forward direction, we propose to include "retraced" transitions for representation / model learning, by enforcing the cycle-consistency constraint between the original and retraced states, hence improve upon the sample efficiency of learning. Moreover, learning via retracing explicitly propagates information about future transitions backward for inferring previous states, thus facilitates stronger representation learning for the downstream reinforcement learning tasks. We introduce Cycle-Consistency World Model (CCWM), a concrete model-based instantiation of learning via retracing. Additionally we propose a novel adaptive "truncation" mechanism for counteracting the negative impacts brought by "irreversible" transitions such that learning via retracing can be maximally effective. Through extensive empirical studies on visual-based continuous control benchmarks, we demonstrate that CCWM achieves state-of-the-art performance in terms of sample efficiency and asymptotic performance, whilst exhibiting behaviours that are indicative of stronger representation learning.
Model-based reinforcement learning has attracted wide attention due to its superior sample efficiency. Despite its impressive success so far, it is still unclear how to appropriately schedule the important hyperparameters to achieve adequate performance, such as the real data ratio for policy optimization in Dyna-style model-based algorithms. In this paper, we first theoretically analyze the role of real data in policy training, which suggests that gradually increasing the ratio of real data yields better performance. Inspired by the analysis, we propose a framework named AutoMBPO to automatically schedule the real data ratio as well as other hyperparameters in training model-based policy optimization (MBPO) algorithm, a representative running case of model-based methods. On several continuous control tasks, the MBPO instance trained with hyperparameters scheduled by AutoMBPO can significantly surpass the original one, and the real data ratio schedule found by AutoMBPO shows consistency with our theoretical analysis.
Top-performing Model-Based Reinforcement Learning (MBRL) agents, such as Dreamer, learn the world model by reconstructing the image observations. Hence, they often fail to discard task-irrelevant details and struggle to handle visual distractions. To address this issue, previous work has proposed to contrastively learn the world model, but the performance tends to be inferior in the absence of distractions. In this paper, we seek to enhance robustness to distractions for MBRL agents. Specifically, we consider incorporating prototypical representations, which have yielded more accurate and robust results than contrastive approaches in computer vision. However, it remains elusive how prototypical representations can benefit temporal dynamics learning in MBRL, since they treat each image independently without capturing temporal structures. To this end, we propose to learn the prototypes from the recurrent states of the world model, thereby distilling temporal structures from past observations and actions into the prototypes. The resulting model, DreamerPro, successfully combines Dreamer with prototypes, making large performance gains on the DeepMind Control suite both in the standard setting and when there are complex background distractions. Code available at https://github.com/fdeng18/dreamer-pro .
Reinforcement Learning (RL) has been shown to be effective in many scenarios. However, it typically requires the exploration of a sufficiently large number of state-action pairs, some of which may be unsafe. Consequently, its application to safety-critical systems remains a challenge. An increasingly common approach to address safety involves the addition of a safety layer that projects the RL actions onto a safe set of actions. In turn, a difficulty for such frameworks is how to effectively couple RL with the safety layer to improve the learning performance. In this paper, we frame safety as a differentiable robust-control-barrier-function layer in a model-based RL framework. Moreover, we also propose an approach to modularly learn the underlying reward-driven task, independent of safety constraints. We demonstrate that this approach both ensures safety and effectively guides exploration during training in a range of experiments, including zero-shot transfer when the reward is learned in a modular way.
Many model-based reinforcement learning (RL) methods follow a similar template: fit a model to previously observed data, and then use data from that model for RL or planning. However, models that achieve better training performance (e.g., lower MSE) are not necessarily better for control: an RL agent may seek out the small fraction of states where an accurate model makes mistakes, or it might act in ways that do not expose the errors of an inaccurate model. As noted in prior work, there is an objective mismatch: models are useful if they yield good policies, but they are trained to maximize their accuracy, rather than the performance of the policies that result from them. In this work, we propose a single objective for jointly training the model and the policy, such that updates to either component increase a lower bound on expected return. To the best of our knowledge, this is the first lower bound for model-based RL that holds globally and can be efficiently estimated in continuous settings; it is the only lower bound that mends the objective mismatch problem. A version of this bound becomes tight under certain assumptions. Optimizing this bound resembles a GAN: a classifier distinguishes between real and fake transitions, the model is updated to produce transitions that look realistic, and the policy is updated to avoid states where the model predictions are unrealistic. Numerical simulations demonstrate that optimizing this bound yields reward maximizing policies and yields dynamics that (perhaps surprisingly) can aid in exploration. We also show that a deep RL algorithm loosely based on our lower bound can achieve performance competitive with prior model-based methods, and better performance on certain hard exploration tasks.
We contribute to micro-data model-based reinforcement learning (MBRL) by rigorously comparing popular generative models using a fixed (random shooting) control agent. We find that on an environment that requires multimodal posterior predictives, mixture density nets outperform all other models by a large margin. When multimodality is not required, our surprising finding is that we do not need probabilistic posterior predictives: deterministic models are on par, in fact they consistently (although non-significantly) outperform their probabilistic counterparts. We also found that heteroscedasticity at training time, perhaps acting as a regularizer, improves predictions at longer horizons. At the methodological side, we design metrics and an experimental protocol which can be used to evaluate the various models, predicting their asymptotic performance when using them on the control problem. Using this framework, we improve the state-of-the-art sample complexity of MBRL on Acrobot by two to four folds, using an aggressive training schedule which is outside of the hyperparameter interval usually considered
Training visual control policies from scratch on a new robot typically requires generating large amounts of robot-specific data. How might we leverage data previously collected on another robot to reduce or even completely remove this need for robot-specific data? We propose a "robot-aware control" paradigm that achieves this by exploiting readily available knowledge about the robot. We then instantiate this in a robot-aware model-based RL policy by training modular dynamics models that couple a transferable, robot-aware world dynamics module with a robot-specific, potentially analytical, robot dynamics module. This also enables us to set up visual planning costs that separately consider the robot agent and the world. Our experiments on tabletop manipulation tasks with simulated and real robots demonstrate that these plug-in improvements dramatically boost the transferability of visual model-based RL policies, even permitting zero-shot transfer of visual manipulation skills onto new robots. Project website: https://www.seas.upenn.edu/~hued/rac
Model-based Reinforcement Learning (RL) is a popular learning paradigm due to its potential sample efficiency compared to model-free RL. However, existing empirical model-based RL approaches lack the ability to explore. This work studies a computationally and statistically efficient model-based algorithm for both Kernelized Nonlinear Regulators (KNR) and linear Markov Decision Processes (MDPs). For both models, our algorithm guarantees polynomial sample complexity and only uses access to a planning oracle. Experimentally, we first demonstrate the flexibility and efficacy of our algorithm on a set of exploration challenging control tasks where existing empirical model-based RL approaches completely fail. We then show that our approach retains excellent performance even in common dense reward control benchmarks that do not require heavy exploration. Finally, we demonstrate that our method can also perform reward-free exploration efficiently. Our code can be found at https://github.com/yudasong/PCMLP.
Inducing causal relationships from observations is a classic problem in machine learning. Most work in causality starts from the premise that the causal variables themselves are observed. However, for AI agents such as robots trying to make sense of their environment, the only observables are low-level variables like pixels in images. To generalize well, an agent must induce high-level variables, particularly those which are causal or are affected by causal variables. A central goal for AI and causality is thus the joint discovery of abstract representations and causal structure. However, we note that existing environments for studying causal induction are poorly suited for this objective because they have complicated task-specific causal graphs which are impossible to manipulate parametrically (e.g., number of nodes, sparsity, causal chain length, etc.). In this work, our goal is to facilitate research in learning representations of high-level variables as well as causal structures among them. In order to systematically probe the ability of methods to identify these variables and structures, we design a suite of benchmarking RL environments. We evaluate various representation learning algorithms from the literature and find that explicitly incorporating structure and modularity in models can help causal induction in model-based reinforcement learning.
Current model-based reinforcement learning methods struggle when operating from complex visual scenes due to their inability to prioritize task-relevant features. To mitigate this problem, we propose learning Task Informed Abstractions (TIA) that explicitly separates reward-correlated visual features from distractors. For learning TIA, we introduce the formalism of Task Informed MDP (TiMDP) that is realized by training two models that learn visual features via cooperative reconstruction, but one model is adversarially dissociated from the reward signal. Empirical evaluation shows that TIA leads to significant performance gains over state-of-the-art methods on many visual control tasks where natural and unconstrained visual distractions pose a formidable challenge.
Learning efficiently a causal model of the environment is a key challenge of model-based RL agents operating in POMDPs. We consider here a scenario where the learning agent has the ability to collect online experiences through direct interactions with the environment (interventional data), but has also access to a large collection of offline experiences, obtained by observing another agent interacting with the environment (observational data). A key ingredient, that makes this situation non-trivial, is that we allow the observed agent to interact with the environment based on hidden information, which is not observed by the learning agent. We then ask the following questions: can the online and offline experiences be safely combined for learning a causal model ? And can we expect the offline experiences to improve the agent's performances ? To answer these questions, we import ideas from the well-established causal framework of do-calculus, and we express model-based reinforcement learning as a causal inference problem. Then, we propose a general yet simple methodology for leveraging offline data during learning. In a nutshell, the method relies on learning a latent-based causal transition model that explains both the interventional and observational regimes, and then using the recovered latent variable to infer the standard POMDP transition model via deconfounding. We prove our method is correct and efficient in the sense that it attains better generalization guarantees due to the offline data (in the asymptotic case), and we illustrate its effectiveness empirically on synthetic toy problems. Our contribution aims at bridging the gap between the fields of reinforcement learning and causality.
This work shows that value-aware model learning, known for its numerous theoretical benefits, is also practically viable for solving challenging continuous control tasks in prevalent model-based reinforcement learning algorithms. First, we derive a novel value-aware model learning objective by bounding the model-advantage i.e. model performance difference, between two MDPs or models given a fixed policy, achieving superior performance to prior value-aware objectives in most continuous control environments. Second, we identify the issue of stale value estimates in naively substituting value-aware objectives in place of maximum-likelihood in dyna-style model-based RL algorithms. Our proposed remedy to this issue bridges the long-standing gap in theory and practice of value-aware model learning by enabling successful deployment of all value-aware objectives in solving several continuous control robotic manipulation and locomotion tasks. Our results are obtained with minimal modifications to two popular and open-source model-based RL algorithms -- SLBO and MBPO, without tuning any existing hyper-parameters, while also demonstrating better performance of value-aware objectives than these baseline in some environments.