We propose a novel generalization of constrained Markov decision processes (CMDPs) that we call the \emph{semi-infinitely constrained Markov decision process} (SICMDP). Particularly, we consider a continuum of constraints instead of a finite number of constraints as in the case of ordinary CMDPs. We also devise two reinforcement learning algorithms for SICMDPs that we call SI-CRL and SI-CPO. SI-CRL is a model-based reinforcement learning algorithm. Given an estimate of the transition model, we first transform the reinforcement learning problem into a linear semi-infinitely programming (LSIP) problem and then use the dual exchange method in the LSIP literature to solve it. SI-CPO is a policy optimization algorithm. Borrowing the ideas from the cooperative stochastic approximation approach, we make alternative updates to the policy parameters to maximize the reward or minimize the cost. To the best of our knowledge, we are the first to apply tools from semi-infinitely programming (SIP) to solve constrained reinforcement learning problems. We present theoretical analysis for SI-CRL and SI-CPO, identifying their iteration complexity and sample complexity. We also conduct extensive numerical examples to illustrate the SICMDP model and demonstrate that our proposed algorithms are able to solve complex sequential decision-making tasks leveraging modern deep reinforcement learning techniques.
Despite remarkable successes, deep reinforcement learning algorithms remain sample inefficient: they require an enormous amount of trial and error to find good policies. Model-based algorithms promise sample efficiency by building an environment model that can be used for planning. Posterior Sampling for Reinforcement Learning is such a model-based algorithm that has attracted significant interest due to its performance in the tabular setting. This paper introduces Posterior Sampling for Deep Reinforcement Learning (PSDRL), the first truly scalable approximation of Posterior Sampling for Reinforcement Learning that retains its model-based essence. PSDRL combines efficient uncertainty quantification over latent state space models with a specially tailored continual planning algorithm based on value-function approximation. Extensive experiments on the Atari benchmark show that PSDRL significantly outperforms previous state-of-the-art attempts at scaling up posterior sampling while being competitive with a state-of-the-art (model-based) reinforcement learning method, both in sample efficiency and computational efficiency.
Model-based reinforcement learning is a powerful tool, but collecting data to fit an accurate model of the system can be costly. Exploring an unknown environment in a sample-efficient manner is hence of great importance. However, the complexity of dynamics and the computational limitations of real systems make this task challenging. In this work, we introduce FLEX, an exploration algorithm for nonlinear dynamics based on optimal experimental design. Our policy maximizes the information of the next step and results in an adaptive exploration algorithm, compatible with generic parametric learning models and requiring minimal resources. We test our method on a number of nonlinear environments covering different settings, including time-varying dynamics. Keeping in mind that exploration is intended to serve an exploitation objective, we also test our algorithm on downstream model-based classical control tasks and compare it to other state-of-the-art model-based and model-free approaches. The performance achieved by FLEX is competitive and its computational cost is low.
A key challenge in sequential decision making is optimizing systems safely under partial information. While much of the literature has focused on the cases of either partially known states or partially known dynamics, it is further exacerbated in cases where both states and dynamics are partially known. Computing heparin doses for patients fits this paradigm since the concentration of heparin in the patient cannot be measured directly and the rates at which patients metabolize heparin vary greatly between individuals. While many proposed solutions are model free, they require complex models and have difficulty ensuring safety. However, if some of the structure of the dynamics is known, a model based approach can be leveraged to provide safe policies. In this paper we propose such a framework to address the challenge of optimizing personalized heparin doses. We use a predictive model parameterized individually by patient to predict future therapeutic effects. We then leverage this model using a scenario generation based approach that is capable of ensuring patient safety. We validate our models with numerical experiments by comparing the predictive capabilities of our model against existing machine learning techniques and demonstrating how our dosing algorithm can treat patients in a simulated ICU environment.
We propose a model-based reinforcement learning (RL) approach for noisy time-dependent gate optimization with improved sample complexity over model-free RL. Sample complexity is the number of controller interactions with the physical system. Leveraging an inductive bias, inspired by recent advances in neural ordinary differential equations (ODEs), we use an auto-differentiable ODE parametrised by a learnable Hamiltonian ansatz to represent the model approximating the environment whose time-dependent part, including the control, is fully known. Control alongside Hamiltonian learning of continuous time-independent parameters is addressed through interactions with the system. We demonstrate an order of magnitude advantage in the sample complexity of our method over standard model-free RL in preparing some standard unitary gates with closed and open system dynamics, in realistic numerical experiments incorporating single shot measurements, arbitrary Hilbert space truncations and uncertainty in Hamiltonian parameters. Also, the learned Hamiltonian can be leveraged by existing control methods like GRAPE for further gradient-based optimization with the controllers found by RL as initializations. Our algorithm that we apply on nitrogen vacancy (NV) centers and transmons in this paper is well suited for controlling partially characterised one and two qubit systems.
Model-based reinforcement learning (MBRL) provides a way to learn a transition model of the environment, which can then be used to plan personalized policies for different patient cohorts and to understand the dynamics involved in the decision-making process. However, standard MBRL algorithms are either sensitive to changes in the reward function or achieve suboptimal performance on the task when the transition model is restricted. Motivated by the need to use simple and interpretable models in critical domains such as healthcare, we propose a novel robust decision-focused (RDF) algorithm that learns a transition model that achieves high returns while being robust to changes in the reward function. We demonstrate our RDF algorithm can be used with several model classes and planning algorithms. We also provide theoretical and empirical evidence, on a variety of simulators and real patient data, that RDF can learn simple yet effective models that can be used to plan personalized policies.
Real-world control applications in complex and uncertain environments require adaptability to handle model uncertainties and robustness against disturbances. This paper presents an online, output-feedback, critic-only, model-based reinforcement learning architecture that simultaneously learns and implements an optimal controller while maintaining stability during the learning phase. Using multiplier matrices, a convenient way to search for observer gains is designed along with a controller that learns from simulated experience to ensure stability and convergence of trajectories of the closed-loop system to a neighborhood of the origin. Local uniform ultimate boundedness of the trajectories is established using a Lyapunov-based analysis and demonstrated through simulation results, under mild excitation conditions.
Many sequential decision-making problems that are currently automated, such as those in manufacturing or recommender systems, operate in an environment where there is either little uncertainty, or zero risk of catastrophe. As companies and researchers attempt to deploy autonomous systems in less constrained environments, it is increasingly important that we endow sequential decision-making algorithms with the ability to reason about uncertainty and risk. In this thesis, we will address both planning and reinforcement learning (RL) approaches to sequential decision-making. In the planning setting, it is assumed that a model of the environment is provided, and a policy is optimised within that model. Reinforcement learning relies upon extensive random exploration, and therefore usually requires a simulator in which to perform training. In many real-world domains, it is impossible to construct a perfectly accurate model or simulator. Therefore, the performance of any policy is inevitably uncertain due to the incomplete knowledge about the environment. Furthermore, in stochastic domains, the outcome of any given run is also uncertain due to the inherent randomness of the environment. These two sources of uncertainty are usually classified as epistemic, and aleatoric uncertainty, respectively. The over-arching goal of this thesis is to contribute to developing algorithms that mitigate both sources of uncertainty in sequential decision-making problems. We make a number of contributions towards this goal, with a focus on model-based algorithms...
World models learn the consequences of actions in vision-based interactive systems. However, in practical scenarios like autonomous driving, noncontrollable dynamics that are independent or sparsely dependent on action signals often exist, making it challenging to learn effective world models. To address this issue, we propose Iso-Dream++, a model-based reinforcement learning approach that has two main contributions. First, we optimize the inverse dynamics to encourage the world model to isolate controllable state transitions from the mixed spatiotemporal variations of the environment. Second, we perform policy optimization based on the decoupled latent imaginations, where we roll out noncontrollable states into the future and adaptively associate them with the current controllable state. This enables long-horizon visuomotor control tasks to benefit from isolating mixed dynamics sources in the wild, such as self-driving cars that can anticipate the movement of other vehicles, thereby avoiding potential risks. On top of our previous work, we further consider the sparse dependencies between controllable and noncontrollable states, address the training collapse problem of state decoupling, and validate our approach in transfer learning setups. Our empirical study demonstrates that Iso-Dream++ outperforms existing reinforcement learning models significantly on CARLA and DeepMind Control.
Embodied agents operate in a structured world, often solving tasks with spatial, temporal, and permutation symmetries. Most algorithms for planning and model-based reinforcement learning (MBRL) do not take this rich geometric structure into account, leading to sample inefficiency and poor generalization. We introduce the Equivariant Diffuser for Generating Interactions (EDGI), an algorithm for MBRL and planning that is equivariant with respect to the product of the spatial symmetry group SE(3), the discrete-time translation group Z, and the object permutation group Sn. EDGI follows the Diffuser framework (Janner et al., 2022) in treating both learning a world model and planning in it as a conditional generative modeling problem, training a diffusion model on an offline trajectory dataset. We introduce a new SE(3)xZxSn-equivariant diffusion model that supports multiple representations. We integrate this model in a planning loop, where conditioning and classifier guidance let us softly break the symmetry for specific tasks as needed. On object manipulation and navigation tasks, EDGI is substantially more sample efficient and generalizes better across the symmetry group than non-equivariant models.
Early stopping based on the validation set performance is a popular approach to find the right balance between under- and overfitting in the context of supervised learning. However, in reinforcement learning, even for supervised sub-problems such as world model learning, early stopping is not applicable as the dataset is continually evolving. As a solution, we propose a new general method that dynamically adjusts the update to data (UTD) ratio during training based on under- and overfitting detection on a small subset of the continuously collected experience not used for training. We apply our method to DreamerV2, a state-of-the-art model-based reinforcement learning algorithm, and evaluate it on the DeepMind Control Suite and the Atari $100$k benchmark. The results demonstrate that one can better balance under- and overestimation by adjusting the UTD ratio with our approach compared to the default setting in DreamerV2 and that it is competitive with an extensive hyperparameter search which is not feasible for many applications. Our method eliminates the need to set the UTD hyperparameter by hand and even leads to a higher robustness with regard to other learning-related hyperparameters further reducing the amount of necessary tuning.
Optimal policies in standard MDPs can be obtained using either value iteration or policy iteration. However, in the case of zero-sum Markov games, there is no efficient policy iteration algorithm; e.g., it has been shown that one has to solve Omega(1/(1-alpha)) MDPs, where alpha is the discount factor, to implement the only known convergent version of policy iteration. Another algorithm, called naive policy iteration, is easy to implement but is only provably convergent under very restrictive assumptions. Prior attempts to fix naive policy iteration algorithm have several limitations. Here, we show that a simple variant of naive policy iteration for games converges exponentially fast. The only addition we propose to naive policy iteration is the use of lookahead policies, which are anyway used in practical algorithms. We further show that lookahead can be implemented efficiently in the function approximation setting of linear Markov games, which are the counterpart of the much-studied linear MDPs. We illustrate the application of our algorithm by providing bounds for policy-based RL (reinforcement learning) algorithms. We extend the results to the function approximation setting.
Model-based Reinforcement Learning (RL) integrates learning and planning and has received increasing attention in recent years. However, learning the model can incur a significant cost (in terms of sample complexity), due to the need to obtain a sufficient number of samples for each state-action pair. In this paper, we investigate the benefits of leveraging structural information about the system in terms of reducing sample complexity. Specifically, we consider the setting where the transition probability matrix is a known function of a number of structural parameters, whose values are initially unknown. We then consider the problem of estimating those parameters based on the interactions with the environment. We characterize the difference between the Q estimates and the optimal Q value as a function of the number of samples. Our analysis shows that there can be a significant saving in sample complexity by leveraging structural information about the model. We illustrate the findings by considering several problems including controlling a queuing system with heterogeneous servers, and seeking an optimal path in a stochastic windy gridworld.
One of the key behavioral characteristics used in neuroscience to determine whether the subject of study -- be it a rodent or a human -- exhibits model-based learning is effective adaptation to local changes in the environment, a particular form of adaptivity that is the focus of this work. In reinforcement learning, however, recent work has shown that modern deep model-based reinforcement-learning (MBRL) methods adapt poorly to local environment changes. An explanation for this mismatch is that MBRL methods are typically designed with sample-efficiency on a single task in mind and the requirements for effective adaptation are substantially higher, both in terms of the learned world model and the planning routine. One particularly challenging requirement is that the learned world model has to be sufficiently accurate throughout relevant parts of the state-space. This is challenging for deep-learning-based world models due to catastrophic forgetting. And while a replay buffer can mitigate the effects of catastrophic forgetting, the traditional first-in-first-out replay buffer precludes effective adaptation due to maintaining stale data. In this work, we show that a conceptually simple variation of this traditional replay buffer is able to overcome this limitation. By removing only samples from the buffer from the local neighbourhood of the newly observed samples, deep world models can be built that maintain their accuracy across the state-space, while also being able to effectively adapt to local changes in the reward function. We demonstrate this by applying our replay-buffer variation to a deep version of the classical Dyna method, as well as to recent methods such as PlaNet and DreamerV2, demonstrating that deep model-based methods can adapt effectively as well to local changes in the environment.
Learning physical dynamics in a series of non-stationary environments is a challenging but essential task for model-based reinforcement learning (MBRL) with visual inputs. It requires the agent to consistently adapt to novel tasks without forgetting previous knowledge. In this paper, we present a new continual learning approach for visual dynamics modeling and explore its efficacy in visual control and forecasting. The key assumption is that an ideal world model can provide a non-forgetting environment simulator, which enables the agent to optimize the policy in a multi-task learning manner based on the imagined trajectories from the world model. To this end, we first propose the mixture world model that learns task-specific dynamics priors with a mixture of Gaussians, and then introduce a new training strategy to overcome catastrophic forgetting, which we call predictive experience replay. Finally, we extend these methods to continual RL and further address the value estimation problems with the exploratory-conservative behavior learning approach. Our model remarkably outperforms the naive combinations of existing continual learning and visual RL algorithms on DeepMind Control and Meta-World benchmarks with continual visual control tasks. It is also shown to effectively alleviate the forgetting of spatiotemporal dynamics in video prediction datasets with evolving domains.
Deep neural networks have been successful in many reinforcement learning settings. However, compared to human learners they are overly data hungry. To build a sample-efficient world model, we apply a transformer to real-world episodes in an autoregressive manner: not only the compact latent states and the taken actions but also the experienced or predicted rewards are fed into the transformer, so that it can attend flexibly to all three modalities at different time steps. The transformer allows our world model to access previous states directly, instead of viewing them through a compressed recurrent state. By utilizing the Transformer-XL architecture, it is able to learn long-term dependencies while staying computationally efficient. Our transformer-based world model (TWM) generates meaningful, new experience, which is used to train a policy that outperforms previous model-free and model-based reinforcement learning algorithms on the Atari 100k benchmark.
Playing an important role in Model-Based Reinforcement Learning (MBRL), environment models aim to predict future states based on the past. Existing works usually ignore instantaneous dependence in the state, that is, assuming that the future state variables are conditionally independent given the past states. However, instantaneous dependence is prevalent in many RL environments. For instance, in the stock market, instantaneous dependence can exist between two stocks because the fluctuation of one stock can quickly affect the other and the resolution of price change is lower than that of the effect. In this paper, we prove that with few exceptions, ignoring instantaneous dependence can result in suboptimal policy learning in MBRL. To address the suboptimality problem, we propose a simple plug-and-play method to enable existing MBRL algorithms to take instantaneous dependence into account. Through experiments on two benchmarks, we (1) confirm the existence of instantaneous dependence with visualization; (2) validate our theoretical findings that ignoring instantaneous dependence leads to suboptimal policy; (3) verify that our method effectively enables reinforcement learning with instantaneous dependence and improves policy performance.
Data-driven simulation has become a favorable way to train and test autonomous driving algorithms. The idea of replacing the actual environment with a learned simulator has also been explored in model-based reinforcement learning in the context of world models. In this work, we show data-driven traffic simulation can be formulated as a world model. We present TrafficBots, a multi-agent policy built upon motion prediction and end-to-end driving, and based on TrafficBots we obtain a world model tailored for the planning module of autonomous vehicles. Existing data-driven traffic simulators are lacking configurability and scalability. To generate configurable behaviors, for each agent we introduce a destination as navigational information, and a time-invariant latent personality that specifies the behavioral style. To improve the scalability, we present a new scheme of positional encoding for angles, allowing all agents to share the same vectorized context and the use of an architecture based on dot-product attention. As a result, we can simulate all traffic participants seen in dense urban scenarios. Experiments on the Waymo open motion dataset show TrafficBots can simulate realistic multi-agent behaviors and achieve good performance on the motion prediction task.
Model-based reinforcement learning is one approach to increase sample efficiency. However, the accuracy of the dynamics model and the resulting compounding error over modelled trajectories are commonly regarded as key limitations. A natural question to ask is: How much more sample efficiency can be gained by improving the learned dynamics models? Our paper empirically answers this question for the class of model-based value expansion methods in continuous control problems. Value expansion methods should benefit from increased model accuracy by enabling longer rollout horizons and better value function approximations. Our empirical study, which leverages oracle dynamics models to avoid compounding model errors, shows that (1) longer horizons increase sample efficiency, but the gain in improvement decreases with each additional expansion step, and (2) the increased model accuracy only marginally increases the sample efficiency compared to learned models with identical horizons. Therefore, longer horizons and increased model accuracy yield diminishing returns in terms of sample efficiency. These improvements in sample efficiency are particularly disappointing when compared to model-free value expansion methods. Even though they introduce no computational overhead, we find their performance to be on-par with model-based value expansion methods. Therefore, we conclude that the limitation of model-based value expansion methods is not the model accuracy of the learned models. While higher model accuracy is beneficial, our experiments show that even a perfect model will not provide an un-rivalled sample efficiency but that the bottleneck lies elsewhere.
Model-based reinforcement learning (MBRL) with real-time planning has shown great potential in locomotion and manipulation control tasks. However, the existing planning methods, such as the Cross-Entropy Method (CEM), do not scale well to complex high-dimensional environments. One of the key reasons for underperformance is the lack of exploration, as these planning methods only aim to maximize the cumulative extrinsic reward over the planning horizon. Furthermore, planning inside the compact latent space in the absence of observations makes it challenging to use curiosity-based intrinsic motivation. We propose Curiosity CEM (CCEM), an improved version of the CEM algorithm for encouraging exploration via curiosity. Our proposed method maximizes the sum of state-action Q values over the planning horizon, in which these Q values estimate the future extrinsic and intrinsic reward, hence encouraging reaching novel observations. In addition, our model uses contrastive representation learning to efficiently learn latent representations. Experiments on image-based continuous control tasks from the DeepMind Control suite show that CCEM is by a large margin more sample-efficient than previous MBRL algorithms and compares favorably with the best model-free RL methods.