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.
In the sequential decision making setting, an agent aims to achieve systematic generalization over a large, possibly infinite, set of environments. Such environments are modeled as discrete Markov decision processes with both states and actions represented through a feature vector. The underlying structure of the environments allows the transition dynamics to be factored into two components: one that is environment-specific and another that is shared. Consider a set of environments that share the laws of motion as an example. In this setting, the agent can take a finite amount of reward-free interactions from a subset of these environments. The agent then must be able to approximately solve any planning task defined over any environment in the original set, relying on the above interactions only. Can we design a provably efficient algorithm that achieves this ambitious goal of systematic generalization? In this paper, we give a partially positive answer to this question. First, we provide a tractable formulation of systematic generalization by employing a causal viewpoint. Then, under specific structural assumptions, we provide a simple learning algorithm that guarantees any desired planning error up to an unavoidable sub-optimality term, while showcasing a polynomial sample complexity.
Abstract object properties and their relations are deeply rooted in human common sense, allowing people to predict the dynamics of the world even in situations that are novel but governed by familiar laws of physics. Standard machine learning models in model-based reinforcement learning are inadequate to generalize in this way. Inspired by the classic framework of noisy indeterministic deictic (NID) rules, we introduce here Neural NID, a method that learns abstract object properties and relations between objects with a suitably regularized graph neural network. We validate the greater generalization capability of Neural NID on simple benchmarks specifically designed to assess the transition dynamics learned by the model.
To achieve the ambitious goals of artificial intelligence, reinforcement learning must include planning with a model of the world that is abstract in state and time. Deep learning has made progress with state abstraction, but temporal abstraction has rarely been used, despite extensively developed theory based on the options framework. One reason for this is that the space of possible options is immense, and the methods previously proposed for option discovery do not take into account how the option models will be used in planning. Options are typically discovered by posing subsidiary tasks, such as reaching a bottleneck state or maximizing the cumulative sum of a sensory signal other than reward. Each subtask is solved to produce an option, and then a model of the option is learned and made available to the planning process. In most previous work, the subtasks ignore the reward on the original problem, whereas we propose subtasks that use the original reward plus a bonus based on a feature of the state at the time the option terminates. We show that option models obtained from such reward-respecting subtasks are much more likely to be useful in planning than eigenoptions, shortest path options based on bottleneck states, or reward-respecting options generated by the option-critic. Reward respecting subtasks strongly constrain the space of options and thereby also provide a partial solution to the problem of option discovery. Finally, we show how values, policies, options, and models can all be learned online and off-policy using standard algorithms and general value functions.
Obtaining reliable, adaptive confidence sets for prediction functions (hypotheses) is a central challenge in sequential decision-making tasks, such as bandits and model-based reinforcement learning. These confidence sets typically rely on prior assumptions on the hypothesis space, e.g., the known kernel of a Reproducing Kernel Hilbert Space (RKHS). Hand-designing such kernels is error prone, and misspecification may lead to poor or unsafe performance. In this work, we propose to meta-learn a kernel from offline data (Meta-KeL). For the case where the unknown kernel is a combination of known base kernels, we develop an estimator based on structured sparsity. Under mild conditions, we guarantee that our estimated RKHS yields valid confidence sets that, with increasing amounts of offline data, become as tight as those given the true unknown kernel. We demonstrate our approach on the kernelized bandit problem (a.k.a.~Bayesian optimization), where we establish regret bounds competitive with those given the true kernel. We also empirically evaluate the effectiveness of our approach on a Bayesian optimization task.
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.
In model-based reinforcement learning for safety-critical control systems, it is important to formally certify system properties (e.g., safety, stability) under the learned controller. However, as existing methods typically apply formal verification \emph{after} the controller has been learned, it is sometimes difficult to obtain any certificate, even after many iterations between learning and verification. To address this challenge, we propose a framework that jointly conducts reinforcement learning and formal verification by formulating and solving a novel bilevel optimization problem, which is differentiable by the gradients from the value function and certificates. Experiments on a variety of examples demonstrate the significant advantages of our framework over the model-based stochastic value gradient (SVG) method and the model-free proximal policy optimization (PPO) method in finding feasible controllers with barrier functions and Lyapunov functions that ensure system safety and stability.
Model-free and model-based reinforcement learning are two ends of a spectrum. Learning a good policy without a dynamic model can be prohibitively expensive. Learning the dynamic model of a system can reduce the cost of learning the policy, but it can also introduce bias if it is not accurate. We propose a middle ground where instead of the transition model, the sensitivity of the trajectories with respect to the perturbation of the parameters is learned. This allows us to predict the local behavior of the physical system around a set of nominal policies without knowing the actual model. We assay our method on a custom-built physical robot in extensive experiments and show the feasibility of the approach in practice. We investigate potential challenges when applying our method to physical systems and propose solutions to each of them.
Driven by the key challenges of cell therapy manufacturing, including high complexity, high uncertainty, and very limited process observations, we propose a hybrid model-based reinforcement learning (RL) to efficiently guide process control. We first create a probabilistic knowledge graph (KG) hybrid model characterizing the risk- and science-based understanding of biomanufacturing process mechanisms and quantifying inherent stochasticity, e.g., batch-to-batch variation. It can capture the key features, including nonlinear reactions, nonstationary dynamics, and partially observed state. This hybrid model can leverage existing mechanistic models and facilitate learning from heterogeneous process data. A computational sampling approach is used to generate posterior samples quantifying model uncertainty. Then, we introduce hybrid model-based Bayesian RL, accounting for both inherent stochasticity and model uncertainty, to guide optimal, robust, and interpretable dynamic decision making. Cell therapy manufacturing examples are used to empirically demonstrate that the proposed framework can outperform the classical deterministic mechanistic model assisted process optimization.
The model-based reinforcement learning paradigm, which uses planning algorithms and neural network models, has recently achieved unprecedented results in diverse applications, leading to what is now known as deep reinforcement learning. These agents are quite complex and involve multiple components, factors that can create challenges for research. In this work, we propose a new modular software architecture suited for these types of agents, and a set of building blocks that can be easily reused and assembled to construct new model-based reinforcement learning agents. These building blocks include planning algorithms, policies, and loss functions. We illustrate the use of this architecture by combining several of these building blocks to implement and test agents that are optimized to three different test environments: Cartpole, Minigrid, and Tictactoe. One particular planning algorithm, made available in our implementation and not previously used in reinforcement learning, which we called averaged minimax, achieved good results in the three tested environments. Experiments performed with this architecture have shown that the best combination of planning algorithm, policy, and loss function is heavily problem dependent. This result provides evidence that the proposed architecture, which is modular and reusable, is useful for reinforcement learning researchers who want to study new environments and techniques.
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).
We develop a probabilistic framework for analysing model-based reinforcement learning in the episodic setting. We then apply it to study finite-time horizon stochastic control problems with linear dynamics but unknown coefficients and convex, but possibly irregular, objective function. Using probabilistic representations, we study regularity of the associated cost functions and establish precise estimates for the performance gap between applying optimal feedback control derived from estimated and true model parameters. We identify conditions under which this performance gap is quadratic, improving the linear performance gap in recent work [X. Guo, A. Hu, and Y. Zhang, arXiv preprint, arXiv:2104.09311, (2021)], which matches the results obtained for stochastic linear-quadratic problems. Next, we propose a phase-based learning algorithm for which we show how to optimise exploration-exploitation trade-off and achieve sublinear regrets in high probability and expectation. When assumptions needed for the quadratic performance gap hold, the algorithm achieves an order $\mathcal{O}(\sqrt{N} \ln N)$ high probability regret, in the general case, and an order $\mathcal{O}((\ln N)^2)$ expected regret, in self-exploration case, over $N$ episodes, matching the best possible results from the literature. The analysis requires novel concentration inequalities for correlated continuous-time observations, which we derive.
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 $\href{https://github.com/KevinHuang8/CEM-GD}{\text{https://github.com/KevinHuang8/CEM-GD}}$.
In many practical applications of RL, it is expensive to observe state transitions from the environment. For example, in the problem of plasma control for nuclear fusion, computing the next state for a given state-action pair requires querying an expensive transition function which can lead to many hours of computer simulation or dollars of scientific research. Such expensive data collection prohibits application of standard RL algorithms which usually require a large number of observations to learn. In this work, we address the problem of efficiently learning a policy while making a minimal number of state-action queries to the transition function. In particular, we leverage ideas from Bayesian optimal experimental design to guide the selection of state-action queries for efficient learning. We propose an acquisition function that quantifies how much information a state-action pair would provide about the optimal solution to a Markov decision process. At each iteration, our algorithm maximizes this acquisition function, to choose the most informative state-action pair to be queried, thus yielding a data-efficient RL approach. We experiment with a variety of simulated continuous control problems and show that our approach learns an optimal policy with up to $5$ -- $1,000\times$ less data than model-based RL baselines and $10^3$ -- $10^5\times$ less data than model-free RL baselines. We also provide several ablated comparisons which point to substantial improvements arising from the principled method of obtaining data.
Using a model of the environment and a value function, an agent can construct many estimates of a state's value, by unrolling the model for different lengths and bootstrapping with its value function. Our key insight is that one can treat this set of value estimates as a type of ensemble, which we call an \emph{implicit value ensemble} (IVE). Consequently, the discrepancy between these estimates can be used as a proxy for the agent's epistemic uncertainty; we term this signal \emph{model-value inconsistency} or \emph{self-inconsistency} for short. Unlike prior work which estimates uncertainty by training an ensemble of many models and/or value functions, this approach requires only the single model and value function which are already being learned in most model-based reinforcement learning algorithms. We provide empirical evidence in both tabular and function approximation settings from pixels that self-inconsistency is useful (i) as a signal for exploration, (ii) for acting safely under distribution shifts, and (iii) for robustifying value-based planning with a learned model.
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.
Recent advances in reinforcement learning have demonstrated its ability to solve hard agent-environment interaction tasks on a super-human level. However, the application of reinforcement learning methods to practical and real-world tasks is currently limited due to most RL state-of-art algorithms' sample inefficiency, i.e., the need for a vast number of training episodes. For example, OpenAI Five algorithm that has beaten human players in Dota 2 has trained for thousands of years of game time. Several approaches exist that tackle the issue of sample inefficiency, that either offers a more efficient usage of already gathered experience or aim to gain a more relevant and diverse experience via a better exploration of an environment. However, to our knowledge, no such approach exists for model-based algorithms, that showed their high sample efficiency in solving hard control tasks with high-dimensional state space. This work connects exploration techniques and model-based reinforcement learning. We have designed a novel exploration method that takes into account features of the model-based approach. We also demonstrate through experiments that our method significantly improves the performance of the model-based algorithm Dreamer.
During a multi-speed transmission development process, the final calibration of the gearshift controller parameters is usually performed on a physical test bench. Engineers typically treat the mapping from the controller parameters to the gearshift quality as a black-box, and use methods rooted in experimental design -- a purely statistical approach -- to infer the parameter combination that will maximize a chosen gearshift performance indicator. This approach unfortunately requires thousands of gearshift trials, ultimately discouraging the exploration of different control strategies. In this work, we calibrate the feedforward and feedback parameters of a gearshift controller using a model-based reinforcement learning algorithm adapted from Pilco. Experimental results show that the method optimizes the controller parameters with few gearshift trials. This approach can accelerate the exploration of gearshift control strategies, which is especially important for the emerging technology of multi-speed transmissions for electric vehicles.
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.