We build a profitable electronic trading agent with Reinforcement Learning that places buy and sell orders in the stock market. An environment model is built only with historical observational data, and the RL agent learns the trading policy by interacting with the environment model instead of with the real-market to minimize the risk and potential monetary loss. Trained in unsupervised and self-supervised fashion, our environment model learned a temporal and causal representation of the market in latent space through deep neural networks. We demonstrate that the trading policy trained entirely within the environment model can be transferred back into the real market and maintain its profitability. We believe that this environment model can serve as a robust simulator that predicts market movement as well as trade impact for further studies.
Multi-step greedy policies have been extensively used in model-based reinforcement learning (RL), both when a model of the environment is available (e.g.,~in the game of Go) and when it is learned. In this paper, we explore their benefits in model-free RL, when employed using multi-step dynamic programming algorithms: $\kappa$-Policy Iteration ($\kappa$-PI) and $\kappa$-Value Iteration ($\kappa$-VI). These methods iteratively compute the next policy ($\kappa$-PI) and value function ($\kappa$-VI) by solving a surrogate decision problem with a shaped reward and a smaller discount factor. We derive model-free RL algorithms based on $\kappa$-PI and $\kappa$-VI in which the surrogate problem can be solved by any discrete or continuous action RL method, such as DQN and TRPO. We identify the importance of a hyper-parameter that controls the extent to which the surrogate problem is solved and suggest a way to set this parameter. When evaluated on a range of Atari and MuJoCo benchmark tasks, our results indicate that for the right range of $\kappa$, our algorithms outperform DQN and TRPO. This shows that our multi-step greedy algorithms are general enough to be applied over any existing RL algorithm and can significantly improve its performance.
Model-based reinforcement learning (MBRL) aims to learn a dynamic model to reduce the number of interactions with real-world environments. However, due to estimation error, rollouts in the learned model, especially those of long horizons, fail to match the ones in real-world environments. This mismatching has seriously impacted the sample complexity of MBRL. The phenomenon can be attributed to the fact that previous works employ supervised learning to learn the one-step transition models, which has inherent difficulty ensuring the matching of distributions from multi-step rollouts. Based on the claim, we propose to learn the transition model by matching the distributions of multi-step rollouts sampled from the transition model and the real ones via WGAN. We theoretically show that matching the two can minimize the difference of cumulative rewards between the real transition and the learned one. Our experiments also show that the proposed Model Imitation method can compete or outperform the state-of-the-art in terms of sample complexity and average return.
In tabular case, when the reward and environment dynamics are known, policy evaluation can be written as $\bm{V}_{\bm{\pi}} = (I - \gamma P_{\bm{\pi}})^{-1} \bm{r}_{\bm{\pi}}$, where $P_{\bm{\pi}}$ is the state transition matrix given policy ${\bm{\pi}}$ and $\bm{r}_{\bm{\pi}}$ is the reward signal given ${\bm{\pi}}$. What annoys us is that $P_{\bm{\pi}}$ and $\bm{r}_{\bm{\pi}}$ are both mixed with ${\bm{\pi}}$, which means every time when we update ${\bm{\pi}}$, they will change together. In this paper, we leverage the notation from \cite{wang2007dual} to disentangle ${\bm{\pi}}$ and environment dynamics which makes optimization over policy more straightforward. We show that policy gradient theorem \cite{sutton2018reinforcement} and TRPO \cite{schulman2015trust} can be put into a more general framework and such notation has good potential to be extended to model-based reinforcement learning.
This paper proposes a novel deep reinforcement learning architecture that was inspired by previous tree structured architectures which were only useable in discrete action spaces. Policy Prediction Network offers a way to improve sample complexity and performance on continuous control problems in exchange for extra computation at training time but at no cost in computation at rollout time. Our approach integrates a mix between model-free and model-based reinforcement learning. Policy Prediction Network is the first to introduce implicit model-based learning to Policy Gradient algorithms for continuous action space and is made possible via the empirically justified clipping scheme. Our experiments are focused on the MuJoCo environments so that they can be compared with similar work done in this area.
Traditional model-based reinforcement learning approaches learn a model of the environment dynamics without explicitly considering how it will be used by the agent. In the presence of misspecified model classes, this can lead to poor estimates, as some relevant available information is ignored. In this paper, we introduce a novel model-based policy search approach that exploits the knowledge of the current agent policy to learn an approximate transition model, focusing on the portions of the environment that are most relevant for policy improvement. We leverage a weighting scheme, derived from the minimization of the error on the model-based policy gradient estimator, in order to define a suitable objective function that is optimized for learning the approximate transition model. Then, we integrate this procedure into a batch policy improvement algorithm, named Gradient-Aware Model-based Policy Search (GAMPS), which iteratively learns a transition model and uses it, together with the collected trajectories, to compute the new policy parameters. Finally, we empirically validate GAMPS on benchmark domains analyzing and discussing its properties.
Model-based Reinforcement Learning (MBRL) allows data-efficient learning which is required in real world applications such as robotics. However, despite the impressive data-efficiency, MBRL does not achieve the final performance of state-of-the-art Model-free Reinforcement Learning (MFRL) methods. We leverage the strengths of both realms and propose an approach that obtains high performance with a small amount of data. In particular, we combine MFRL and Model Predictive Control (MPC). While MFRL's strength in exploration allows us to train a better forward dynamics model for MPC, MPC improves the performance of the MFRL policy by sampling-based planning. The experimental results in standard continuous control benchmarks show that our approach can achieve MFRL`s level of performance while being as data-efficient as MBRL.
Deep reinforcement learning has over the past few years shown great potential in learning near-optimal control in complex simulated environments with little visible information. Rainbow (Q-Learning) and PPO (Policy Optimisation) have shown outstanding performance in a variety of tasks, including Atari 2600, MuJoCo, and Roboschool test suite. While these algorithms are fundamentally different, both suffer from high variance, low sample efficiency, and hyperparameter sensitivity that in practice, make these algorithms a no-go for critical operations in the industry. On the other hand, model-based reinforcement learning focuses on learning the transition dynamics between states in an environment. If these environment dynamics are adequately learned, a model-based approach is perhaps the most sample efficient method for learning agents to act in an environment optimally. The traits of model-based reinforcement are ideal for real-world environments where sampling is slow and for mission-critical operations. In the warehouse industry, there is an increasing motivation to minimise time and to maximise production. Currently, autonomous agents act suboptimally using handcrafted policies for significant portions of the state-space. In this paper, we present The Dreaming Variational Autoencoder v2 (DVAE-2), a model-based reinforcement learning algorithm that increases sample efficiency, hence enable algorithms with low sample efficiency function better in real-world environments. We introduce Deep Warehouse, a simulated environment for industry-near testing of autonomous agents in grid-based warehouses. Finally, we illustrate that DVAE-2 improves the sample efficiency for the Deep Warehouse compared to model-free methods.
Most known regret bounds for reinforcement learning are either episodic or assume an environment without traps. We derive a regret bound without making either assumption, by allowing the algorithm to occasionally delegate an action to an external advisor. We thus arrive at a setting of active one-shot model-based reinforcement learning that we call DRL (delegative reinforcement learning.) The algorithm we construct in order to demonstrate the regret bound is a variant of Posterior Sampling Reinforcement Learning supplemented by a subroutine that decides which actions should be delegated. The algorithm is not anytime, since the parameters must be adjusted according to the target time discount. Currently, our analysis is limited to Markov decision processes with finite numbers of hypotheses, states and actions.
In this paper, we present a Bayesian view on model-based reinforcement learning. We use expert knowledge to impose structure on the transition model and present an efficient learning scheme based on variational inference. This scheme is applied to a heteroskedastic and bimodal benchmark problem on which we compare our results to NFQ and show how our approach yields human-interpretable insight about the underlying dynamics while also increasing data-efficiency.
What is a good exploration strategy for an agent that interacts with an environment in the absence of external rewards? Ideally, we would like to get a policy driving towards a uniform state-action visitation (highly exploring) in a minimum number of steps (fast mixing), in order to ease efficient learning of any goal-conditioned policy later on. Unfortunately, it is remarkably arduous to directly learn an optimal policy of this nature. In this paper, we propose a novel surrogate objective for learning highly exploring and fast mixing policies, which focuses on maximizing a lower bound to the entropy of the steady-state distribution induced by the policy. In particular, we introduce three novel lower bounds, that lead to as many optimization problems, that tradeoff the theoretical guarantees with computational complexity. Then, we present a model-based reinforcement learning algorithm, IDE$^{3}$AL, to learn an optimal policy according to the introduced objective. Finally, we provide an empirical evaluation of this algorithm on a set of hard-exploration tasks.
In recent studies on model-based reinforcement learning (MBRL), incorporating uncertainty in forward dynamics is a state-of-the-art strategy to enhance learning performance, making MBRLs competitive to cutting-edge model free methods, especially in simulated robotics tasks. Probabilistic ensembles with trajectory sampling (PETS) is a leading type of MBRL, which employs Bayesian inference to dynamics modeling and model predictive control (MPC) with stochastic optimization via the cross entropy method (CEM). In this paper, we propose a novel extension to the uncertainty-aware MBRL. Our main contributions are twofold: Firstly, we introduce a variational inference MPC, which reformulates various stochastic methods, including CEM, in a Bayesian fashion. Secondly, we propose a novel instance of the framework, called probabilistic action ensembles with trajectory sampling (PaETS). As a result, our Bayesian MBRL can involve multimodal uncertainties both in dynamics and optimal trajectories. In comparison to PETS, our method consistently improves asymptotic performance on several challenging locomotion tasks.
Conventionally, model-based reinforcement learning (MBRL) aims to learn a global model for the dynamics of the environment. A good model can potentially enable planning algorithms to generate a large variety of behaviors and solve diverse tasks. However, learning an accurate model for complex dynamical systems is difficult, and even then, the model might not generalize well outside the distribution of states on which it was trained. In this work, we combine model-based learning with model-free learning of primitives that make model-based planning easy. To that end, we aim to answer the question: how can we discover skills whose outcomes are easy to predict? We propose an unsupervised learning algorithm, Dynamics-Aware Discovery of Skills (DADS), which simultaneously discovers predictable behaviors and learns their dynamics. Our method can leverage continuous skill spaces, theoretically, allowing us to learn infinitely many behaviors even for high-dimensional state-spaces. We demonstrate that zero-shot planning in the learned latent space significantly outperforms standard MBRL and model-free goal-conditioned RL, can handle sparse-reward tasks, and substantially improves over prior hierarchical RL methods for unsupervised skill discovery.
Model-based reinforcement learning (MBRL) is widely seen as having the potential to be significantly more sample efficient than model-free RL. However, research in model-based RL has not been very standardized. It is fairly common for authors to experiment with self-designed environments, and there are several separate lines of research, which are sometimes closed-sourced or not reproducible. Accordingly, it is an open question how these various existing MBRL algorithms perform relative to each other. To facilitate research in MBRL, in this paper we gather a wide collection of MBRL algorithms and propose over 18 benchmarking environments specially designed for MBRL. We benchmark these algorithms with unified problem settings, including noisy environments. Beyond cataloguing performance, we explore and unify the underlying algorithmic differences across MBRL algorithms. We characterize three key research challenges for future MBRL research: the dynamics bottleneck, the planning horizon dilemma, and the early-termination dilemma. Finally, to maximally facilitate future research on MBRL, we open-source our benchmark in http://www.cs.toronto.edu/~tingwuwang/mbrl.html.
Model-based reinforcement learning has the potential to be more sample efficient than model-free approaches. However, existing model-based methods are vulnerable to model bias, which leads to poor generalization and asymptotic performance compared to model-free counterparts. In addition, they are typically based on the model predictive control (MPC) framework, which not only is computationally inefficient at decision time but also does not enable policy transfer due to the lack of an explicit policy representation. In this paper, we propose a novel uncertainty-aware model-based policy optimization framework which solves those issues. In this framework, the agent simultaneously learns an uncertainty-aware dynamics model and optimizes the policy according to these learned models. In the optimization step, the policy gradient is computed by automatic differentiation through the models. With respect to sample efficiency alone, our approach shows promising results on challenging continuous control benchmarks with competitive asymptotic performance and significantly lower sample complexity than state-of-the-art baselines.
Estimates of predictive uncertainty are important for accurate model-based planning and reinforcement learning. However, predictive uncertainties---especially ones derived from modern deep learning systems---can be inaccurate and impose a bottleneck on performance. This paper explores which uncertainties are needed for model-based reinforcement learning and argues that good uncertainties must be calibrated, i.e. their probabilities should match empirical frequencies of predicted events. We describe a simple way to augment any model-based reinforcement learning agent with a calibrated model and show that doing so consistently improves planning, sample complexity, and exploration. On the \textsc{HalfCheetah} MuJoCo task, our system achieves state-of-the-art performance using 50\% fewer samples than the current leading approach. Our findings suggest that calibration can improve the performance of model-based reinforcement learning with minimal computational and implementation overhead.
Model-based reinforcement learning (MBRL) with model-predictive control or online planning has shown great potential for locomotion control tasks in terms of both sample efficiency and asymptotic performance. Despite their initial successes, the existing planning methods search from candidate sequences randomly generated in the action space, which is inefficient in complex high-dimensional environments. In this paper, we propose a novel MBRL algorithm, model-based policy planning (POPLIN), that combines policy networks with online planning. More specifically, we formulate action planning at each time-step as an optimization problem using neural networks. We experiment with both optimization w.r.t. the action sequences initialized from the policy network, and also online optimization directly w.r.t. the parameters of the policy network. We show that POPLIN obtains state-of-the-art performance in the MuJoCo benchmarking environments, being about 3x more sample efficient than the state-of-the-art algorithms, such as PETS, TD3 and SAC. To explain the effectiveness of our algorithm, we show that the optimization surface in parameter space is smoother than in action space. Further more, we found the distilled policy network can be effectively applied without the expansive model predictive control during test time for some environments such as Cheetah. Code is released in https://github.com/WilsonWangTHU/POPLIN.
Dyna is an architecture for model-based reinforcement learning (RL), where simulated experience from a model is used to update policies or value functions. A key component of Dyna is search-control, the mechanism to generate the state and action from which the agent queries the model, which remains largely unexplored. In this work, we propose to generate such states by using the trajectory obtained from Hill Climbing (HC) the current estimate of the value function. This has the effect of propagating value from high-value regions and of preemptively updating value estimates of the regions that the agent is likely to visit next. We derive a noisy projected natural gradient algorithm for hill climbing, and highlight a connection to Langevin dynamics. We provide an empirical demonstration on four classical domains that our algorithm, HC-Dyna, can obtain significant sample efficiency improvements. We study the properties of different sampling distributions for search-control, and find that there appears to be a benefit specifically from using the samples generated by climbing on current value estimates from low-value to high-value region.
Designing effective model-based reinforcement learning algorithms is difficult because the ease of data generation must be weighed against the bias of model-generated data. In this paper, we study the role of model usage in policy optimization both theoretically and empirically. We first formulate and analyze a model-based reinforcement learning algorithm with a guarantee of monotonic improvement at each step. In practice, this analysis is overly pessimistic and suggests that real off-policy data is always preferable to model-generated on-policy data, but we show that an empirical estimate of model generalization can be incorporated into such analysis to justify model usage. Motivated by this analysis, we then demonstrate that a simple procedure of using short model-generated rollouts branched from real data has the benefits of more complicated model-based algorithms without the usual pitfalls. In particular, this approach surpasses the sample efficiency of prior model-based methods, matches the asymptotic performance of the best model-free algorithms, and scales to horizons that cause other model-based methods to fail entirely.
We propose a lifelong learning architecture, the Neural Computer Agent (NCA), where a Reinforcement Learning agent is paired with a predictive model of the environment learned by a Differentiable Neural Computer (DNC). The agent and DNC model are trained in conjunction iteratively. The agent improves its policy in simulations generated by the DNC model and rolls out the policy to the live environment, collecting experiences in new portions or tasks of the environment for further learning. Experiments in two synthetic environments show that DNC models can continually learn from pixels alone to simulate new tasks as they are encountered by the agent, while the agents can be successfully trained to solve the tasks using Proximal Policy Optimization entirely in simulations.