Thomas M. Moerland

Thomas M. Moerland, Matthias Müller-Brockhausen, Zhao Yang et al.

Due to the empirical success of reinforcement learning, an increasing number of students study the subject. However, from our practical teaching experience, we see students entering the field (bachelor, master and early PhD) often struggle. On the one hand, textbooks and (online) lectures provide the fundamentals, but students find it hard to translate between equations and code. On the other hand, public codebases do provide practical examples, but the implemented algorithms tend to be complex, and the underlying test environments contain multiple reinforcement learning challenges at once. Although this is realistic from a research perspective, it often hinders educational conceptual understanding. To solve this issue we introduce EduGym, a set of educational reinforcement learning environments and associated interactive notebooks tailored for education. Each EduGym environment is specifically designed to illustrate a certain aspect/challenge of reinforcement learning (e.g., exploration, partial observability, stochasticity, etc.), while the associated interactive notebook explains the challenge and its possible solution approaches, connecting equations and code in a single document. An evaluation among RL students and researchers shows 86% of them think EduGym is a useful tool for reinforcement learning education. All notebooks are available from https://www.edugym.org/, while the full software package can be installed from https://github.com/RLG-Leiden/edugym.

Mike Huisman, Thomas M. Moerland, Aske Plaat et al.

Deep learning requires large amounts of data to learn new tasks well, limiting its applicability to domains where such data is available. Meta-learning overcomes this limitation by learning how to learn. In 2001, Hochreiter et al. showed that an LSTM trained with backpropagation across different tasks is capable of meta-learning. Despite promising results of this approach on small problems, and more recently, also on reinforcement learning problems, the approach has received little attention in the supervised few-shot learning setting. We revisit this approach and test it on modern few-shot learning benchmarks. We find that LSTM, surprisingly, outperform the popular meta-learning technique MAML on a simple few-shot sine wave regression benchmark, but that LSTM, expectedly, fall short on more complex few-shot image classification benchmarks. We identify two potential causes and propose a new method called Outer Product LSTM (OP-LSTM) that resolves these issues and displays substantial performance gains over the plain LSTM. Compared to popular meta-learning baselines, OP-LSTM yields competitive performance on within-domain few-shot image classification, and performs better in cross-domain settings by 0.5% to 1.9% in accuracy score. While these results alone do not set a new state-of-the-art, the advances of OP-LSTM are orthogonal to other advances in the field of meta-learning, yield new insights in how LSTM work in image classification, allowing for a whole range of new research directions. For reproducibility purposes, we publish all our research code publicly.

Zhao Yang, Thomas. M. Moerland, Mike Preuss et al.

While deep reinforcement learning has shown important empirical success, it tends to learn relatively slow due to slow propagation of rewards information and slow update of parametric neural networks. Non-parametric episodic memory, on the other hand, provides a faster learning alternative that does not require representation learning and uses maximum episodic return as state-action values for action selection. Episodic memory and reinforcement learning both have their own strengths and weaknesses. Notably, humans can leverage multiple memory systems concurrently during learning and benefit from all of them. In this work, we propose a method called Two-Memory reinforcement learning agent (2M) that combines episodic memory and reinforcement learning to distill both of their strengths. The 2M agent exploits the speed of the episodic memory part and the optimality and the generalization capacity of the reinforcement learning part to complement each other. Our experiments demonstrate that the 2M agent is more data efficient and outperforms both pure episodic memory and pure reinforcement learning, as well as a state-of-the-art memory-augmented RL agent. Moreover, the proposed approach provides a general framework that can be used to combine any episodic memory agent with other off-policy reinforcement learning algorithms.

Koen Ponse, Felix Kleuker, Márton Fejér et al.

The transition to sustainable energy is a key challenge of our time, requiring modifications in the entire pipeline of energy production, storage, transmission, and consumption. At every stage, new sequential decision-making challenges emerge, ranging from the operation of wind farms to the management of electrical grids or the scheduling of electric vehicle charging stations. All such problems are well suited for reinforcement learning, the branch of machine learning that learns behavior from data. Therefore, numerous studies have explored the use of reinforcement learning for sustainable energy. This paper surveys this literature with the intention of bridging both the underlying research communities: energy and machine learning. After a brief introduction of both fields, we systematically list relevant sustainability challenges, how they can be modeled as a reinforcement learning problem, and what solution approaches currently exist in the literature. Afterwards, we zoom out and identify overarching reinforcement learning themes that appear throughout sustainability, such as multi-agent, offline, and safe reinforcement learning. Lastly, we also cover standardization of environments, which will be crucial for connecting both research fields, and highlight potential directions for future work. In summary, this survey provides an extensive overview of reinforcement learning methods for sustainable energy, which may play a vital role in the energy transition.

Jinke He, Thomas M. Moerland, Joery A. de Vries et al.

Model-based reinforcement learning (MBRL) has drawn considerable interest in recent years, given its promise to improve sample efficiency. Moreover, when using deep-learned models, it is possible to learn compact and generalizable models from data. In this work, we study MuZero, a state-of-the-art deep model-based reinforcement learning algorithm that distinguishes itself from existing algorithms by learning a value-equivalent model. Despite MuZero's success and impact in the field of MBRL, existing literature has not thoroughly addressed why MuZero performs so well in practice. Specifically, there is a lack of in-depth investigation into the value-equivalent model learned by MuZero and its effectiveness in model-based credit assignment and policy improvement, which is vital for achieving sample efficiency in MBRL. To fill this gap, we explore two fundamental questions through our empirical analysis: 1) to what extent does MuZero achieve its learning objective of a value-equivalent model, and 2) how useful are these models for policy improvement? Our findings reveal that MuZero's model struggles to generalize when evaluating unseen policies, which limits its capacity for additional policy improvement. However, MuZero's incorporation of the policy prior in MCTS alleviates this problem, which biases the search towards actions where the model is more accurate.

Zhao Yang, Thomas M. Moerland, Mike Preuss et al.

Go-Explore achieved breakthrough performance on challenging reinforcement learning (RL) tasks with sparse rewards. The key insight of Go-Explore was that successful exploration requires an agent to first return to an interesting state ('Go'), and only then explore into unknown terrain ('Explore'). We refer to such exploration after a goal is reached as 'post-exploration'. In this paper, we present a clear ablation study of post-exploration in a general intrinsically motivated goal exploration process (IMGEP) framework, that the Go-Explore paper did not show. We study the isolated potential of post-exploration, by turning it on and off within the same algorithm under both tabular and deep RL settings on both discrete navigation and continuous control tasks. Experiments on a range of MiniGrid and Mujoco environments show that post-exploration indeed helps IMGEP agents reach more diverse states and boosts their performance. In short, our work suggests that RL researchers should consider to use post-exploration in IMGEP when possible since it is effective, method-agnostic and easy to implement.

Zhao Yang, Thomas M. Moerland, Mike Preuss et al.

Reinforcement learning (RL) is an appealing paradigm for training intelligent agents, enabling policy acquisition from the agent's own autonomously acquired experience. However, the training process of RL is far from automatic, requiring extensive human effort to reset the agent and environments. To tackle the challenging reset-free setting, we first demonstrate the superiority of model-based (MB) RL methods in such setting, showing that a straightforward adaptation of MBRL can outperform all the prior state-of-the-art methods while requiring less supervision. We then identify limitations inherent to this direct extension and propose a solution called model-based reset-free (MoReFree) agent, which further enhances the performance. MoReFree adapts two key mechanisms, exploration and policy learning, to handle reset-free tasks by prioritizing task-relevant states. It exhibits superior data-efficiency across various reset-free tasks without access to environmental reward or demonstrations while significantly outperforming privileged baselines that require supervision. Our findings suggest model-based methods hold significant promise for reducing human effort in RL. Website: https://yangzhao-666.github.io/morefree

Joery A. de Vries, Thomas M. Moerland, Aske Plaat

Hierarchical Reinforcement Learning (HRL) has held longstanding promise to advance reinforcement learning. Yet, it has remained a considerable challenge to develop practical algorithms that exhibit some of these promises. To improve our fundamental understanding of HRL, we investigate hierarchical credit assignment from the perspective of conventional multistep reinforcement learning. We show how e.g., a 1-step `hierarchical backup' can be seen as a conventional multistep backup with $n$ skip connections over time connecting each subsequent state to the first independent of actions inbetween. Furthermore, we find that generalizing hierarchy to multistep return estimation methods requires us to consider how to partition the environment trace, in order to construct backup paths. We leverage these insight to develop a new hierarchical algorithm Hier$Q_k(λ)$, for which we demonstrate that hierarchical credit assignment alone can already boost agent performance (i.e., when eliminating generalization or exploration). Altogether, our work yields fundamental insight into the nature of hierarchical backups and distinguishes this as an additional basis for reinforcement learning research.

Jonathan Collu, Riccardo Majellaro, Aske Plaat et al.

The ability to perceive and reason about individual objects and their interactions is a goal to be achieved for building intelligent artificial systems. State-of-the-art approaches use a feedforward encoder to extract object embeddings and a latent graph neural network to model the interaction between these object embeddings. However, the feedforward encoder can not extract {\it object-centric} representations, nor can it disentangle multiple objects with similar appearance. To solve these issues, we introduce {\it Slot Structured World Models} (SSWM), a class of world models that combines an {\it object-centric} encoder (based on Slot Attention) with a latent graph-based dynamics model. We evaluate our method in the Spriteworld benchmark with simple rules of physical interaction, where Slot Structured World Models consistently outperform baselines on a range of (multi-step) prediction tasks with action-conditional object interactions. All code to reproduce paper experiments is available from \url{https://github.com/JonathanCollu/Slot-Structured-World-Models}.

Koen Ponse, Aske Plaat, Niki van Stein et al.

Accurate economic simulations often require many experimental runs, particularly when combined with reinforcement learning. Unfortunately, training reinforcement learning agents in multi-agent economic environments can be slow. This paper introduces EconoJax, a fast simulated economy, based on the AI economist. EconoJax, and its training pipeline, are completely written in JAX. This allows EconoJax to scale to large population sizes and perform large experiments, while keeping training times within minutes. Through experiments with populations of 100 agents, we show how real-world economic behavior emerges through training within 15 minutes, in contrast to previous work that required several days. We additionally perform experiments in varying sized action spaces to test if some multi-agent methods produce more diverse behavior compared to others. Here, our findings indicate no notable differences in produced behavior with different methods as is sometimes suggested in earlier works. To aid further research, we open-source EconoJax on Github.

Lindsay Spoor, Álvaro Serra-Gómez, Aske Plaat et al.

In safety-critical domains such as robotics, navigation and power systems, constrained optimization problems arise where maximizing performance must be carefully balanced with associated constraints. Safe reinforcement learning provides a framework to address these challenges, with Lagrangian methods being a popular choice. However, the effectiveness of Lagrangian methods crucially depends on the choice of the Lagrange multiplier $λ$, which governs the trade-off between return and constraint cost. A common approach is to update the multiplier automatically during training. Although this is standard in practice, there remains limited empirical evidence on the robustness of an automated update and its influence on overall performance. Therefore, we analyze (i) optimality and (ii) stability of Lagrange multipliers in safe reinforcement learning across a range of tasks. We provide $λ$-profiles that give a complete visualization of the trade-off between return and constraint cost of the optimization problem. These profiles show the highly sensitive nature of $λ$ and moreover confirm the lack of general intuition for choosing the optimal value $λ^*$. Our findings additionally show that automated multiplier updates are able to recover and sometimes even exceed the optimal performance found at $λ^*$ due to the vast difference in their learning trajectories. Furthermore, we show that automated multiplier updates exhibit oscillatory behavior during training, which can be mitigated through PID-controlled updates. However, this method requires careful tuning to achieve consistently better performance across tasks. This highlights the need for further research on stabilizing Lagrangian methods in safe reinforcement learning. The code used to reproduce our results can be found at https://github.com/lindsayspoor/Lagrangian_SafeRL.

Joery A. de Vries, Ken S. Voskuil, Thomas M. Moerland et al.

MuZero, a model-based reinforcement learning algorithm that uses a value equivalent dynamics model, achieved state-of-the-art performance in Chess, Shogi and the game of Go. In contrast to standard forward dynamics models that predict a full next state, value equivalent models are trained to predict a future value, thereby emphasizing value relevant information in the representations. While value equivalent models have shown strong empirical success, there is no research yet that visualizes and investigates what types of representations these models actually learn. Therefore, in this paper we visualize the latent representation of MuZero agents. We find that action trajectories may diverge between observation embeddings and internal state transition dynamics, which could lead to instability during planning. Based on this insight, we propose two regularization techniques to stabilize MuZero's performance. Additionally, we provide an open-source implementation of MuZero along with an interactive visualizer of learned representations, which may aid further investigation of value equivalent algorithms.

Zhao Yang, Thomas M. Moerland, Mike Preuss et al.

Non-parametric episodic memory can be used to quickly latch onto high-rewarded experience in reinforcement learning tasks. In contrast to parametric deep reinforcement learning approaches in which reward signals need to be back-propagated slowly, these methods only need to discover the solution once, and may then repeatedly solve the task. However, episodic control solutions are stored in discrete tables, and this approach has so far only been applied to discrete action space problems. Therefore, this paper introduces Continuous Episodic Control (CEC), a novel non-parametric episodic memory algorithm for sequential decision making in problems with a continuous action space. Results on several sparse-reward continuous control environments show that our proposed method learns faster than state-of-the-art model-free RL and memory-augmented RL algorithms, while maintaining good long-run performance as well. In short, CEC can be a fast approach for learning in continuous control tasks.

Koen Ponse, Jan Felix Kleuker, Aske Plaat et al.

Deep Reinforcement Learning can play a key role in addressing sustainable energy challenges. For instance, many grid systems are heavily congested, highlighting the urgent need to enhance operational efficiency. However, reinforcement learning approaches have traditionally been slow due to the high sample complexity and expensive simulation requirements. While recent works have effectively used GPUs to accelerate data generation by converting environments to JAX, these works have largely focussed on classical toy problems. This paper introduces Chargax, a JAX-based environment for realistic simulation of electric vehicle charging stations designed for accelerated training of RL agents. We validate our environment in a variety of scenarios based on real data, comparing reinforcement learning agents against baselines. Chargax delivers substantial computational performance improvements of over 100x-1000x over existing environments. Additionally, Chargax' modular architecture enables the representation of diverse real-world charging station configurations.

Jacopo Di Ventura, Jan Felix Kleuker, Aske Plaat et al.

Zero-shot reinforcement learning (RL) has emerged as a setting for developing general agents in an unsupervised manner, capable of solving downstream tasks without additional training or planning at test-time. Unlike conventional RL, which optimizes policies for a fixed reward, zero-shot RL requires agents to encode representations rich enough to support immediate adaptation to any objective, drawing parallels to vision and language foundation models. Despite growing interest, the field lacks a common analytical lens. We present the first unified framework for zero-shot RL. Our formulation introduces a consistent notation and taxonomy that organizes existing approaches and allows direct comparison between them. Central to our framework is the classification of algorithms into two families: direct representations, which learn end-to-end mappings from rewards to policies, and compositional representations, which decompose the representation leveraging the substructure of the value function. Within this framework, we highlight shared principles and key differences across methods, and we derive an extended bound for successor-feature methods, offering a new perspective on their performance in the zero-shot regime. By consolidating existing work under a common lens, our framework provides a principled foundation for future research in zero-shot RL and outlines a clear path toward developing more general agents.

Álvaro Serra-Gomez, Daniel Jarne Ornia, Dhruva Tirumala et al.

Effective exploration remains a central challenge in model-based reinforcement learning (MBRL), particularly in high-dimensional continuous control tasks where sample efficiency is crucial. A prominent line of recent work leverages learned policies as proposal distributions for Model-Predictive Path Integral (MPPI) planning. Initial approaches update the sampling policy independently of the planner distribution, typically maximizing a learned value function with deterministic policy gradient and entropy regularization. However, because the states encountered during training depend on the MPPI planner, aligning the sampling policy with the planner improves the accuracy of value estimation and long-term performance. To this end, recent methods update the sampling policy by minimizing KL divergence to the planner distribution or by introducing planner-guided regularization into the policy update. In this work, we unify these MPPI-based reinforcement learning methods under a single framework by introducing Policy Optimization-Model Predictive Control (PO-MPC), a family of KL-regularized MBRL methods that integrate the planner's action distribution as a prior in policy optimization. By aligning the learned policy with the planner's behavior, PO-MPC allows more flexibility in the policy updates to trade off Return maximization and KL divergence minimization. We clarify how prior approaches emerge as special cases of this family, and we explore previously unstudied variations. Our experiments show that these extended configurations yield significant performance improvements, advancing the state of the art in MPPI-based RL.

Catalin-Viorel Dinu, Thomas Moerland

Quantum Tiq-Taq-Toe is a well-known benchmark and playground for both quantum computing and machine learning. Despite its popularity, no reinforcement learning (RL) methods have been applied to Quantum Tiq-Taq-Toe. Although there has been some research on Quantum Chess this game is significantly more complex in terms of computation and analysis. Therefore, we study the combination of quantum computing and reinforcement learning in Quantum Tiq-Taq-Toe, which may serve as an accessible testbed for the integration of both fields. Quantum games are challenging to represent classically due to their inherent partial observability and the potential for exponential state complexity. In Quantum Tiq-Taq-Toe, states are observed through Measurement (a 3x3 matrix of state probabilities) and Move History (a 9x9 matrix of entanglement relations), making strategy complex as each move can collapse the quantum state.

Bram M. Renting, Thomas M. Moerland, Holger H. Hoos et al.

The research field of automated negotiation has a long history of designing agents that can negotiate with other agents. Such negotiation strategies are traditionally based on manual design and heuristics. More recently, reinforcement learning approaches have also been used to train agents to negotiate. However, negotiation problems are diverse, causing observation and action dimensions to change, which cannot be handled by default linear policy networks. Previous work on this topic has circumvented this issue either by fixing the negotiation problem, causing policies to be non-transferable between negotiation problems or by abstracting the observations and actions into fixed-size representations, causing loss of information and expressiveness due to feature design. We developed an end-to-end reinforcement learning method for diverse negotiation problems by representing observations and actions as a graph and applying graph neural networks in the policy. With empirical evaluations, we show that our method is effective and that we can learn to negotiate with other agents on never-before-seen negotiation problems. Our result opens up new opportunities for reinforcement learning in negotiation agents.

Riccardo Majellaro, Jonathan Collu, Aske Plaat et al.

Extracting structured representations from raw visual data is an important and long-standing challenge in machine learning. Recently, techniques for unsupervised learning of object-centric representations have raised growing interest. In this context, enhancing the robustness of the latent features can improve the efficiency and effectiveness of the training of downstream tasks. A promising step in this direction is to disentangle the factors that cause variation in the data. Previously, Invariant Slot Attention disentangled position, scale, and orientation from the remaining features. Extending this approach, we focus on separating the shape and texture components. In particular, we propose a novel architecture that biases object-centric models toward disentangling shape and texture components into two non-overlapping subsets of the latent space dimensions. These subsets are known a priori, hence before the training process. Experiments on a range of object-centric benchmarks reveal that our approach achieves the desired disentanglement while also numerically improving baseline performance in most cases. In addition, we show that our method can generate novel textures for a specific object or transfer textures between objects with distinct shapes.

Zhao Yang, Thomas M. Moerland, Mike Preuss et al.

Go-Explore achieved breakthrough performance on challenging reinforcement learning (RL) tasks with sparse rewards. The key insight of Go-Explore was that successful exploration requires an agent to first return to an interesting state ('Go'), and only then explore into unknown terrain ('Explore'). We refer to such exploration after a goal is reached as 'post-exploration'. In this paper we present a systematic study of post-exploration, answering open questions that the Go-Explore paper did not answer yet. First, we study the isolated potential of post-exploration, by turning it on and off within the same algorithm. Subsequently, we introduce new methodology to adaptively decide when to post-explore and for how long to post-explore. Experiments on a range of MiniGrid environments show that post-exploration indeed boosts performance (with a bigger impact than tuning regular exploration parameters), and this effect is further enhanced by adaptively deciding when and for how long to post-explore. In short, our work identifies adaptive post-exploration as a promising direction for RL exploration research.

Thomas M. Moerland, Joost Broekens, Aske Plaat et al.

Sequential decision making, commonly formalized as Markov Decision Process (MDP) optimization, is a important challenge in artificial intelligence. Two key approaches to this problem are reinforcement learning (RL) and planning. This paper presents a survey of the integration of both fields, better known as model-based reinforcement learning. Model-based RL has two main steps. First, we systematically cover approaches to dynamics model learning, including challenges like dealing with stochasticity, uncertainty, partial observability, and temporal abstraction. Second, we present a systematic categorization of planning-learning integration, including aspects like: where to start planning, what budgets to allocate to planning and real data collection, how to plan, and how to integrate planning in the learning and acting loop. After these two sections, we also discuss implicit model-based RL as an end-to-end alternative for model learning and planning, and we cover the potential benefits of model-based RL. Along the way, the survey also draws connections to several related RL fields, like hierarchical RL and transfer learning. Altogether, the survey presents a broad conceptual overview of the combination of planning and learning for MDP optimization.

Thomas M. Moerland, Joost Broekens, Aske Plaat et al.

Sequential decision making, commonly formalized as optimization of a Markov Decision Process, is a key challenge in artificial intelligence. Two successful approaches to MDP optimization are reinforcement learning and planning, which both largely have their own research communities. However, if both research fields solve the same problem, then we might be able to disentangle the common factors in their solution approaches. Therefore, this paper presents a unifying algorithmic framework for reinforcement learning and planning (FRAP), which identifies underlying dimensions on which MDP planning and learning algorithms have to decide. At the end of the paper, we compare a variety of well-known planning, model-free and model-based RL algorithms along these dimensions. Altogether, the framework may help provide deeper insight in the algorithmic design space of planning and reinforcement learning.

Thomas M Moerland, Joost Broekens, Aske Plaat et al.

Monte Carlo Tree Search (MCTS) efficiently balances exploration and exploitation in tree search based on count-derived uncertainty. However, these local visit counts ignore a second type of uncertainty induced by the size of the subtree below an action. We first show how, due to the lack of this second uncertainty type, MCTS may completely fail in well-known sparse exploration problems, known from the reinforcement learning community. We then introduce a new algorithm, which estimates the size of the subtree below an action, and leverages this information in the UCB formula to better direct exploration. Subsequently, we generalize these ideas by showing that loops, i.e., the repeated occurrence of (approximately) the same state in the same trace, are actually a special case of subtree depth variation. Testing on a variety of tasks shows that our algorithms increase sample efficiency, especially when the planning budget per timestep is small.

Thomas M. Moerland, Anna Deichler, Simone Baldi et al.

Planning and reinforcement learning are two key approaches to sequential decision making. Multi-step approximate real-time dynamic programming, a recently successful algorithm class of which AlphaZero [Silver et al., 2018] is an example, combines both by nesting planning within a learning loop. However, the combination of planning and learning introduces a new question: how should we balance time spend on planning, learning and acting? The importance of this trade-off has not been explicitly studied before. We show that it is actually of key importance, with computational results indicating that we should neither plan too long nor too short. Conceptually, we identify a new spectrum of planning-learning algorithms which ranges from exhaustive search (long planning) to model-free RL (no planning), with optimal performance achieved midway.

Thomas M. Moerland, Joost Broekens, Catholijn M. Jonker

This paper studies the potential of the return distribution for exploration in deterministic reinforcement learning (RL) environments. We study network losses and propagation mechanisms for Gaussian, Categorical and Gaussian mixture distributions. Combined with exploration policies that leverage this return distribution, we solve, for example, a randomized Chain task of length 100, which has not been reported before when learning with neural networks.

Thomas M. Moerland, Joost Broekens, Aske Plaat et al.

A core novelty of Alpha Zero is the interleaving of tree search and deep learning, which has proven very successful in board games like Chess, Shogi and Go. These games have a discrete action space. However, many real-world reinforcement learning domains have continuous action spaces, for example in robotic control, navigation and self-driving cars. This paper presents the necessary theoretical extensions of Alpha Zero to deal with continuous action space. We also provide some preliminary experiments on the Pendulum swing-up task, empirically showing the feasibility of our approach. Thereby, this work provides a first step towards the application of iterated search and learning in domains with a continuous action space.

Thomas M. Moerland, Joost Broekens, Aske Plaat et al.

We present an extension of Monte Carlo Tree Search (MCTS) that strongly increases its efficiency for trees with asymmetry and/or loops. Asymmetric termination of search trees introduces a type of uncertainty for which the standard upper confidence bound (UCB) formula does not account. Our first algorithm (MCTS-T), which assumes a non-stochastic environment, backs-up tree structure uncertainty and leverages it for exploration in a modified UCB formula. Results show vastly improved efficiency in a well-known asymmetric domain in which MCTS performs arbitrarily bad. Next, we connect the ideas about asymmetric termination to the presence of loops in the tree, where the same state appears multiple times in a single trace. An extension to our algorithm (MCTS-T+), which in addition to non-stochasticity assumes full state observability, further increases search efficiency for domains with loops as well. Benchmark testing on a set of OpenAI Gym and Atari 2600 games indicates that our algorithms always perform better than or at least equivalent to standard MCTS, and could be first-choice tree search algorithms for non-stochastic, fully-observable environments.

Thomas M. Moerland, Joost Broekens, Catholijn M. Jonker

This paper studies directed exploration for reinforcement learning agents by tracking uncertainty about the value of each available action. We identify two sources of uncertainty that are relevant for exploration. The first originates from limited data (parametric uncertainty), while the second originates from the distribution of the returns (return uncertainty). We identify methods to learn these distributions with deep neural networks, where we estimate parametric uncertainty with Bayesian drop-out, while return uncertainty is propagated through the Bellman equation as a Gaussian distribution. Then, we identify that both can be jointly estimated in one network, which we call the Double Uncertain Value Network. The policy is directly derived from the learned distributions based on Thompson sampling. Experimental results show that both types of uncertainty may vastly improve learning in domains with a strong exploration challenge.

Wouter Wolfslag, Mukunda Bharatheesha, Thomas Moerland et al.

Sampling-based kinodynamic planners, such as Rapidly-exploring Random Trees (RRTs), pose two fundamental challenges: computing a reliable (pseudo-)metric for the distance between two randomly sampled nodes, and computing a steering input to connect the nodes. The core of these challenges is a Two Point Boundary Value Problem, which is known to be NP-hard. Recently, the distance metric has been approximated using supervised learning, reducing computation time drastically. The previous work on such learning RRTs use direct optimal control to generate the data for supervised learning. This paper proposes to use indirect optimal control instead, because it provides two benefits: it reduces the computational effort to generate the data, and it provides a low dimensional parametrization of the action space. The latter allows us to learn both the distance metric and the steering input to connect two nodes. This eliminates the need for a local planner in learning RRTs. Experimental results on a pendulum swing up show 10-fold speed-up in both the offline data generation and the online planning time, leading to at least a 10-fold speed-up in the overall planning time.

Thomas M. Moerland, Joost Broekens, Catholijn M. Jonker

In this paper we study how to learn stochastic, multimodal transition dynamics in reinforcement learning (RL) tasks. We focus on evaluating transition function estimation, while we defer planning over this model to future work. Stochasticity is a fundamental property of many task environments. However, discriminative function approximators have difficulty estimating multimodal stochasticity. In contrast, deep generative models do capture complex high-dimensional outcome distributions. First we discuss why, amongst such models, conditional variational inference (VI) is theoretically most appealing for model-based RL. Subsequently, we compare different VI models on their ability to learn complex stochasticity on simulated functions, as well as on a typical RL gridworld with multimodal dynamics. Results show VI successfully predicts multimodal outcomes, but also robustly ignores these for deterministic parts of the transition dynamics. In summary, we show a robust method to learn multimodal transitions using function approximation, which is a key preliminary for model-based RL in stochastic domains.