The quest for interpretable reinforcement learning is a grand challenge for the deployment of autonomous decision-making systems in safety-critical applications. Modern deep reinforcement learning approaches, while powerful, tend to produce opaque policies that compromise verification, reduce transparency, and impede human oversight. To address this, we introduce BASIL (Best-Action Symbolic Interpretable Learning), a systematic approach for generating symbolic, rule-based policies via online evolutionary search with quality-diversity (QD) optimization. BASIL represents policies as ordered lists of symbolic predicates over state variables, ensuring full interpretability and tractable policy complexity. By using a QD archive, the methodology in the proposed study encourages behavioral and structural diversity between top-performing solutions, while a complexity-aware fitness encourages the synthesis of compact representations. The evolutionary system supports the use of exact constraints for rule count and system adaptability for balancing transparency with expressiveness. Empirical comparisons with three benchmark tasks CartPole-v1, MountainCar-v0, and Acrobot-v1 show that BASIL consistently synthesizes interpretable controllers with compact representations comparable to deep reinforcement learning baselines. Herein, this article introduces a new interpretable policy synthesis method that combines symbolic expressiveness, evolutionary diversity, and online learning through a unifying framework.
This paper reviews the topological groundwork for the study of reinforcement learning (RL) by focusing on the structure of state, action, and policy spaces. We begin by recalling key mathematical concepts such as complete metric spaces, which form the foundation for expressing RL problems. By leveraging the Banach contraction principle, we illustrate how the Banach fixed-point theorem explains the convergence of RL algorithms and how Bellman operators, expressed as operators on Banach spaces, ensure this convergence. The work serves as a bridge between theoretical mathematics and practical algorithm design, offering new approaches to enhance the efficiency of RL. In particular, we investigate alternative formulations of Bellman operators and demonstrate their impact on improving convergence rates and performance in standard RL environments such as MountainCar, CartPole, and Acrobot. Our findings highlight how a deeper mathematical understanding of RL can lead to more effective algorithms for decision-making problems.
This short paper describes our proposed solution for the third edition of the "AI Olympics with RealAIGym" competition, held at ICRA 2025. We employed Monte-Carlo Probabilistic Inference for Learning Control (MC-PILCO), an MBRL algorithm recognized for its exceptional data efficiency across various low-dimensional robotic tasks, including cart-pole, ball \& plate, and Furuta pendulum systems. MC-PILCO optimizes a system dynamics model using interaction data, enabling policy refinement through simulation rather than direct system data optimization. This approach has proven highly effective in physical systems, offering greater data efficiency than Model-Free (MF) alternatives. Notably, MC-PILCO has previously won the first two editions of this competition, demonstrating its robustness in both simulated and real-world environments. Besides briefly reviewing the algorithm, we discuss the most critical aspects of the MC-PILCO implementation in the tasks at hand: learning a global policy for the pendubot and acrobot systems.
The 3rd AI Olympics with RealAIGym competition poses the challenge of developing a global policy that can swing up and stabilize an underactuated 2-link system Acrobot and/or Pendubot from any configuration in the state space. This paper presents an optimal control-based approach using a real-time Nonlinear Model Predictive Control (MPC). The results show that the controller achieves good performance and robustness and can reliably handle disturbances.
Redundant manipulators, with their higher Degrees of Freedom (DOFs), offer enhanced kinematic performance and versatility, making them suitable for applications like manufacturing, surgical robotics, and human-robot collaboration. However, motion planning for these manipulators is challenging due to increased DOFs and complex, dynamic environments. While traditional motion planning algorithms struggle with high-dimensional spaces, deep learning-based methods often face instability and inefficiency in complex tasks. This paper introduces RobotDiffuse, a diffusion model-based approach for motion planning in redundant manipulators. By integrating physical constraints with a point cloud encoder and replacing the U-Net structure with an encoder-only transformer, RobotDiffuse improves the model's ability to capture temporal dependencies and generate smoother, more coherent motion plans. We validate the approach using a complex simulator, and release a new dataset with 35M robot poses and 0.14M obstacle avoidance scenarios. Experimental results demonstrate the effectiveness of RobotDiffuse and the promise of diffusion models for motion planning tasks. The code can be accessed at https://github.com/ACRoboT-buaa/RobotDiffuse.
This report presents a solution for the swing-up and stabilisation tasks of the acrobot and the pendubot, developed for the AI Olympics competition at IROS 2024. Our approach employs the Average-Reward Entropy Advantage Policy Optimization (AR-EAPO), a model-free reinforcement learning (RL) algorithm that combines average-reward RL and maximum entropy RL. Results demonstrate that our controller achieves improved performance and robustness scores compared to established baseline methods in both the acrobot and pendubot scenarios, without the need for a heavily engineered reward function or system model. The current results are applicable exclusively to the simulation stage setup.
Neural Network based approximations of the Value function make up the core of leading Policy Based methods such as Trust Regional Policy Optimization (TRPO) and Proximal Policy Optimization (PPO). While this adds significant value when dealing with very complex environments, we note that in sufficiently low State and action space environments, a computationally expensive Neural Network architecture offers marginal improvement over simpler Value approximation methods. We present an implementation of Natural Actor Critic algorithms with actor updates through Natural Policy Gradient methods. This paper proposes that Natural Policy Gradient (NPG) methods with Linear Function Approximation as a paradigm for value approximation may surpass the performance and speed of Neural Network based models such as TRPO and PPO within these environments. Over Reinforcement Learning benchmarks Cart Pole and Acrobot, we observe that our algorithm trains much faster than complex neural network architectures, and obtains an equivalent or greater result. This allows us to recommend the use of NPG methods with Linear Function Approximation over TRPO and PPO for both traditional and sparse reward low dimensional problems.
We present a solution of the swing-up and balance task for the pendubot and acrobot for the participation in the AI Olympics competition at IJCAI 2023. Our solution is based on the Soft Actor Crtic (SAC) reinforcement learning (RL) algorithm for training a policy for the swing-up and entering the region of attraction of a linear quadratic regulator(LQR) controller for stabilizing the double pendulum at the top position. Our controller achieves competitive scores in performance and robustness for both, pendubot and acrobot, problem scenarios.
In light of the increasing adoption of edge computing in areas such as intelligent furniture, robotics, and smart homes, this paper introduces HyperSNN, an innovative method for control tasks that uses spiking neural networks (SNNs) in combination with hyperdimensional computing. HyperSNN substitutes expensive 32-bit floating point multiplications with 8-bit integer additions, resulting in reduced energy consumption while enhancing robustness and potentially improving accuracy. Our model was tested on AI Gym benchmarks, including Cartpole, Acrobot, MountainCar, and Lunar Lander. HyperSNN achieves control accuracies that are on par with conventional machine learning methods but with only 1.36% to 9.96% of the energy expenditure. Furthermore, our experiments showed increased robustness when using HyperSNN. We believe that HyperSNN is especially suitable for interactive, mobile, and wearable devices, promoting energy-efficient and robust system design. Furthermore, it paves the way for the practical implementation of complex algorithms like model predictive control (MPC) in real-world industrial scenarios.
Reinforcement Learning (RL) provides a powerful framework for decision-making in complex environments. However, implementing RL in hardware-efficient and bio-inspired ways remains a challenge. This paper presents a novel Spiking Neural Network (SNN) architecture for solving RL problems with real-valued observations. The proposed model incorporates multi-layered event-based clustering, with the addition of Temporal Difference (TD)-error modulation and eligibility traces, building upon prior work. An ablation study confirms the significant impact of these components on the proposed model's performance. A tabular actor-critic algorithm with eligibility traces and a state-of-the-art Proximal Policy Optimization (PPO) algorithm are used as benchmarks. Our network consistently outperforms the tabular approach and successfully discovers stable control policies on classic RL environments: mountain car, cart-pole, and acrobot. The proposed model offers an appealing trade-off in terms of computational and hardware implementation requirements. The model does not require an external memory buffer nor a global error gradient computation, and synaptic updates occur online, driven by local learning rules and a broadcasted TD-error signal. Thus, this work contributes to the development of more hardware-efficient RL solutions.
Solving control tasks in complex environments automatically through learning offers great potential. While contemporary techniques from deep reinforcement learning (DRL) provide effective solutions, their decision-making is not transparent. We aim to provide insights into the decisions faced by the agent by learning an automaton model of environmental behavior under the control of an agent. However, for most control problems, automata learning is not scalable enough to learn a useful model. In this work, we raise the capabilities of automata learning such that it is possible to learn models for environments that have complex and continuous dynamics. The core of the scalability of our method lies in the computation of an abstract state-space representation, by applying dimensionality reduction and clustering on the observed environmental state space. The stochastic transitions are learned via passive automata learning from observed interactions of the agent and the environment. In an iterative model-based RL process, we sample additional trajectories to learn an accurate environment model in the form of a discrete-state Markov decision process (MDP). We apply our automata learning framework on popular RL benchmarking environments in the OpenAI Gym, including LunarLander, CartPole, Mountain Car, and Acrobot. Our results show that the learned models are so precise that they enable the computation of policies solving the respective control tasks. Yet the models are more concise and more general than neural-network-based policies and by using MDPs we benefit from a wealth of tools available for analyzing them. When solving the task of LunarLander, the learned model even achieved similar or higher rewards than deep RL policies learned with stable-baselines3.
Application of IDA-PBC to mechanical systems has received much attention in recent decades, but its application is still limited by the solvability of the so-called matching conditions. In this work, it is shown that total energy-shaping control of under-actuated mechanical systems has a control-by-interconnection interpretation. Using this interpretation, alternate matching conditions are formulated that defines constraints on the added energy, rather then the total closed-loop energy. It is additionally shown that, for systems that are under-actuated degree one with the mass matrix depending on a single coordinate, the kinetic energy matching conditions resolve to ODEs which can be evaluated numerically. Using this approach controllers are proposed for the benchmark cart-pole and acrobot systems.
We present KeyCLD, a framework to learn Lagrangian dynamics from images. Learned keypoints represent semantic landmarks in images and can directly represent state dynamics. We show that interpreting this state as Cartesian coordinates, coupled with explicit holonomic constraints, allows expressing the dynamics with a constrained Lagrangian. KeyCLD is trained unsupervised end-to-end on sequences of images. Our method explicitly models the mass matrix, potential energy and the input matrix, thus allowing energy based control. We demonstrate learning of Lagrangian dynamics from images on the dm_control pendulum, cartpole and acrobot environments. KeyCLD can be learned on these systems, whether they are unactuated, underactuated or fully actuated. Trained models are able to produce long-term video predictions, showing that the dynamics are accurately learned. We compare with Lag-VAE, Lag-caVAE and HGN, and investigate the benefit of the Lagrangian prior and the constraint function. KeyCLD achieves the highest valid prediction time on all benchmarks. Additionally, a very straightforward energy shaping controller is successfully applied on the fully actuated systems. Please refer to our project page for code and additional results: https://rdaems.github.io/keycld/
Using function approximation to represent a value function is necessary for continuous and high-dimensional state spaces. Linear function approximation has desirable theoretical guarantees and often requires less compute and samples than neural networks, but most approaches suffer from an exponential growth in the number of functions as the dimensionality of the state space increases. In this work, we introduce the wavelet basis for reinforcement learning. Wavelets can effectively be used as a fixed basis and additionally provide the ability to adaptively refine the basis set as learning progresses, making it feasible to start with a minimal basis set. This adaptive method can either increase the granularity of the approximation at a point in state space, or add in interactions between different dimensions as necessary. We prove that wavelets are both necessary and sufficient if we wish to construct a function approximator that can be adaptively refined without loss of precision. We further demonstrate that a fixed wavelet basis set performs comparably against the high-performing Fourier basis on Mountain Car and Acrobot, and that the adaptive methods provide a convenient approach to addressing an oversized initial basis set, while demonstrating performance comparable to, or greater than, the fixed wavelet basis.
Transfer learning approaches in reinforcement learning aim to assist agents in learning their target domains by leveraging the knowledge learned from other agents that have been trained on similar source domains. For example, recent research focus within this space has been placed on knowledge transfer between tasks that have different transition dynamics and reward functions; however, little focus has been placed on knowledge transfer between tasks that have different action spaces. In this paper, we approach the task of transfer learning between domains that differ in action spaces. We present a reward shaping method based on source embedding similarity that is applicable to domains with both discrete and continuous action spaces. The efficacy of our approach is evaluated on transfer to restricted action spaces in the Acrobot-v1 and Pendulum-v0 domains. A comparison with two baselines shows that our method does not outperform these baselines in these continuous action spaces but does show an improvement in these discrete action spaces. We conclude our analysis with future directions for this work.
With rising uncertainty in the real world, online Reinforcement Learning (RL) has been receiving increasing attention due to its fast learning capability and improving data efficiency. However, online RL often suffers from complex Value Function Approximation (VFA) and catastrophic interference, creating difficulty for the deep neural network to be applied to an online RL algorithm in a fully online setting. Therefore, a simpler and more adaptive approach is introduced to evaluate value function with the kernel-based model. Sparse representations are superior at handling interference, indicating that competitive sparse representations should be learnable, non-prior, non-truncated and explicit when compared with current sparse representation methods. Moreover, in learning sparse representations, attention mechanisms are utilized to represent the degree of sparsification, and a smooth attentive function is introduced into the kernel-based VFA. In this paper, we propose an Online Attentive Kernel-Based Temporal Difference (OAKTD) algorithm using two-timescale optimization and provide convergence analysis of our proposed algorithm. Experimental evaluations showed that OAKTD outperformed several Online Kernel-based Temporal Difference (OKTD) learning algorithms in addition to the Temporal Difference (TD) learning algorithm with Tile Coding on public Mountain Car, Acrobot, CartPole and Puddle World tasks.
We contribute to micro-data model-based reinforcement learning (MBRL) by rigorously comparing popular generative models using a fixed (random shooting) control agent. We find that on an environment that requires multimodal posterior predictives, mixture density nets outperform all other models by a large margin. When multimodality is not required, our surprising finding is that we do not need probabilistic posterior predictives: deterministic models are on par, in fact they consistently (although non-significantly) outperform their probabilistic counterparts. We also found that heteroscedasticity at training time, perhaps acting as a regularizer, improves predictions at longer horizons. At the methodological side, we design metrics and an experimental protocol which can be used to evaluate the various models, predicting their asymptotic performance when using them on the control problem. Using this framework, we improve the state-of-the-art sample complexity of MBRL on Acrobot by two to four folds, using an aggressive training schedule which is outside of the hyperparameter interval usually considered
This work explores learning agent-agnostic synthetic environments (SEs) for Reinforcement Learning. SEs act as a proxy for target environments and allow agents to be trained more efficiently than when directly trained on the target environment. We formulate this as a bi-level optimization problem and represent an SE as a neural network. By using Natural Evolution Strategies and a population of SE parameter vectors, we train agents in the inner loop on evolving SEs while in the outer loop we use the performance on the target task as a score for meta-updating the SE population. We show empirically that our method is capable of learning SEs for two discrete-action-space tasks (CartPole-v0 and Acrobot-v1) that allow us to train agents more robustly and with up to 60% fewer steps. Not only do we show in experiments with 4000 evaluations that the SEs are robust against hyperparameter changes such as the learning rate, batch sizes and network sizes, we also show that SEs trained with DDQN agents transfer in limited ways to a discrete-action-space version of TD3 and very well to Dueling DDQN.
We present computational and experimental results on how artificial intelligence (AI) learns to control an Acrobot using reinforcement learning (RL). Thereby the experimental setup is designed as an embedded system, which is of interest for robotics and energy harvesting applications. Specifically, we study the control of angular velocity of the Acrobot, as well as control of its total energy, which is the sum of the kinetic and the potential energy. By this means the RL algorithm is designed to drive the angular velocity or the energy of the first pendulum of the Acrobot towards a desired value. With this, libration or full rotation of the unactuated pendulum of the Acrobot is achieved. Moreover, investigations of the Acrobot control are carried out, which lead to insights about the influence of the state space discretization, the episode length, the action space or the mass of the driven pendulum on the RL control. By further numerous simulations and experiments the effects of parameter variations are evaluated.
The dominant paradigms for video prediction rely on opaque transition models where neither the equations of motion nor the underlying physical quantities of the system are easily inferred. The equations of motion, as defined by Newton's second law, describe the time evolution of a physical system state and can therefore be applied toward the determination of future system states. In this paper, we introduce a video prediction model where the equations of motion are explicitly constructed from learned representations of the underlying physical quantities. To achieve this, we simultaneously learn a low-dimensional state representation and system Lagrangian. The kinetic and potential energy terms of the Lagrangian are distinctly modelled and the low-dimensional equations of motion are explicitly constructed using the Euler-Lagrange equations. We demonstrate the efficacy of this approach for video prediction on image sequences rendered in modified OpenAI gym Pendulum-v0 and Acrobot environments.