The use of learned dynamics models, also known as world models, can improve the sample efficiency of reinforcement learning. Recent work suggests that the underlying causal graphs of such dynamics models are sparsely connected, with each of the future state variables depending only on a small subset of the current state variables, and that learning may therefore benefit from sparsity priors. Similarly, temporal sparsity, i.e. sparsely and abruptly changing local dynamics, has also been proposed as a useful inductive bias. In this work, we critically examine these assumptions by analyzing ground truth dynamics from a set of robotic reinforcement learning environments in the MuJoCo Playground benchmark suite, aiming to determine whether the proposed notions of state and temporal sparsity actually tend to hold in typical reinforcement learning tasks. We study (i) whether the causal graphs of environment dynamics are sparse, (ii) whether such sparsity is state-dependent, and (iii) whether local system dynamics change sparsely. Our results indicate that global sparsity is rare, but instead the tasks show local, state-dependent sparsity in their dynamics and this sparsity exhibits distinct structures, appearing in temporally localized clusters (e.g., during contact events) and affecting specific subsets of state dimensions. These findings challenge common sparsity prior assumptions in dynamics learning, emphasizing the need for grounded inductive biases that reflect the state-dependent sparsity structure of real-world dynamics.

One of the critical aspects of assistive robotics is to provide a control system of a high-dimensional robot from a low-dimensional user input (i.e. a 2D joystick). Data-driven teleoperation seeks to provide an intuitive user interface called an action map to map the low dimensional input to robot velocities from human demonstrations. Action maps are machine learning models trained on robotic demonstration data to map user input directly to desired movements as opposed to aspects of robot pose ("move to cup or pour content" vs. "move along x- or y-axis"). Many works have investigated nonlinear action maps with multi-layer perceptrons, but recent work suggests that local-linear neural approximations provide better control of the system. However, local linear models assume actions exist on a linear subspace and may not capture nuanced motions in training data. In this work, we hypothesize that local-linear neural networks are effective because they make the action map odd w.r.t. the user input, enhancing the intuitiveness of the controller. Based on this assumption, we propose two nonlinear means of encoding odd behavior that do not constrain the action map to a local linear function. However, our analysis reveals that these models effectively behave like local linear models for relevant mappings between user joysticks and robot movements. We support this claim in simulation, and show on a realworld use case that there is no statistical benefit of using non-linear maps, according to the users experience. These negative results suggest that further investigation into model architectures beyond local linear models may offer diminishing returns for improving user experience in data-driven teleoperation systems.

In classic reinforcement learning algorithms, agents make decisions at discrete and fixed time intervals. The duration between decisions becomes a crucial hyperparameter, as setting it too short may increase the problem's difficulty by requiring the agent to make numerous decisions to achieve its goal while setting it too long can result in the agent losing control over the system. However, physical systems do not necessarily require a constant control frequency, and for learning agents, it is often preferable to operate with a low frequency when possible and a high frequency when necessary. We propose a framework called Continuous-Time Continuous-Options (CTCO), where the agent chooses options as sub-policies of variable durations. These options are time-continuous and can interact with the system at any desired frequency providing a smooth change of actions. We demonstrate the effectiveness of CTCO by comparing its performance to classical RL and temporal-abstraction RL methods on simulated continuous control tasks with various action-cycle times. We show that our algorithm's performance is not affected by the choice of environment interaction frequency. Furthermore, we demonstrate the efficacy of CTCO in facilitating exploration in a real-world visual reaching task for a 7 DOF robotic arm with sparse rewards.

Movement primitives are trainable parametric models that reproduce robotic movements starting from a limited set of demonstrations. Previous works proposed simple linear models that exhibited high sample efficiency and generalization power by allowing temporal modulation of move-ments (reproducing movements faster or slower), blending (merging two movements into one), via-point conditioning (constraining a movement to meet some particular via-points) and context conditioning (generation of movements based on an observed variable, e.g., position of an object). Previous works have proposed neural network-based motor primitive models, having demonstrated their capacity to perform tasks with some forms of input conditioning or time-modulation representations. However, there has not been a single unified deep movement primitive's model proposed that is capable of all previous operations, limiting neural movement primitive's potential applications. This paper proposes a deep movement primitive architecture that encodes all the operations above and uses a Bayesian context aggregator that allows a more sound context conditioning and blending. Our results demonstrate our approach can scale to reproduce complex motions on a larger variety of input choices compared to baselines while maintaining operations of linear movement primitives provide.

Policy gradient (PG) estimators are ineffective in dealing with softmax policies that are sub-optimally saturated, which refers to the situation when the policy concentrates its probability mass on sub-optimal actions. Sub-optimal policy saturation may arise from bad policy initialization or sudden changes in the environment that occur after the policy has already converged. Current softmax PG estimators require a large number of updates to overcome policy saturation, which causes low sample efficiency and poor adaptability to new situations. To mitigate this problem, we propose a novel PG estimator for softmax policies that utilizes the bias in the critic estimate and the noise present in the reward signal to escape the saturated regions of the policy parameter space. Our theoretical analysis and experiments, conducted on bandits and various reinforcement learning environments, show that this new estimator is significantly more robust to policy saturation.

Despite the increasing popularity of policy gradient methods, they are yet to be widely utilized in sample-scarce applications, such as robotics. The sample efficiency could be improved by making best usage of available information. As a key component in reinforcement learning, the reward function is usually devised carefully to guide the agent. Hence, the reward function is usually known, allowing access to not only scalar reward signals but also reward gradients. To benefit from reward gradients, previous works require the knowledge of environment dynamics, which are hard to obtain. In this work, we develop the Reward Policy Gradient estimator, a novel approach that integrates reward gradients without learning a model. Bypassing the model dynamics allows our estimator to achieve a better bias-variance trade-off, which results in a higher sample efficiency, as shown in the empirical analysis. Our method also boosts the performance of Proximal Policy Optimization on different MuJoCo control tasks.

The policy gradient theorem (Sutton et al., 2000) prescribes the usage of a cumulative discounted state distribution under the target policy to approximate the gradient. Most algorithms based on this theorem, in practice, break this assumption, introducing a distribution shift that can cause the convergence to poor solutions. In this paper, we propose a new approach of reconstructing the policy gradient from the start state without requiring a particular sampling strategy. The policy gradient calculation in this form can be simplified in terms of a gradient critic, which can be recursively estimated due to a new Bellman equation of gradients. By using temporal-difference updates of the gradient critic from an off-policy data stream, we develop the first estimator that side-steps the distribution shift issue in a model-free way. We prove that, under certain realizability conditions, our estimator is unbiased regardless of the sampling strategy. We empirically show that our technique achieves a superior bias-variance trade-off and performance in presence of off-policy samples.

Off-policy reinforcement learning (RL) holds the promise of better data efficiency as it allows sample reuse and potentially enables safe interaction with the environment. Current off-policy policy gradient methods either suffer from high bias or high variance, delivering often unreliable estimates. The price of inefficiency becomes evident in real-world scenarios such as interaction-driven robot learning, where the success of RL has been rather limited, and a very high sample cost hinders straightforward application. In this paper, we propose a nonparametric Bellman equation, which can be solved in closed form. The solution is differentiable w.r.t the policy parameters and gives access to an estimation of the policy gradient. In this way, we avoid the high variance of importance sampling approaches, and the high bias of semi-gradient methods. We empirically analyze the quality of our gradient estimate against state-of-the-art methods, and show that it outperforms the baselines in terms of sample efficiency on classical control tasks.

Parameterized movement primitives have been extensively used for imitation learning of robotic tasks. However, the high-dimensionality of the parameter space hinders the improvement of such primitives in the reinforcement learning (RL) setting, especially for learning with physical robots. In this paper we propose a novel view on handling the demonstrated trajectories for acquiring low-dimensional, non-linear latent dynamics, using mixtures of probabilistic principal component analyzers (MPPCA) on the movements’ parameter space. Moreover, we introduce a new contextual off-policy RL algorithm, named LAtent-Movements Policy Optimization (LAMPO). LAMPO can provide gradient estimates from previous experience using self-normalized importance sampling, hence, making full use of samples collected in previous learning iterations. These advantages combined provide a complete framework for sample-efficient off-policy optimization of movement primitives for robot learning of high-dimensional manipulation skills. Our experimental results conducted both in simulation and on a real robot show that LAMPO provides sample-efficient policies against common approaches in literature. Code available at https://github.com/SamuelePolimi/lampo.

Reinforcement learning (RL) algorithms still suffer from high sample complexity despite outstanding recent successes. The need for intensive interactions with the environment is especially observed in many widely popular policy gradient algorithms that perform updates using on-policy samples. The priceof such inefficiency becomes evident in real world scenarios such as interaction-driven robot learning, where the success of RL has been rather limited. We address this issue by building on the general sample efficiency of off-policy algorithms. With nonparametric regression and density estimation methods we construct a nonparametric Bellman equation in a principled manner, which allows us to obtain closed-form estimates of the value function, and to analytically express the full policy gradient. We provide a theoretical analysis of our estimate to show that it is consistent under mild smoothness assumptions and empirically show that our approach has better sample efficiency than state-of-the-art policy gradient methods.

Exploring high-dimensional state spaces and finding sparse rewards are central problems in reinforcement learning. Exploration strategies are frequently either naïve (e.g., simplistic-greedy or Boltzmann policies), intractable (i.e., full Bayesian treatment of reinforcement learning) or rely heavily on heuristics. The lack of a tractable but principled exploration approach unnecessarily complicates the application of reinforcement learning to a broader range of problems. Efficient exploration can be accomplished by relying on the uncertainty of the state-action value function. To obtain the uncertainty, we maintain an ensemble of value function estimates and present an optimistic Bellman equation (OBE) for such ensembles. This OBE is derived from a relative entropy maximization principle and yields an implicit exploration bonus resulting in improved exploration during action selection. The implied exploration bonus can be seen as a well-principled type of intrinsic motivation and exhibits favorable theoretical properties. OBE can be applied to a wide range of algorithms. We propose two algorithms as an application of the principle: Optimistic Q-learning and Optimistic DQN which outperform comparison methods on standard benchmarks.

This paper is about the study of B-FQI, an Approximated Value Iteration (AVI) algorithm that exploits a boosting procedure to estimate the action-value function in reinforcement learning problems. B-FQI is an iterative off-line algorithm that, given a dataset of transitions, builds an approximation of the optimal action-value function by summing the approximations of the Bellman residuals across all iterations. The advantage of such approach w.r.t. to other AVI methods is twofold: (1) while keeping the same function space at each iteration, B-FQI can represent more complex functions by considering an additive model; (2) since the Bellman residual decreases as the optimal value function is approached, regression problems become easier as iterations proceed. We study B-FQI both theoretically, providing also a finite-sample error upper bound for it, and empirically, by comparing its performance to the one of FQI in different domains and using different regression techniques.