Decision trees have gained popularity as interpretable surrogate models for learning-based control policies.

This work advances the theoretical foundations of reservoir computing (RC) by providing a unified treatment of fading memory and the echo state property (ESP) in both deterministic and stochastic settings. We investigate state-space systems, a central model class in time series learning, and establish that fading memory and solution stability hold generically -- even in the absence of the ESP -- offering a robust explanation for the empirical success of RC models without strict contractivity conditions. In the stochastic case, we critically assess stochastic echo states, proposing a novel distributional perspective rooted in attractor dynamics on the space of probability distributions, which leads to a rich and coherent theory. Our results extend and generalize previous work on non-autonomous dynamical systems, offering new insights into causality, stability, and memory in RC models. This lays the groundwork for reliable generative modeling of temporal data in both deterministic and stochastic regimes.

In this paper, we propose a new solution to reward adaptation (RA), the problem where the learning agent adapts to a target reward function based on one or multiple existing behaviors learned a priori under the same domain dynamics but different reward functions. Learning the target behavior from scratch is possible but often inefficient given the available source behaviors. Our work represents a new approach to RA via the manipulation of Q-functions. Assuming that the target reward function is a known function of the source reward functions, our approach to RA computes bounds of the Q function. We introduce an iterative process to tighten the bounds, similar to value iteration. This enables action pruning in the target domain before learning even starts. We refer to such a method as Q-Manipulation (Q-M). We formally prove that our pruning strategy does not affect the optimality of the returned policy while empirically show that it improves the sample complexity. Q-M is evaluated in a variety of synthetic and simulation domains to demonstrate its effectiveness, generalizability, and practicality.

In this work, we prove that, in linear MDPs, the feature dimension $d$ is lower bounded by $S/U$ in order to aptly represent transition probabilities, where $S$ is the size of the state space and $U$ is the maximum size of directly reachable states. Hence, $d$ can still scale with $S$ depending on the direct reachability of the environment. To address this limitation of linear MDPs, we propose a novel structural aggregation framework based on dynamics, named as the "dynamics aggregation". For this newly proposed framework, we design a provably efficient hierarchical reinforcement learning algorithm in linear function approximation that leverages aggregated sub-structures. Our proposed algorithm exhibits statistical efficiency, achieving a regret of $ \tilde{O} ( d_{\psi}^{3/2} H^{3/2}\sqrt{ N T} )$, where $d_{\psi}$ represents the feature dimension of aggregated subMDPs and $N$ signifies the number of aggregated subMDPs. We establish that the condition $d_{\psi}^3 N \ll d^{3}$ is readily met in most real-world environments with hierarchical structures, enabling a substantial improvement in the regret bound compared to LSVI-UCB, which enjoys a regret of $ \tilde{O} (d^{3/2} H^{3/2} \sqrt{ T})$. To the best of our knowledge, this work presents the first HRL algorithm with linear function approximation that offers provable guarantees.

In multi-task reinforcement learning, agents train on a fixed set of tasks and have to generalise to new ones. Recent work has shown that increased exploration improves this generalisation, but it remains unclear why exactly that is. In this paper, we introduce the concept of reachability in multi-task reinforcement learning and show that an initial exploration phase increases the number of reachable tasks the agent is trained on. This, and not the increased exploration, is responsible for the improved generalisation, even to unreachable tasks. Inspired by this, we propose a novel method Explore-Go that implements such an exploration phase at the beginning of each episode. Explore-Go only modifies the way experience is collected and can be used with most existing on-policy or off-policy reinforcement learning algorithms. We demonstrate the effectiveness of our method when combined with some popular algorithms and show an increase in generalisation performance across several environments.

State symmetries play an important role in planning and generalized planning. In the first case, state symmetries can be used to reduce the size of the search; in the second, to reduce the size of the training set. In the case of general planning, however, it is also critical to distinguish non-symmetric states, i.e., states that represent non-isomorphic relational structures. However, while the language of first-order logic distinguishes non-symmetric states, the languages and architectures used to represent and learn general policies do not. In particular, recent approaches for learning general policies use state features derived from description logics or learned via graph neural networks (GNNs) that are known to be limited by the expressive power of C_2, first-order logic with two variables and counting. In this work, we address the problem of detecting symmetries in planning and generalized planning and use the results to assess the expressive requirements for learning general policies over various planning domains. For this, we map planning states to plain graphs, run off-the-shelf algorithms to determine whether two states are isomorphic with respect to the goal, and run coloring algorithms to determine if C_2 features computed logically or via GNNs distinguish non-isomorphic states. Symmetry detection results in more effective learning, while the failure to detect non-symmetries prevents general policies from being learned at all in certain domains.

The intrinsic complexity of deep neural networks (DNNs) makes it challenging to verify not only the networks themselves but also the hosting DNN-controlled systems. Reachability analysis of these systems faces the same challenge. Existing approaches rely on over-approximating DNNs using simpler polynomial models. However, they suffer from low efficiency and large overestimation, and are restricted to specific types of DNNs. This paper presents a novel abstraction-based approach to bypass the crux of over-approximating DNNs in reachability analysis. Specifically, we extend conventional DNNs by inserting an additional abstraction layer, which abstracts a real number to an interval for training. The inserted abstraction layer ensures that the values represented by an interval are indistinguishable to the network for both training and decision-making. Leveraging this, we devise the first black-box reachability analysis approach for DNN-controlled systems, where trained DNNs are only queried as black-box oracles for the actions on abstract states. Our approach is sound, tight, efficient, and agnostic to any DNN type and size. The experimental results on a wide range of benchmarks show that the DNNs trained by using our approach exhibit comparable performance, while the reachability analysis of the corresponding systems becomes more amenable with significant tightness and efficiency improvement over the state-of-the-art white-box approaches.

Accurately forecasting the motion of traffic actors is crucial for the deployment of autonomous vehicles at a large scale. Current trajectory forecasting approaches primarily concentrate on optimizing a loss function with a specific metric, which can result in predictions that do not adhere to physical laws or violate external constraints. Our objective is to incorporate explicit knowledge priors that allow a network to forecast future trajectories in compliance with both the kinematic constraints of a vehicle and the geometry of the driving environment. To achieve this, we introduce a non-parametric pruning layer and attention layers to integrate the defined knowledge priors. Our proposed method is designed to ensure reachability guarantees for traffic actors in both complex and dynamic situations. By conditioning the network to follow physical laws, we can obtain accurate and safe predictions, essential for maintaining autonomous vehicles' safety and efficiency in real-world settings.In summary, this paper presents concepts that prevent off-road predictions for safe and reliable motion forecasting by incorporating knowledge priors into the training process.

To make decisions that are good in the long run, we're more interested in what being in a state means w.r.t. This small environment contains three terminal states (i.e., when the agent reaches one of them, the episode ends): Two states mean "game over" with an infinite negative reward, while reaching the state in the lower right corner means receiving a large positive immediate reward. Of course, the expected return is highly dependent on the agent's policy \(\pi\) (i.e., the actions it takes), e.g., if the agent would always move to the left, then it would never be able to reach the goal, i.e., the expected return starting from any state (except the goal state itself) would always be negative. If we assume an optimal policy (i.e., the agent always takes the quickest way to the goal), then the value of each state corresponds to the ones shown in the graphic, i.e., for each state "100 minus the number of steps to reach the goal from here". Knowing these values, the agent can now very easily select the best next action in each state, by simply choosing that action, which brings it to the next reachable state with the highest value.