Matthia Sabatelli

Viktor Veselý, Aleksandar Todorov, Erwan Escudie et al.

Temporal credit assignment is central to both biological and artificial intelligence, yet its interaction with non-linear function approximation is poorly understood. We identify a systematic failure mode in deep reinforcement learning (RL) termed Trace-Mediated Peak Bias (TMPB). At intermediate eligibility trace depths, agents irrationally prefer trajectories with high-magnitude reward ``peaks'' over alternatives with higher cumulative returns. This provides a mechanistic account of the Peak-End Rule: a human memory bias where experiences are judged by their most intense moments rather than integrated utility. We show that TMPB emerges because traces amplify distal Temporal Difference errors into ``gradient shocks'' that fixed-step-size Stochastic Gradient Descent cannot normalize, leading to global overestimation. Conversely, adaptive optimizers mitigate this pathology via second-moment normalization. Our results suggest that human-like saliency distortions may emerge naturally from the mathematical constraints of credit assignment in distributed systems, and that adaptive optimization is a theoretical necessity for rational value estimation.

Remo Sasso, Matthia Sabatelli, Marco A. Wiering

A crucial challenge in reinforcement learning is to reduce the number of interactions with the environment that an agent requires to master a given task. Transfer learning proposes to address this issue by re-using knowledge from previously learned tasks. However, determining which source task qualifies as the most appropriate for knowledge extraction, as well as the choice regarding which algorithm components to transfer, represent severe obstacles to its application in reinforcement learning. The goal of this paper is to address these issues with modular multi-source transfer learning techniques. The proposed techniques automatically learn how to extract useful information from source tasks, regardless of the difference in state-action space and reward function. We support our claims with extensive and challenging cross-domain experiments for visual control.

Erwan C. Escudie, Matthia Sabatelli, Jilles S. Dibangoye

While recent reductions of zero-sum partially observable stochastic games (zs-POSGs) to transition-independent stochastic games (TI-SGs) theoretically admit dynamic programming, practical solutions remain stifled by the inherent non-linearity and exponential complexity of the simultaneous minimax backup. In this work, we surmount this computational barrier by rigorously recasting the simultaneous interaction as a sequential decision process via the principle of separation. We introduce distinct sufficient statistics for valuation and execution, the sequential occupancy state and the private occupancy family, which reveal a latent geometry in the optimal value function. This structural insight allows us to linearise the backup operator, reducing the update complexity from exponential to polynomial while enabling the direct extraction of safe policies without heuristic bookkeeping. Experimental results demonstrate that algorithms leveraging this sequential framework significantly outperform state-of-the-art methods, effectively rendering previously intractable domains solvable.

Aleksandar Todorov, Matthia Sabatelli

Deep reinforcement learning (RL) agents commonly rely on high-dimensional neural representations, despite growing evidence that task-relevant value and policy structure may be intrinsically low-dimensional. In this work, we present a simple yet effective representation-level prior that inserts a fixed orthonormal projection to constrain encoder features to a low-dimensional subspace, requiring no auxiliary objectives, pretraining, or changes to the underlying RL algorithm. Under a linear realizability assumption, we prove that when the bottleneck dimension exceeds the intrinsic rank of the optimal value function in feature space, the bottleneck preserves expressivity and leaves the induced gradient dynamics unchanged up to an equivalent low-dimensional parameterization. Empirically, we find that across both single and multi-task benchmarks, baseline performance is either matched or improved once the bottleneck dimension exceeds a small task-dependent threshold; in many cases, value representations can be compressed to extremely low dimensions without loss, and the minimal sufficient dimension depends far more on environment complexity than encoder width. In addition, we analyze representation geometry and find that orthogonal bottlenecks stabilize feature norms and are associated with higher effective rank. Together, these results support a representation-space interpretation of the manifold hypothesis in reinforcement learning and position orthogonal bottlenecks as a lightweight, architecture-agnostic mechanism for shaping RL representations.

Ivo Pascal de Jong, Andreea Ioana Sburlea, Matthia Sabatelli et al.

Aleatoric (data) and epistemic (knowledge) uncertainty are textbook components of Uncertainty Quantification. Jointly estimating these components has been shown to be problematic and non-trivial. As a result, there are multiple ways to disentangle these uncertainties, but current methods to evaluate them are insufficient. We propose that aleatoric and epistemic uncertainty estimates should be orthogonally disentangled - meaning that each uncertainty is not affected by the other - a necessary condition that is often not met. We prove that orthogonality and consistency and necessary and sufficient criteria for disentanglement, and construct Uncertainty Disentanglement Error as a metric to measure these criteria, with further empirical evaluation showing that finetuned models give different orthogonality results than models trained from scratch and that UDE can be optimized for through dropout rate. We demonstrate a Deep Ensemble trained from scratch on ImageNet-1k with Information Theoretic disentangling achieves consistent and orthogonal estimates of epistemic uncertainty, but estimates of aleatoric uncertainty still fail on orthogonality.

Arthur Müller, Matthia Sabatelli

Reinforcement learning (RL) for traffic signal control (TSC) has shown better performance in simulation for controlling the traffic flow of intersections than conventional approaches. However, due to several challenges, no RL-based TSC has been deployed in the field yet. One major challenge for real-world deployment is to ensure that all safety requirements are met at all times during operation. We present an approach to ensure safety in a real-world intersection by using an action space that is safe by design. The action space encompasses traffic phases, which represent the combination of non-conflicting signal colors of the intersection. Additionally, an action masking mechanism makes sure that only appropriate phase transitions are carried out. Another challenge for real-world deployment is to ensure a control behavior that avoids stress for road users. We demonstrate how to achieve this by incorporating domain knowledge through extending the action masking mechanism. We test and verify our approach in a realistic simulation scenario. By ensuring safety and psychologically pleasant control behavior, our approach drives development towards real-world deployment of RL for TSC.

Vincent Tonkes, Matthia Sabatelli

Vision Transformers (VTs) are becoming a valuable alternative to Convolutional Neural Networks (CNNs) when it comes to problems involving high-dimensional and spatially organized inputs such as images. However, their Transfer Learning (TL) properties are not yet well studied, and it is not fully known whether these neural architectures can transfer across different domains as well as CNNs. In this paper we study whether VTs that are pre-trained on the popular ImageNet dataset learn representations that are transferable to the non-natural image domain. To do so we consider three well-studied art classification problems and use them as a surrogate for studying the TL potential of four popular VTs. Their performance is extensively compared against that of four common CNNs across several TL experiments. Our results show that VTs exhibit strong generalization properties and that these networks are more powerful feature extractors than CNNs.

Matias Valdenegro-Toro, Matthia Sabatelli

Overfitting and generalization is an important concept in Machine Learning as only models that generalize are interesting for general applications. Yet some students have trouble learning this important concept through lectures and exercises. In this paper we describe common examples of students misunderstanding overfitting, and provide recommendations for possible solutions. We cover student misconceptions about overfitting, about solutions to overfitting, and implementation mistakes that are commonly confused with overfitting issues. We expect that our paper can contribute to improving student understanding and lectures about this important topic.

Arthur Müller, Matthia Sabatelli

Reinforcement Learning (RL) has been widely explored in Traffic Signal Control (TSC) applications, however, still no such system has been deployed in practice. A key barrier to progress in this area is the reality gap, the discrepancy that results from differences between simulation models and their real-world equivalents. In this paper, we address this challenge by first presenting a comprehensive analysis of potential simulation parameters that contribute to this reality gap. We then also examine two promising strategies that can bridge this gap: Domain Randomization (DR) and Model-Agnostic Meta-Learning (MAML). Both strategies were trained with a traffic simulation model of an intersection. In addition, the model was embedded in LemgoRL, a framework that integrates realistic, safety-critical requirements into the control system. Subsequently, we evaluated the performance of the two methods on a separate model of the same intersection that was developed with a different traffic simulator. In this way, we mimic the reality gap. Our experimental results show that both DR and MAML outperform a state-of-the-art RL algorithm, therefore highlighting their potential to mitigate the reality gap in RLbased TSC systems.

Julius Wagenbach, Matthia Sabatelli

We study whether the learning rate $α$, the discount factor $γ$ and the reward signal $r$ have an influence on the overestimation bias of the Q-Learning algorithm. Our preliminary results in environments which are stochastic and that require the use of neural networks as function approximators, show that all three parameters influence overestimation significantly. By carefully tuning $α$ and $γ$, and by using an exponential moving average of $r$ in Q-Learning's temporal difference target, we show that the algorithm can learn value estimates that are more accurate than the ones of several other popular model-free methods that have addressed its overestimation bias in the past.

Viktor Veselý, Aleksandar Todorov, Matthia Sabatelli

The double descent (DD) paradox, where over-parameterized models see generalization improve past the interpolation point, remains largely unexplored in the non-stationary domain of Deep Reinforcement Learning (DRL). We present preliminary evidence that DD exists in model-free DRL, investigating it systematically across varying model capacity using the Actor-Critic framework. We rely on an information-theoretic metric, Policy Entropy, to measure policy uncertainty throughout training. Preliminary results show a clear epoch-wise DD curve; the policy's entrance into the second descent region correlates with a sustained, significant reduction in Policy Entropy. This entropic decay suggests that over-parameterization acts as an implicit regularizer, guiding the policy towards robust, flatter minima in the loss landscape. These findings establish DD as a factor in DRL and provide an information-based mechanism for designing agents that are more general, transferable, and robust.

Franciszek Szewczyk, Gilles Louppe, Matthia Sabatelli

Lifelike visualizations in design, cinematography, and gaming rely on precise physics simulations, typically requiring extensive computational resources and detailed physical input. This paper presents a method that can infer a system's physical properties from a short video, eliminating the need for explicit parameter input, provided it is close to the training condition. The learned representation is then used within a Graph Network-based Simulator to emulate the trajectories of physical systems. We demonstrate that the video-derived encodings effectively capture the physical properties of the system and showcase a linear dependence between some of the encodings and the system's motion.

Aleksandar Todorov, Juan Cardenas-Cartagena, Rafael F. Cunha et al.

Plasticity loss, a diminishing capacity to adapt as training progresses, is a critical challenge in deep reinforcement learning. We examine this issue in multi-task reinforcement learning (MTRL), where higher representational flexibility is crucial for managing diverse and potentially conflicting task demands. We systematically explore how sparsification methods, particularly Gradual Magnitude Pruning (GMP) and Sparse Evolutionary Training (SET), enhance plasticity and consequently improve performance in MTRL agents. We evaluate these approaches across distinct MTRL architectures (shared backbone, Mixture of Experts, Mixture of Orthogonal Experts) on standardized MTRL benchmarks, comparing against dense baselines, and a comprehensive range of alternative plasticity-inducing or regularization methods. Our results demonstrate that both GMP and SET effectively mitigate key indicators of plasticity degradation, such as neuron dormancy and representational collapse. These plasticity improvements often correlate with enhanced multi-task performance, with sparse agents frequently outperforming dense counterparts and achieving competitive results against explicit plasticity interventions. Our findings offer insights into the interplay between plasticity, network sparsity, and MTRL designs, highlighting dynamic sparsification as a robust but context-sensitive tool for developing more adaptable MTRL systems.

Massimiliano Falzari, Matthia Sabatelli

Deep Reinforcement Learning (DRL) systems often tend to overfit to early experiences, a phenomenon known as the primacy bias (PB). This bias can severely hinder learning efficiency and final performance, particularly in complex environments. This paper presents a comprehensive investigation of PB through the lens of the Fisher Information Matrix (FIM). We develop a framework characterizing PB through distinct patterns in the FIM trace, identifying critical memorization and reorganization phases during learning. Building on this understanding, we propose Fisher-Guided Selective Forgetting (FGSF), a novel method that leverages the geometric structure of the parameter space to selectively modify network weights, preventing early experiences from dominating the learning process. Empirical results across DeepMind Control Suite (DMC) environments show that FGSF consistently outperforms baselines, particularly in complex tasks. We analyze the different impacts of PB on actor and critic networks, the role of replay ratios in exacerbating the effect, and the effectiveness of even simple noise injection methods. Our findings provide a deeper understanding of PB and practical mitigation strategies, offering a FIM-based geometric perspective for advancing DRL.

Josh Bruegger, Diana Ioana Catana, Vanja Macovaz et al.

The attribution of the author of an art piece is typically a laborious manual process, usually relying on subjective evaluations of expert figures. However, there are some situations in which quantitative features of the artwork can support these evaluations. The extraction of these features can sometimes be automated, for instance, with the use of Machine Learning (ML) techniques. An example of these features is represented by repeated, mechanically impressed patterns, called punches, present chiefly in 13th and 14th-century panel paintings from Tuscany. Previous research in art history showcased a strong connection between the shapes of punches and specific artists or workshops, suggesting the possibility of using these quantitative cues to support the attribution. In the present work, we first collect a dataset of large-scale images of these panel paintings. Then, using YOLOv10, a recent and popular object detection model, we train a ML pipeline to perform object detection on the punches contained in the images. Due to the large size of the images, the detection procedure is split across multiple frames by adopting a sliding-window approach with overlaps, after which the predictions are combined for the whole image using a custom non-maximal suppression routine. Our results indicate how art historians working in the field can reliably use our method for the identification and extraction of punches.

Kyriakos Hjikakou, Juan Diego Cardenas Cartagena, Matthia Sabatelli

This paper investigates the generalisability of Koopman-based representations for chaotic dynamical systems, focusing on their transferability across prediction and control tasks. Using the Lorenz system as a testbed, we propose a three-stage methodology: learning Koopman embeddings through autoencoding, pre-training a transformer on next-state prediction, and fine-tuning for safety-critical control. Our results show that Koopman embeddings outperform both standard and physics-informed PCA baselines, achieving accurate and data-efficient performance. Notably, fixing the pre-trained transformer weights during fine-tuning leads to no performance degradation, indicating that the learned representations capture reusable dynamical structure rather than task-specific patterns. These findings support the use of Koopman embeddings as a foundation for multi-task learning in physics-informed machine learning. A project page is available at https://kikisprdx.github.io/.

Juan Cardenas-Cartagena, Massimiliano Falzari, Marco Zullich et al.

Model-Free Reinforcement Learning (RL) algorithms either learn how to map states to expected rewards or search for policies that can maximize a certain performance function. Model-Based algorithms instead, aim to learn an approximation of the underlying model of the RL environment and then use it in combination with planning algorithms. Upside-Down Reinforcement Learning (UDRL) is a novel learning paradigm that aims to learn how to predict actions from states and desired commands. This task is formulated as a Supervised Learning problem and has successfully been tackled by Neural Networks (NNs). In this paper, we investigate whether function approximation algorithms other than NNs can also be used within a UDRL framework. Our experiments, performed over several popular optimal control benchmarks, show that tree-based methods like Random Forests and Extremely Randomized Trees can perform just as well as NNs with the significant benefit of resulting in policies that are inherently more interpretable than NNs, therefore paving the way for more transparent, safe, and robust RL.

Arthur Müller, Felix Grumbach, Matthia Sabatelli

Production scheduling is an essential task in manufacturing, with Reinforcement Learning (RL) emerging as a key solution. In a previous work, RL was utilized to solve an extended permutation flow shop scheduling problem (PFSSP) for a real-world production line with two stages, linked by a central buffer. The RL agent was trained to sequence equallysized product batches to minimize setup efforts and idle times. However, the substantial impact caused by varying the size of these product batches has not yet been explored. In this follow-up study, we investigate the effects of varying batch sizes, exploring both the quality of solutions and the training dynamics of the RL agent. The results demonstrate that it is possible to methodically identify reasonable boundaries for the batch size. These boundaries are determined on one side by the increasing sample complexity associated with smaller batch sizes, and on the other side by the decreasing flexibility of the agent when dealing with larger batch sizes. This provides the practitioner the ability to make an informed decision regarding the selection of an appropriate batch size. Moreover, we introduce and investigate two new curriculum learning strategies to enable the training with small batch sizes. The findings of this work offer the potential for application in several industrial use cases with comparable scheduling problems.

Marius Captari, Remo Sasso, Matthia Sabatelli

Despite the considerable attention given to the questions of \textit{how much} and \textit{how to} explore in deep reinforcement learning, the investigation into \textit{when} to explore remains relatively less researched. While more sophisticated exploration strategies can excel in specific, often sparse reward environments, existing simpler approaches, such as $ε$-greedy, persist in outperforming them across a broader spectrum of domains. The appeal of these simpler strategies lies in their ease of implementation and generality across a wide range of domains. The downside is that these methods are essentially a blind switching mechanism, which completely disregards the agent's internal state. In this paper, we propose to leverage the agent's internal state to decide \textit{when} to explore, addressing the shortcomings of blind switching mechanisms. We present Value Discrepancy and State Counts through homeostasis (VDSC), a novel approach for efficient exploration timing. Experimental results on the Atari suite demonstrate the superiority of our strategy over traditional methods such as $ε$-greedy and Boltzmann, as well as more sophisticated techniques like Noisy Nets.

Tsegaye Misikir Tashu, Eduard-Raul Kontos, Matthia Sabatelli et al.

Recommendation systems, for documents, have become tools to find relevant content on the Web. However, these systems have limitations when it comes to recommending documents in languages different from the query language, which means they might overlook resources in non-native languages. This research focuses on representing documents across languages by using Transformer Leveraged Document Representations (TLDRs) that are mapped to a cross-lingual domain. Four multilingual pre-trained transformer models (mBERT, mT5 XLM RoBERTa, ErnieM) were evaluated using three mapping methods across 20 language pairs representing combinations of five selected languages of the European Union. Metrics like Mate Retrieval Rate and Reciprocal Rank were used to measure the effectiveness of mapped TLDRs compared to non-mapped ones. The results highlight the power of cross-lingual representations achieved through pre-trained transformers and mapping approaches suggesting a promising direction for expanding beyond language connections, between two specific languages.

Matthia Sabatelli, Pierre Geurts

Transfer Learning (TL) is an efficient machine learning paradigm that allows overcoming some of the hurdles that characterize the successful training of deep neural networks, ranging from long training times to the needs of large datasets. While exploiting TL is a well established and successful training practice in Supervised Learning (SL), its applicability in Deep Reinforcement Learning (DRL) is rarer. In this paper, we study the level of transferability of three different variants of Deep-Q Networks on popular DRL benchmarks as well as on a set of novel, carefully designed control tasks. Our results show that transferring neural networks in a DRL context can be particularly challenging and is a process which in most cases results in negative transfer. In the attempt of understanding why Deep-Q Networks transfer so poorly, we gain novel insights into the training dynamics that characterizes this family of algorithms.

Remo Sasso, Matthia Sabatelli, Marco A. Wiering

Reinforcement learning (RL) is well known for requiring large amounts of data in order for RL agents to learn to perform complex tasks. Recent progress in model-based RL allows agents to be much more data-efficient, as it enables them to learn behaviors of visual environments in imagination by leveraging an internal World Model of the environment. Improved sample efficiency can also be achieved by reusing knowledge from previously learned tasks, but transfer learning is still a challenging topic in RL. Parameter-based transfer learning is generally done using an all-or-nothing approach, where the network's parameters are either fully transferred or randomly initialized. In this work we present a simple alternative approach: fractional transfer learning. The idea is to transfer fractions of knowledge, opposed to discarding potentially useful knowledge as is commonly done with random initialization. Using the World Model-based Dreamer algorithm, we identify which type of components this approach is applicable to, and perform experiments in a new multi-source transfer learning setting. The results show that fractional transfer learning often leads to substantially improved performance and faster learning compared to learning from scratch and random initialization.

Pascal Leroy, Damien Ernst, Pierre Geurts et al.

This paper introduces four new algorithms that can be used for tackling multi-agent reinforcement learning (MARL) problems occurring in cooperative settings. All algorithms are based on the Deep Quality-Value (DQV) family of algorithms, a set of techniques that have proven to be successful when dealing with single-agent reinforcement learning problems (SARL). The key idea of DQV algorithms is to jointly learn an approximation of the state-value function $V$, alongside an approximation of the state-action value function $Q$. We follow this principle and generalise these algorithms by introducing two fully decentralised MARL algorithms (IQV and IQV-Max) and two algorithms that are based on the centralised training with decentralised execution training paradigm (QVMix and QVMix-Max). We compare our algorithms with state-of-the-art MARL techniques on the popular StarCraft Multi-Agent Challenge (SMAC) environment. We show competitive results when QVMix and QVMix-Max are compared to well-known MARL techniques such as QMIX and MAVEN and show that QVMix can even outperform them on some of the tested environments, being the algorithm which performs best overall. We hypothesise that this is due to the fact that QVMix suffers less from the overestimation bias of the $Q$ function.

Matthia Sabatelli, Mike Kestemont, Pierre Geurts

We study the generalization properties of pruned neural networks that are the winners of the lottery ticket hypothesis on datasets of natural images. We analyse their potential under conditions in which training data is scarce and comes from a non-natural domain. Specifically, we investigate whether pruned models that are found on the popular CIFAR-10/100 and Fashion-MNIST datasets, generalize to seven different datasets that come from the fields of digital pathology and digital heritage. Our results show that there are significant benefits in transferring and training sparse architectures over larger parametrized models, since in all of our experiments pruned networks, winners of the lottery ticket hypothesis, significantly outperform their larger unpruned counterparts. These results suggest that winning initializations do contain inductive biases that are generic to some extent, although, as reported by our experiments on the biomedical datasets, their generalization properties can be more limiting than what has been so far observed in the literature.

Matthia Sabatelli, Gilles Louppe, Pierre Geurts et al.

This paper makes one step forward towards characterizing a new family of \textit{model-free} Deep Reinforcement Learning (DRL) algorithms. The aim of these algorithms is to jointly learn an approximation of the state-value function ($V$), alongside an approximation of the state-action value function ($Q$). Our analysis starts with a thorough study of the Deep Quality-Value Learning (DQV) algorithm, a DRL algorithm which has been shown to outperform popular techniques such as Deep-Q-Learning (DQN) and Double-Deep-Q-Learning (DDQN) \cite{sabatelli2018deep}. Intending to investigate why DQV's learning dynamics allow this algorithm to perform so well, we formulate a set of research questions which help us characterize a new family of DRL algorithms. Among our results, we present some specific cases in which DQV's performance can get harmed and introduce a novel \textit{off-policy} DRL algorithm, called DQV-Max, which can outperform DQV. We then study the behavior of the $V$ and $Q$ functions that are learned by DQV and DQV-Max and show that both algorithms might perform so well on several DRL test-beds because they are less prone to suffer from the overestimation bias of the $Q$ function.

Matthia Sabatelli, Gilles Louppe, Pierre Geurts et al.

We introduce a novel Deep Reinforcement Learning (DRL) algorithm called Deep Quality-Value (DQV) Learning. DQV uses temporal-difference learning to train a Value neural network and uses this network for training a second Quality-value network that learns to estimate state-action values. We first test DQV's update rules with Multilayer Perceptrons as function approximators on two classic RL problems, and then extend DQV with the use of Deep Convolutional Neural Networks, `Experience Replay' and `Target Neural Networks' for tackling four games of the Atari Arcade Learning environment. Our results show that DQV learns significantly faster and better than Deep Q-Learning and Double Deep Q-Learning, suggesting that our algorithm can potentially be a better performing synchronous temporal difference algorithm than what is currently present in DRL.