Partially observable environments present increased decisionmaking complexity for Reinforcement Learning agents. This paper explores methods for improving automated decision-making in partially observable environments by utilizing Variational Auto-Encoders (VAEs) trained on expert demonstrations to generate intrinsic rewards for reinforcement learning (RL) agents. Specifically, a VAE is pre-trained on expert demonstrations to construct a latent representation of successful decision-making. This latent representation is utilized to generate intrinsic rewards via KL-divergence, augmenting the extrinsic reward signal during Proximal Policy Optimization (PPO) training. Experiments are conducted using a symbolic-matching navigation task within a Unity MLAgents environment, which requires memory formation and hierarchical reasoning. Results indicate that incorporating demonstration-based intrinsic rewards improves the learning efficiency and convergence of PPO agents compared to baseline models without intrinsic rewards. The findings suggest that latent-space representations from demonstrations can effectively guide exploration in challenging RL scenarios, and that certain behaviors are retained from demonstrations.
Similarity functions between sets and in particular, between intervals, are traditionally assumed to verify a monotonicity condition. It requires that if three sets (intervals) are ordered by inclusion, the similarity between the greatest and the smallest must be smaller than the similarity between the middle one and any of the other two. We find this property coherent but too weak since it does not require anything from triplets of sets that are not perfectly ordered. A condition introduced in the last years that involves the concept of infimum and supremum applies to every triplet of intervals and generalizes the classical axiom of monotonicity for similarities. Despite it is a logical and intuitive condition, it is easy to check that it is not satisfied for every similarity. In this contribution we focus on similarities defined from embeddings and more particularly, from two families of embeddings and we study if the two families of similarity measures obtained comply with the general condition of monotonicity introduced two years ago. A positive answer is obtained in all the cases studied.
ChessFormer introduces a novel searchless chess engine leveraging transformer architecture to approximate human decision-making in chess. Trained on a vast dataset of 3 billion chess positions, our model learns its entire decision-making process directly from training data. Evaluations show an improvement in human move-matching accuracy over prior models in high-Elo ranges and the model's ability to distinguish between human and algorithmic decision-making, offering potential applications in chess analysis or cheat detection.
Choquet integrals are a class of non-additive aggregation operators that generalize the weighted arithmetic means and order statistics (for example, the sample median). It is a prevalent example of fuzzy integrals that has been extended in various ways. In particular, replacing the naive difference between assessments in the Choquet integral by restricted dissimilarity functions produces d-Choquet integrals. We define and study differentially private d-Choquet integrals. They are designed to satisfy differential privacy with the introduction of Lagrangian noise calibrated by their sensitivity. In this way, a new additive noise differential privacy mechanism is proposed that generalizes differentially private Choquet integrals. The later case already gave valuable information about the sensitivity of linear combination of order statistics and weighted means, for which the literature on privacy preservation is abundant. To meet the needs of practical implementation, we compute the sensitivity of d-Choquet integrals associated with several types of fuzzy measures and restricted dissimilarity functions. Other theoretical results link these achievements with knowledge about the particular case of differentially private Choquet integrals.
Decision-making in complex systems often involves dealing with imprecise or uncertain information, frequently represented using fuzzy sets, particularly Triangular Fuzzy Numbers (TFNs). A crucial aspect of many fuzzy methods is the quantification of distance between TFNs. Many distance measures assume that all values are in the same scale, requiring a preliminary normalization stage when applied to heterogeneous attributes with different scales or units. This paper proposes the Triangular Fuzzy Rescaling Distance ( d_TR ), a metric designed to address this challenge. The d_TR uniquely integrates Linear Rescaling (LRE) directly into the distance calculation, ensuring normalization during the comparison of fuzzy numbers. We formally prove that d_TR satisfies the properties of a metric, including non-negativity, identity, symmetry, and the triangle inequality. Furthermore, we demonstrate that d_TR is bounded, scale-invariant, and origin-invariant. These properties, combined with a weighting vector for prioritizing dimensions, make d_TR suitable for applications involving heterogeneous fuzzy data, such as the construction of synthetic indicators, distance-based machine learning algorithms or multicriteria-decision aiding.
