To reliably deploy Multi-Agent Reinforcement Learning (MARL) systems, it is crucial to understand individual agent behaviors. While prior work typically evaluates overall team performance based on explicit reward signals, it is unclear how to infer agent contributions in the absence of any value feedback. In this work, we investigate whether meaningful insights into agent behaviors can be extracted solely by analyzing the policy distribution. Inspired by the phenomenon that intelligent agents tend to pursue convergent instrumental values, we introduce Intended Cooperation Values (ICVs), a method based on information-theoretic Shapley values for quantifying each agent’s causal influence on their co-players’ instrumental empowerment. Specifically, ICVs measure an agent’s action effect on its teammates’ policies by assessing their decision (un)certainty and preference alignment. By analyzing action effects on policies and value functions across cooperative and competitive MARL tasks, our method identifies which agent behaviors are beneficial to team success, either by fostering deterministic decisions or by preserving flexibility for future action choices, while also revealing the extent to which agents adopt similar or diverse strategies. Our proposed method offers novel insights into cooperation dynamics and enhances explainability in MARL systems.

Consistent hashing is a technique for distributing data across a network of nodes in a way that minimizes reorganization when nodes join or leave the network. It is extensively applied in modern distributed systems as a fundamental mechanism for routing and data placement. Similarly, distributed storage systems rely on consistent hashing for scalable and fault-tolerant data partitioning. This paper introduces BinomialHash, a consistent hashing algorithm that executes in constant time and requires minimal memory. We provide a detailed explanation of the algorithm, present a pseudocode implementation, and formally establish its strong theoretical guarantees. Finally, we compare its performance against state-of-the-art constant-time consistent hashing algorithms, demonstrating that our solution is both highly competitive and effective, while also validating the theoretical boundaries.

Bayesian networks are a popular class of directed probabilistic graphical models that allow for closed-form learning of the local parameters if complete data are available. However, learning the parameters is challenging when the data are sparse, incomplete, and uncertain. In this work, we present an approach to this problem based on credal networks, a generalization of Bayesian networks based on set-valued local parameters. We derive an algorithm to learn such set-valued parameters from data using qualitative knowledge in the form of monotonic influence statements. Our empirical evaluation shows that using qualitative knowledge reduces uncertainty about the parameters without significant loss in accuracy.

We assume to be given structural equations over discrete variables inducing a directed acyclic graph, namely, a structural causal model, together with data about its internal nodes. The question we want to answer is how can we compute bounds for partially identifiable counterfactual queries from such an input. We start by giving a map from structural casual models to credal networks. This allows us to compute exact counterfactual bounds via algorithms for credal nets on a subclass of structural causal models. Exact computation is going to be inefficient in general given that, as we show, causal inference is NP-hard even on polytrees. We target then approximate bounds via a causal EM scheme. We evaluate their accuracy by providing credible intervals on the quality of the approximation; we show through a synthetic benchmark that the EM scheme delivers accurate results in a fair number of runs. In the course of the discussion, we also point out what seems to be a neglected limitation to the trending idea that counterfactual bounds can be computed without knowledge of the structural equations. We also present a real case study on palliative care to show how our algorithms can readily be used for practical purposes.

Consistent hashing is used in distributed systems and networking applications to spread data evenly and efficiently across a cluster of nodes. In this paper, we present MementoHash, a novel consistent hashing algorithm that eliminates known limitations of state-of-the-art algorithms while keeping optimal performance and minimal memory usage. We describe the algorithm in detail, provide a pseudo-code implementation, and formally establish its solid theoretical guarantees. To measure the efficacy of MementoHash, we compare its performance, in terms of memory usage and lookup time, to that of state-of-the-art algorithms, namely, AnchorHash, DxHash, and JumpHash. Unlike JumpHash, MementoHash can handle random failures. Moreover, MementoHash does not require fixing the overall capacity of the cluster (as AnchorHash and DxHash do), allowing it to scale indefinitely. The number of removed nodes affects the performance of all the considered algorithms. Therefore, we conduct experiments considering three different scenarios: stable (no removed nodes), one-shot removals (90% of the nodes removed at once), and incremental removals. We report experimental results that averaged a varying number of nodes from ten to one million. Results indicate that our algorithm shows optimal lookup performance and minimal memory usage in its best-case scenario. It behaves better than AnchorHash and DxHash in its average-case scenario and at least as well as those two algorithms in its worst-case scenario.

The application of artificial intelligence to simulate air-to-air combat scenarios is attracting increasing attention. To date the high-dimensional state and action spaces, the high complexity of situation information (such as imperfect and filtered information, stochasticity, incomplete knowledge about mission targets) and the nonlinear flight dynamics pose significant challenges for accurate air combat decision-making. These challenges are exacerbated when multiple heterogeneous agents are involved. We propose a hierarchical multi-agent reinforcement learning framework for air-to-air combat with multiple heterogeneous agents. In our framework, the decision-making process is divided into two stages of abstraction, where heterogeneous low-level policies control the action of individual units, and a high-level commander policy issues macro commands given the overall mission targets. Low-level policies are trained for accurate unit combat control. Their training is organized in a learning curriculum with increasingly complex training scenarios and league-based self-play. The commander policy is trained on mission targets given pre-trained low-level policies. The empirical validation advocates the advantages of our design choices.

We address the problem of integrating data from multiple, possibly biased, observational and interventional studies, to eventually compute counterfactuals in structural causal models. We start from the case of a single observational dataset affected by a selection bias. We show that the likelihood of the available data has no local maxima. This enables us to use the causal expectation-maximisation scheme to approximate the bounds for partially identifiable counterfactual queries, which are the focus of this paper. We then show how the same approach can address the general case of multiple datasets, no matter whether interventional or observational, biased or unbiased, by remapping it into the former one via graphical transformations. Systematic numerical experiments and a case study on palliative care show the effectiveness of our approach, while hinting at the benefits of fusing heterogeneous data sources to get informative outcomes in case of partial identifiability.

Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the irrelevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that inferences under strong independence are NP-hard even in trees with binary variables except for a single ternary one. We prove that under epistemic irrelevance the polynomial-time complexity of inferences in credal trees is not likely to extend to more general models (e.g., singly connected topologies). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding their computational complexity. We show that these results remain valid even if we disallow the use of zero probabilities. We also show that the computation of bounds on the probability of the future state in a hidden Markov model is the same whether we assume epistemic irrelevance or strong independence, and we prove a similar result for inference in naive Bayes structures. These inferential equivalences are important for practitioners, as hidden Markov models and naive Bayes structures are used in real applications of imprecise probability.