Coalition formation involves self-organized coalitions generated through strategic collaborations of autonomous selfish agents. In online learning of coalition structures, agents’ preferences toward each other are initially unknown before agents interact. Coalitions are formed iteratively based on preferences that agents learn online from repeated feedback resulting from their interactions. In this work, we introduce online learning in coalition formation through the lens of distributed decision-making, where self-interested agents operate without global coordination or information sharing, and learn only from their own experience. Under the selfish perspective, each agent seeks to maximize her own utility. Hence, we analyze the system in terms of Nash stability, where no agent can improve her utility by unilaterally deviating. Our goal is therefore designing sample-efficient decentralized algorithms for selfish agents that minimize their Nash regret, yielding approximately Nash stable solutions. This poses a natural tension between an algorithm’s performance in the short- and long-term, trading off between the accuracy of the utility estimation at each round and the long-term objective of minimizing Nash regret to reach approximately Nash stable outcomes. Specifically, we first devise an algorithm where each agent sacrifices accuracy at each single time step by using only one utility feedback per round to update her strategy, but still has Nash regret and sample complexity bounds that are optimal up to logarithmic factors. To control the error incurred at any individual time instant, we then propose a method using multiple samples per round, yet at the expense of obtaining suboptimal Nash regret and sample complexity bounds.
This paper investigates quantized mereology, which merges quantum information theory with classical mereology, the formal analysis of the part-whole relationship. It emphasizes that information about crisp mereological relations is captured by classical bits, whereas mereological vagueness involves the use of quantum bits, or qubits, to capture mereological information. Transitioning from classical bits to qubits offers a new understanding of part-whole relations among entities that are subject to mereological vagueness. This paper methodically studies the quantized mereology that arises from the classical RCC5 formalism, one of the most widely studied formalisms in Qualitative Reasoning (QR), a subfield of Artificial Intelligence. The argument is made that this method can be extended to quantize more sophisticated QR formalisms, mirroring how strategies are used in physics to transition from classical to quantum systems. The study explores: (i) the conversion of bits to qubits while understanding that these (qu)bits convey mereological information; (ii) the representation of qubit states via set partitions, acknowledging that set theory aligns more closely with classical logic than with the complex vector spaces employed in quantum physics; (iii) demonstrating that classical QR formalisms can be seen as special cases within quantized formalisms; and (iv) showing that qubits more effectively encapsulate information about vague phenomena.
Background: Counterexample-Guided Abstraction Refinement (CEGAR) is a prominent technique to generate Cartesian abstractions for guiding search in cost-optimal planning. The core idea is to start from the trivial abstraction—an abstract state representing all concrete states—and iteratively refine it in a loop by splitting one abstract state into two. Each iteration of the loop searches an optimal abstract plan and replicates it into the concrete state space until finding a flaw—and splitting such abstract state—or returning a plan for the task if no flaw is found. Previous work finds only a single flaw in progression, by executing the abstract plan from the initial state and stopping when execution cannot be continued. Objectives: A theoretical framework for identifying different flaws of abstract plans, analysing their properties and using them to refine abstractions in different ways leading to higher-quality heuristics. Methods: We show that alternative types of flaw can be defined. Specifically, we search flaws in regression from the goals—resulting in higher heuristic values—and identify sequence flaws along the whole abstract plan by searching them in a Cartesian relaxation of the task after the first flaw, which greatly increases the flexibility of refinements in CEGAR. Results: Our experiments show that across existing benchmarks numerous sequence flaws exist in most abstract plans. We observe that the selected flaw has a high impact on the heuristic, and we propose several strategies that generate more informed abstractions. Overall, this greatly improves the performance of the baseline that only used the first progression flaw. Conclusions: Guiding the CEGAR process by analysing multiple flaws of an abstract plan trace and selecting the best refinement can improve its performance as a tool to generate admissible heuristics in planning. Thus, using our new types of flaw and flaw selection strategies, we get stronger heuristics than the state-of-the-art planners based on Cartesian abstractions.
Gaussian process (GP) regression with a single global GP (GP-glo) incurs cubic computational cost, limiting scalability to large datasets. Product-of-experts GP models (GP-pro), which combine local GP models to capture global correlations, alleviate this computational burden. However, training local experts on disjoint data subsets can lead to overestimated posterior variances. We propose GP-pro-c, a product-of-experts GP model that calibrates these variances using an information-based method. The method exploits the monotonicity and submodularity of information gain in GPs to define a calibration ratio that reduces the posterior variance of individual local GP models. We evaluate GP-pro-c using negative log-likelihood (NLL), root mean squared error (RMSE), and expected normalised calibration error (ENCE). Experiments on four synthetic functions and six regression datasets show that GP-pro-c achieves average reductions of 2.3
Background: In declarative constraint solving, a user formulates a constraint model in terms of variables and constraints, and uses a generic, off-the-shelf solver to solve the problem. Constraint Programming (CP) is one such constraint-solving paradigm, which has a wide support for many types of constraints, including global constraints. Global constraints capture complex relations between several decision variables, and CP solvers have specialized propagators to solve them efficiently. Objectives: While CP solvers support a wide range of global constraints, few solvers support them in a reified or even halfreified context. Hence, for most CP solvers, reified global constraints must be decomposed into non-global constraints. This bypasses the global constraint propagator, which can considerably slow the solving process, suppressing one of the key benefits of modeling with global constraints: a faster solve-time. This is a problem for generic CP-modeling, as reified constraints are often introduced by the modeling system during translation and flattening of compound constraints. Additionally, half-reified global constraints are also used extensively in eXplainable Constraint Programming techniques (XCP). Therefore, XCP techniques suffer from scalability issues when global constraints occur in the model. In this paper, we aim to alleviate this bottleneck, allowing the use of the propagators of global constraints when modeling their half-reification, for all CP-solvers. Methods: We propose a set of reformulation rules that allow the use of half-reification of a global constraint with any CP solver that supports the “normal” global constraint propagator. This is achieved by introducing auxiliary variables for the decision variables in the global constraint and the use of a reified channeling constraint, which most CP solvers support. Additionally, we show how to reduce the overhead of these auxiliary variables, by limiting the number of variables introduced, and by fixing their value when unconstrained. Finally, we prove the propagation strength of our reformulation for a variety of global constraint families. Results: We experimentally evaluate the reformulations on a variety of global constraints and applications where reified constraints can occur. Our results show that this reformulation is much faster compared to decomposing the global constraint, and in some cases, even outperforms solver-level propagation routines for reified global constraints. Conclusions: Using the reformulations proposed in this paper, we make the use of reified global constraints easily available for any CP solver. Hence, we expand the range of available solvers and constraint models that can be used in XCP techniques or for solving CSPs with compound constraints.
