Inconsistency in prediction problems occurs when instances that relate in a certain way on condition attributes, do not follow the same relation on the decision attribute. For example, in ordinal classification with monotonicity constraints, it occurs when an instance dominating another instance on condition attributes has been assigned to a worse decision class. It typically appears as a result of perturbation in data caused by incomplete knowledge (missing attributes) or by random effects that occur during data generation (instability in the assessment of decision attribute values). Inconsistencies with respect to a crisp preorder relation (expressing either dominance or indiscernibility between instances) can be handled using symbolic approaches like rough set theory and by using statistical/machine learning approaches that involve optimization methods. Fuzzy rough sets can also be seen as a symbolic approach to inconsistency handling with respect to a fuzzy relation. In this article, we introduce a new machine learning method for inconsistency handling with respect to a fuzzy preorder relation. The novel approach is motivated by the existing machine learning approach used for crisp relations. We provide statistical foundations for it and develop optimization procedures that can be used to eliminate inconsistencies. The article also proves important properties and contains didactic examples of those procedures.

Evacuation shelters, which are urgently required during natural disasters, are designed to minimize the burden of evacuation on human survivors. However, the larger the scale of the disaster, the more costly it becomes to operate shelters. When the number of evacuees decreases, the operation costs can be reduced by moving the remaining evacuees to other shelters and closing shelters as quickly as possible. On the other hand, relocation between shelters imposes a huge emotional burden on evacuees. In this study, we formulate the "Evacuation Shelter Scheduling Problem," which allocates evacuees to shelters in such a way to minimize the movement costs of the evacuees and the operation costs of the shelters. Since it is difficult to solve this quadratic programming problem directly, we show its transformation into a 0-1 integer programming problem. In addition, such a formulation struggles to calculate the burden of relocating them from historical data because no payments are actually made. To solve this issue, we propose a method that estimates movement costs based on the numbers of evacuees and shelters during an actual disaster. Simulation experiments with records from the Kobe earthquake (Great Hanshin-Awaji Earthquake) showed that our proposed method reduced operation costs by 33.7 million dollars: 32%.

--In the trial-and-error mechanism of reinforcement learning (RL), a notorious contradiction arises when we expect to learn a safe policy: how to learn a safe policy without enough data and prior model about the dangerous region? Existing methods mostly use the posterior penalty for dangerous actions, which means that the agent is not penalized until experiencing danger . This fact causes that the agent cannot learn a zero-violation policy even after convergence . Otherwise, it would not receive any penalty and lose the knowledge about danger . In this paper, we propose the safe set actor-critic (SSAC) algorithm, which confines the policy update using safety-oriented energy functions, or the safety indexes . The safety index is designed to increase rapidly for potentially dangerous actions, which allow us to locate the safe set on the action space, or the control safe set . Therefore, we can identify the dangerous actions prior to taking them, and further obtain a zero constraint-violation policy after convergence. We claim that we can learn the energy function in a model-free manner similar to learning a value function. By using the energy function transition as the constraint objective, we formulate a constrained RL problem. We prove that our Lagrangian-based solutions make sure that the learned policy will converge to the constrained optimum under some assumptions. The proposed algorithm is evaluated on both the complex simulation environments and a hardware-in-loop (HIL) experiment with a real controller from the autonomous vehicle. Experimental results suggest that the converged policy in all environments achieve zero constraint violation and comparable performance with model-based baseline. EINFORCEMENT learning has drawn rapidly growing attention for its superhuman learning capabilities in many sequential decision making problems like Go [1], Atari Games [2], and Starcraft [3].

Optimization problems are crucial in artificial intelligence. Optimization algorithms are generally used to adjust the performance of artificial intelligence models to minimize the error of mapping inputs to outputs. Current evaluation methods on optimization algorithms generally consider the performance in terms of quality. However, not all optimization algorithms for all test cases are evaluated equal from quality, the computation time should be also considered for optimization tasks. In this paper, we investigate the quality and computation time of optimization algorithms in optimization problems, instead of the one-for-all evaluation of quality. We select the well-known optimization algorithms (Bayesian optimization and evolutionary algorithms) and evaluate them on the benchmark test functions in terms of quality and computation time.

The thriving of artificial intelligence (AI) applications is driving the further evolution of wireless networks. It has been envisioned that 6G will be transformative and will revolutionize the evolution of wireless from "connected things" to "connected intelligence". However, state-of-the-art deep learning and big data analytics based AI systems require tremendous computation and communication resources, causing significant latency, energy consumption, network congestion, and privacy leakage in both of the training and inference processes. By embedding model training and inference capabilities into the network edge, edge AI stands out as a disruptive technology for 6G to seamlessly integrate sensing, communication, computation, and intelligence, thereby improving the efficiency, effectiveness, privacy, and security of 6G networks. In this paper, we shall provide our vision for scalable and trustworthy edge AI systems with integrated design of wireless communication strategies and decentralized machine learning models. New design principles of wireless networks, service-driven resource allocation optimization methods, as well as a holistic end-to-end system architecture to support edge AI will be described. Standardization, software and hardware platforms, and application scenarios are also discussed to facilitate the industrialization and commercialization of edge AI systems.

--In this paper, a transmission-distribution systems flexibility market is introduced, in which system operators (SOs) jointly procure flexibility from different systems to meet their needs (balancing and congestion management) using a common market. This common market is, then, formulated as a cooperative game aiming at identifying a stable and efficient split of costs of the jointly procured flexibility among the participating SOs to incentivize their cooperation. The non-emptiness of the core of this game is then mathematically proven, implying the stability of the game and the naturally-arising incentive for cooperation among the SOs. Several cost allocation mechanisms are then introduced, while characterizing their mathematical properties. Numerical results focusing on an interconnected system (composed of the IEEE 14-bus transmission system and the Matpower 18-bus, 69-bus, and 141-bus distributions systems) showcase the cooperation-induced reduction in system-wide flexibility procurement costs, and identifies the varying costs borne by different SOs under various cost allocations methods. The increasing integration of distributed energy resources (DERs) and electrification of the consumer energy space (e.g., transportation and heating) pose challenges for grid operation, due to the induced uncertainty and changing load patterns. In this respect, the introduction of market mechanisms for the procurement of flexibility from flexibility services provides (FSPs) has been increasingly recommended in policies [1], and has been the center of several recent works in the literature [2]-[7] and demonstration projects [8]. As FSPs could provide their flexibility as a service to different system operators (SOs), a major branch of the literature has focused on the SOs' joint procurement (i.e. In particular, a key focus has been shed on the need for coordination between SOs to achieve joint procurement, not only for optimization of economic efficiency but also to ensure that the activated flexibility meets grid operational constraints of all the grids involved [2]-[5], [9], [10]. The authors are with the Flemish Institute for Technological Research VITO/EnergyVille, Thor Park 8310, 3600 Genk, Belgium. The authors have equally contributed to this work. This work is supported by the EU's Horizon 2020 research and innovation programme under grant agreement No 824414 - CoordiNet project. Flexibility is the ability to dynamically modify consumption and generation patterns providing, as a result, a service to system operators. Towards this end, we first introduce a novel flexibility market model including a TSO and multiple DSOs for jointly procuring congestion management and balancing services while explicitly accounting for grid constraints. This framework is developed by first introducing disjoint TSO and DSO level markets and joining them in a common market setting.

Constrained tensor and matrix factorization models allow to extract interpretable patterns from multiway data. Therefore identifiability properties and efficient algorithms for constrained low-rank approximations are nowadays important research topics. This work deals with columns of factor matrices of a low-rank approximation being sparse in a known and possibly overcomplete basis, a model coined as Dictionary-based Low-Rank Approximation (DLRA). While earlier contributions focused on finding factor columns inside a dictionary of candidate columns, i.e. one-sparse approximations, this work is the first to tackle DLRA with sparsity larger than one. I propose to focus on the sparse-coding subproblem coined Mixed Sparse-Coding (MSC) that emerges when solving DLRA with an alternating optimization strategy. Several algorithms based on sparse-coding heuristics (greedy methods, convex relaxations) are provided to solve MSC. The performance of these heuristics is evaluated on simulated data. Then, I show how to adapt an efficient MSC solver based on the LASSO to compute Dictionary-based Matrix Factorization and Canonical Polyadic Decomposition in the context of hyperspectral image processing and chemometrics. These experiments suggest that DLRA extends the modeling capabilities of low-rank approximations, helps reducing estimation variance and enhances the identifiability and interpretability of estimated factors.

By concisely representing a joint function of many variables as the combination of small functions, discrete graphical models (GMs) provide a powerful framework to analyze stochastic and deterministic systems of interacting variables. One of the main queries on such models is to identify the extremum of this joint function. This is known as the Weighted Constraint Satisfaction Problem (WCSP) on deterministic Cost Function Networks and as Maximum a Posteriori (MAP) inference on stochastic Markov Random Fields. Algorithms for approximate WCSP inference typically rely on local consistency algorithms or belief propagation. These methods are intimately related to linear programming (LP) relaxations and often coupled with reparametrizations defined by the dual solution of the associated LP. Since the seminal work of Goemans and Williamson, it is well understood that convex SDP relaxations can provide superior guarantees to LP. But the inherent computational cost of interior point methods has limited their application. The situation has improved with the introduction of non-convex Burer-Monteiro style methods which are well suited to handle the SDP relaxation of combinatorial problems with binary variables (such as MAXCUT, MaxSAT or MAP/Ising). We compute low rank SDP upper and lower bounds for discrete pairwise graphical models with arbitrary number of values and arbitrary binary cost functions by extending a Burer-Monteiro style method based on row-by-row updates. We consider a traditional dualized constraint approach and a dedicated Block Coordinate Descent approach which avoids introducing large penalty coefficients to the formulation. On increasingly hard and dense WCSP/CFN instances, we observe that the BCD approach can outperform the dualized approach and provide tighter bounds than local consistencies/convergent message passing approaches.

Most set prediction models in deep learning use set-equivariant operations, but they actually operate on multisets. We show that set-equivariant functions cannot represent certain functions on multisets, so we introduce the more appropriate notion of multiset-equivariance. We identify that the existing Deep Set Prediction Network (DSPN) can be multiset-equivariant without being hindered by set-equivariance and improve it with approximate implicit differentiation, allowing for better optimization while being faster and saving memory. In a range of toy experiments, we show that the perspective of multiset-equivariance is beneficial and that our changes to DSPN achieve better results in most cases. On CLEVR object property prediction, we substantially improve over the state-of-the-art Slot Attention from 8% to 77% in one of the strictest evaluation metrics because of the benefits made possible by implicit differentiation.

The discovery of Behavior Trees (BTs) impacted the field of Artificial Intelligence (AI) in games, by providing flexible and natural representation of non-player characters (NPCs) logic, manageable by game-designers. Nevertheless, increased pressure on ever better NPCs AI-agents forced complexity of handcrafted BTs to became barely-tractable and error-prone. On the other hand, while many just-launched on-line games suffer from player-shortage, the existence of AI with a broad-range of capabilities could increase players retention. Therefore, to handle above challenges, recent trends in the field focused on automatic creation of AI-agents: from deep- and reinforcementlearning techniques to combinatorial (constrained) optimization and evolution of BTs. In this paper, we present a novel approach to semi-automatic construction of AI-agents, that mimic and generalize given human gameplays by adapting and tuning of expert-created BT under a developed similarity metric between source and BT gameplays. To this end, we formulated mixed discrete-continuous optimization problem, in which topological and functional changes of the BT are reflected in numerical variables, and constructed a dedicated hybrid-metaheuristic. The performance of presented approach was verified experimentally in a prototype real-time strategy game. Carried out experiments confirmed efficiency and perspectives of presented approach, which is going to be applied in a commercial game.