Computing diverse solutions for a given problem, in particular evolutionary diversity optimisation (EDO), is a hot research topic in the evolutionary computation community. This paper studies the Boolean satisfiability problem (SAT) in the context of EDO. SAT is of great importance in computer science and differs from the other problems studied in EDO literature, such as KP and TSP. SAT is heavily constrained, and the conventional evolutionary operators are inefficient in generating SAT solutions. Our approach avails of the following characteristics of SAT: 1) the possibility of adding more constraints (clauses) to the problem to forbid solutions or to fix variables, and 2) powerful solvers in the literature, such as minisat. We utilise such a solver to construct a diverse set of solutions. Moreover, maximising diversity provides us with invaluable information about the solution space of a given SAT problem, such as how large the feasible region is. In this study, we introduce evolutionary algorithms (EAs) employing a well-known SAT solver to maximise diversity among a set of SAT solutions explicitly. The experimental investigations indicate the introduced algorithms' capability to maximise diversity among the SAT solutions.
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Order execution is a fundamental task in quantitative finance, aiming at finishing acquisition or liquidation for a number of trading orders of the specific assets. Recent advance in model-free reinforcement learning (RL) provides a data-driven solution to the order execution problem. However, the existing works always optimize execution for an individual order, overlooking the practice that multiple orders are specified to execute simultaneously, resulting in suboptimality and bias. In this paper, we first present a multi-agent RL (MARL) method for multi-order execution considering practical constraints. Specifically, we treat every agent as an individual operator to trade one specific order, while keeping communicating with each other and collaborating for maximizing the overall profits. Nevertheless, the existing MARL algorithms often incorporate communication among agents by exchanging only the information of their partial observations, which is inefficient in complicated financial market. To improve collaboration, we then propose a learnable multi-round communication protocol, for the agents communicating the intended actions with each other and refining accordingly. It is optimized through a novel action value attribution method which is provably consistent with the original learning objective yet more efficient. The experiments on the data from two real-world markets have illustrated superior performance with significantly better collaboration effectiveness achieved by our method.
Numerous researchers from various disciplines have explored commonalities and divergences in the evolution of complex social formations. Here, we explore whether there is a 'characteristic' time-course for the evolution of social complexity in a handful of different geographic areas. Data from the Seshat: Global History Databank is shifted so that the overlapping time series can be fitted to a single logistic regression model for all 23 geographic areas under consideration. The resulting regression shows convincing out-of-sample predictions and its period of extensive growth in social complexity can be identified via bootstrapping as a time interval of roughly 2500 years. To analyse the endogenous growth of social complexity, each time series is restricted to a central time interval without major disruptions in cultural or institutional continuity and both approaches result in a similar logistic regression curve. Our results suggest that these different areas have indeed experienced a similar course in the their evolution of social complexity, but that this is a lengthy process involving both internal developments and external influences.
Many food products involve mixtures of ingredients, where the mixtures can be expressed as combinations of ingredient proportions. In many cases, the quality and the consumer preference may also depend on the way in which the mixtures are processed. The processing is generally defined by the settings of one or more process variables. Experimental designs studying the joint impact of the mixture ingredient proportions and the settings of the process variables are called mixture-process variable experiments. In this article, we show how to combine mixture-process variable experiments and discrete choice experiments, to quantify and model consumer preferences for food products that can be viewed as processed mixtures. First, we describe the modeling of data from such combined experiments. Next, we describe how to generate D- and I-optimal designs for choice experiments involving mixtures and process variables, and we compare the two kinds of designs using two examples.
We tackle the problems of latent variables identification and "out-of-support" image generation in representation learning. We show that both are possible for a class of decoders that we call additive, which are reminiscent of decoders used for object-centric representation learning (OCRL) and well suited for images that can be decomposed as a sum of object-specific images. We provide conditions under which exactly solving the reconstruction problem using an additive decoder is guaranteed to identify the blocks of latent variables up to permutation and block-wise invertible transformations. This guarantee relies only on very weak assumptions about the distribution of the latent factors, which might present statistical dependencies and have an almost arbitrarily shaped support. Our result provides a new setting where nonlinear independent component analysis (ICA) is possible and adds to our theoretical understanding of OCRL methods. We also show theoretically that additive decoders can generate novel images by recombining observed factors of variations in novel ways, an ability we refer to as Cartesian-product extrapolation. We show empirically that additivity is crucial for both identifiability and extrapolation on simulated data.
To integrate large systems of nonlinear differential equations in time, we consider a variant of nonlinear waveform relaxation (also known as dynamic iteration or Picard-Lindel\"of iteration), where at each iteration a linear inhomogeneous system of differential equations has to be solved. This is done by the exponential block Krylov subspace (EBK) method. Thus, we have an inner-outer iterative method, where iterative approximations are determined over a certain time interval, with no time stepping involved. This approach has recently been shown to be efficient as a time-parallel integrator within the PARAEXP framework. In this paper, convergence behavior of this method is assessed theoretically and practically. We examine efficiency of the method by testing it on nonlinear Burgers and Liouville-Bratu-Gelfand equations and comparing its performance with that of conventional time-stepping integrators.
This paper presents an exhaustive quantitative and qualitative evaluation of Large Language Models (LLMs) for Knowledge Graph (KG) construction and reasoning. We employ eight distinct datasets that encompass aspects including entity, relation and event extraction, link prediction, and question answering. Empirically, our findings suggest that GPT-4 outperforms ChatGPT in the majority of tasks and even surpasses fine-tuned models in certain reasoning and question-answering datasets. Moreover, our investigation extends to the potential generalization ability of LLMs for information extraction, which culminates in the presentation of the Virtual Knowledge Extraction task and the development of the VINE dataset. Drawing on these empirical findings, we further propose AutoKG, a multi-agent-based approach employing LLMs for KG construction and reasoning, which aims to chart the future of this field and offer exciting opportunities for advancement. We anticipate that our research can provide invaluable insights for future undertakings of KG\footnote{Code and datasets will be available in //github.com/zjunlp/AutoKG.
In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.
We describe ACE0, a lightweight platform for evaluating the suitability and viability of AI methods for behaviour discovery in multiagent simulations. Specifically, ACE0 was designed to explore AI methods for multi-agent simulations used in operations research studies related to new technologies such as autonomous aircraft. Simulation environments used in production are often high-fidelity, complex, require significant domain knowledge and as a result have high R&D costs. Minimal and lightweight simulation environments can help researchers and engineers evaluate the viability of new AI technologies for behaviour discovery in a more agile and potentially cost effective manner. In this paper we describe the motivation for the development of ACE0.We provide a technical overview of the system architecture, describe a case study of behaviour discovery in the aerospace domain, and provide a qualitative evaluation of the system. The evaluation includes a brief description of collaborative research projects with academic partners, exploring different AI behaviour discovery methods.
Knowledge graph completion aims to predict missing relations between entities in a knowledge graph. While many different methods have been proposed, there is a lack of a unifying framework that would lead to state-of-the-art results. Here we develop PathCon, a knowledge graph completion method that harnesses four novel insights to outperform existing methods. PathCon predicts relations between a pair of entities by: (1) Considering the Relational Context of each entity by capturing the relation types adjacent to the entity and modeled through a novel edge-based message passing scheme; (2) Considering the Relational Paths capturing all paths between the two entities; And, (3) adaptively integrating the Relational Context and Relational Path through a learnable attention mechanism. Importantly, (4) in contrast to conventional node-based representations, PathCon represents context and path only using the relation types, which makes it applicable in an inductive setting. Experimental results on knowledge graph benchmarks as well as our newly proposed dataset show that PathCon outperforms state-of-the-art knowledge graph completion methods by a large margin. Finally, PathCon is able to provide interpretable explanations by identifying relations that provide the context and paths that are important for a given predicted relation.
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.
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