Puzzle solving has recently become a popular research topic. Existing solvers often overlook puzzles with missing pieces. The missing pieces, together with gaps between pieces, pose significant challenges, amplified by a large solution space. To tackle the challenges, we propose Co-Evolutionary Agents for Reassembling and Inpainting (CEARI), one agent to inpaint missing contents and the other to reassemble the puzzle, with a shared perception network to perceive the puzzle status. The reassembly agent utilizes an evolutionary algorithm to explore the large solution space, to discover a sequence of fragment-swapping actions to efficiently reassemble the puzzle, while the inpainting agent evolves from using a local outpainting network at the early stage to using a global inpainting network at the latter stage. Furthermore, a co-evolutionary training paradigm is designed to iteratively evolve the two agents in a coherent and collaborative manner, improving reassembly accuracy and inpainting quality simultaneously. Experimental results on three datasets show that CEARI largely outperforms state-of-the-art methods in terms of both reassembly accuracy and inpainting quality.

The shift towards transportation electrification, marked by the rising use of electric vehicles (EVs) and the development of fast charging stations (FCS), plays a crucial role in transport decarbonization initiatives. To optimize the rollout of FCS and set appropriate charging service fees (CSF)-a process referred to as the coupled FCS multi-stage bi-level operation problem (FCS-MBOP)-is essential for improving both investment and operational efficiency within the integrated power distribution and transportation network (CPTN). For operators, it's not only necessary to adapt to short-term fluctuations within the environment but also to swiftly respond to changes in the FCS layout resulting from various long-term investment decisions. To address this complexity, we introduce a dual-timescale evolutionary assist deep reinforcement learning framework, which includes two specialized agents with distinct functions: an investment agent (planner) and an operational agent (operator). The planner focuses on annual investments, evolving long-term strategies that weigh social benefits against investment costs through the use of a genetic algorithm (GA). In contrast, the operator acts on an hourly basis, fine-tuning CSF to alleviate traffic congestion and minimize the social costs, while taking into account the planner's feasible investment decisions. Leveraging the integrated capabilities of a graph neural network (GNN), long-short-term memory (LSTM), and attention mechanisms, our framework's agents are adept at extracting both temporal and spatial features and facilitating the transfer of experiences across different investment stages. Empirical evidence underscores the effectiveness of our approach, showcasing its ability to surpass conventional methodologies in delivering high-quality solutions.

Portfolio optimization is a strategic approach aiming at achieving an optimal balance between risk and returns through the judicious allocation of limited capital across various assets. In recent years, there has been a growing interest in leveraging Deep Reinforcement Learning (DRL) to tackle the complexities of portfolio optimization. Despite its potential, a notable limitation of DRL algorithms is their inherent difficulty in integrating conflicted objectives with the reward functions throughout the learning process. Typically, DRL's reward function prioritizes the maximization of returns or other performance indicators, often overlooking the integration of risk aspects. Furthermore, the standard DRL framework struggles to incorporate practical constraints, such as cardinality and bounding, into the decision process. Without these constraints, the investment strategies developed might be unrealistic and unmanageable. To this end, in this paper, we propose an adaptive and safe DRL framework, which can dynamically optimize the portfolio weights while strictly respecting practical constraints. In our method, any infeasible action (i.e., one that violates the constraints) decided by the RL agent will be mapped to a feasible region using a safety layer. The extended Markowitz Mean-Variance (M-V) model is explicitly encoded in the safety layer to ensure the feasibility of the actions from the alternative views. In addition, we utilize Projection-based Interior-point Policy Optimization (IPO) to resolve multiple objectives and constraints in the examined problem. Extensive results on real-world datasets show that our method is effective in strictly respecting constraints under dynamic market environments, in contrast to prevailing data- driven trading strategies and conventional model-based static solutions.

Abstract A domain-theoretic framework is presented for validated robustness analysis of neural networks. First, global robustness of a general class of networks is analyzed. Then, using the fact that Edalat’s domain-theoretic L -derivative coincides with Clarke’s generalized gradient, the framework is extended for attack-agnostic local robustness analysis. The proposed framework is ideal for designing algorithms which are correct by construction. This claim is exemplified by developing a validated algorithm for estimation of Lipschitz constant of feedforward regressors. The completeness of the algorithm is proved over differentiable networks and also over general position ${\mathrm{ReLU}}$ networks. Computability results are obtained within the framework of effectively given domains. Using the proposed domain model, differentiable and non-differentiable networks can be analyzed uniformly. The validated algorithm is implemented using arbitrary-precision interval arithmetic, and the results of some experiments are presented. The software implementation is truly validated, as it handles floating-point errors as well.

We construct a continuous domain, as a model of interval analysis, for temporal discretization of differential equations. By using this domain, and the domain of Lipschitz maps, we formulate a generalization of the Euler operator, which exhibits second-order convergence. We prove computability of the operator within the framework of effectively given domains. The operator only requires the vector field of the differential equation to be Lipschitz continuous, in contrast to the related operators in the literature which require the vector field to be at least continuously differentiable. Within the same framework, we also analyze temporal discretization and computability of another variant of the Euler operator formulated according to Runge-Kutta theory. We prove that, compared with this variant, the second-order operator that we formulate directly, not only imposes weaker assumptions on the vector field, but also exhibits superior convergence rate. We implement the first-order, second-order, and Runge-Kutta Euler operators using arbitrary-precision interval arithmetic, and report on some experiments. The experiments confirm our theoretical results. In particular, we observe the superior convergence rate of our second-order operator compared with the Runge-Kutta Euler and the common (first-order) Euler operators.