Solving jigsaw puzzles has been extensively studied. While most existing models focus on solving either small-scale puzzles or puzzles with no gap between fragments, solving large-scale puzzles with gaps presents distinctive challenges in both image understanding and combinatorial optimization. To tackle these challenges, we propose a framework of Evolutionary Reinforcement Learning with Multi-head Puzzle Perception (ERL-MPP) to derive a better set of swapping actions for solving the puzzles. Specifically, to tackle the challenges of perceiving the puzzle with gaps, a Multi-head Puzzle Perception Network (MPPN) with a shared encoder is designed, where multiple puzzlet heads comprehensively perceive the local assembly status, and a discriminator head provides a global assessment of the puzzle. To explore the large swapping action space efficiently, an Evolutionary Reinforcement Learning (EvoRL) agent is designed, where an actor recommends a set of suitable swapping actions from a large action space based on the perceived puzzle status, a critic updates the actor using the estimated rewards and the puzzle status, and an evaluator coupled with evolutionary strategies evolves the actions aligning with the historical assembly experience. The proposed ERL-MPP is comprehensively evaluated on the JPLEG-5 dataset with large gaps and the MIT dataset with large-scale puzzles. It significantly outperforms all state-of-the-art models on both datasets.

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.

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.

Jigsaw puzzle solving has recently become an emerging research area. The developed techniques have been widely used in applications beyond puzzle solving. This paper focuses on solving Jigsaw Puzzles with Large Eroded Gaps (JPwLEG). We formulate the puzzle reassembly as a combinatorial optimization problem and propose a Siamese-Discriminant Deep Reinforcement Learning (SD2RL) to solve it. A Deep Q-network (DQN) is designed to visually understand the puzzles, which consists of two sets of Siamese Discriminant Networks, one set to perceive the pairwise relations between vertical neighbors and another set for horizontal neighbors. The proposed DQN considers not only the evidence from the incumbent fragment but also the support from its four neighbors. The DQN is trained using replay experience with carefully designed rewards to guide the search for a sequence of fragment swaps to reach the correct puzzle solution. Two JPwLEG datasets are constructed to evaluate the proposed method, and the experimental results show that the proposed SD2RL significantly outperforms state-of-the-art methods.

Solving Jigsaw puzzles has recently become an emerging research topic. Traditionally, boundary similarities are utilized for puzzle reassembly. In this paper, we solve Jigsaw Puzzles of Large Eroded Gaps (JPLEG), where boundary similarities are weak and image semantics are the only feasible clues. Inspired by human strategy in solving a puzzle, we introduce the concept of puzzlet, where fragments are gradually combined to form puzzlets of different sizes until the completion of the puzzle. Two sets of Puzzlet Discriminant Networks are designed to visually perceive whether these puzzlets are correctly reassembled. The puzzle reassembly is then formulated as a combinatorial optimization problem, and solved using a genetic algorithm. The proposed method is evaluated on two large datasets, which shows that it significantly outperforms the state-of-the-art methods for puzzle solving.