This paper proposes a bidirectional rapidly-exploring random trees (RRT) algorithm to solve the motion planning problem for hybrid systems. The proposed algorithm, called HyRRT-Connect, propagates in both forward and backward directions in hybrid time until an overlap between the forward and backward propagation results is detected. Then, HyRRT-Connect constructs a motion plan through the reversal and concatenation of functions defined on hybrid time domains, ensuring the motion plan thoroughly satisfies the given hybrid dynamics. To address the potential discontinuity along the flow caused by tolerating some distance between the forward and backward partial motion plans, we reconstruct the backward partial motion plan by a forward-in-hybrid-time simulation from the final state of the forward partial motion plan. By applying the reversed input of the backward partial motion plan, the reconstruction process effectively eliminates the discontinuity and ensures that as the tolerance distance decreases to zero, the distance between the endpoint of the reconstructed motion plan and the final state set approaches zero. The proposed algorithm is applied to an actuated bouncing ball example and a walking robot example so as to highlight its generality and computational improvement.

An exciting frontier in robotic manipulation is the use of multiple arms at once. However, planning concurrent motions is a challenging task using current methods. The high-dimensional composite state space renders many well-known motion planning algorithms intractable. Recently, Multi-Agent Path-Finding (MAPF) algorithms have shown promise in discrete 2D domains, providing rigorous guarantees. However, widely used conflict-based methods in MAPF assume an efficient single-agent motion planner. This poses challenges in adapting them to manipulation cases where this assumption does not hold, due to the high dimensionality of configuration spaces and the computational bottlenecks associated with collision checking. To this end, we propose an approach for accelerating conflict-based search algorithms by leveraging their repetitive and incremental nature -- making them tractable for use in complex scenarios involving multi-arm coordination in obstacle-laden environments. We show that our method preserves completeness and bounded sub-optimality guarantees, and demonstrate its practical efficacy through a set of experiments with up to 10 robotic arms.

Generative Adversarial Networks (GANs) have shown great success in generating high quality images and are thus used as one of the main approaches to generate art images. However, usually the image generation process involves sampling from the latent space of the learned art representations, allowing little control over the output. In this work, we first employ GANs that are trained to produce creative images using an architecture known as Creative Adversarial Networks (CANs), then, we employ an evolutionary approach to navigate within the latent space of the models to discover images. We use automatic aesthetic and collaborative interactive human evaluation metrics to assess the generated images. In the human interactive evaluation case, we propose a collaborative evaluation based on the assessments of several participants. Furthermore, we also experiment with an intelligent mutation operator that aims to improve the quality of the images through local search based on an aesthetic measure. We evaluate the effectiveness of this approach by comparing the results produced by the automatic and collaborative interactive evolution. The results show that the proposed approach can generate highly attractive art images when the evolution is guided by collaborative human feedback.

Fully-observable non-deterministic (FOND) planning is at the core of artificial intelligence planning with uncertainty. It models uncertainty through actions with non-deterministic effects. A* with Non-Determinism (AND*) (Messa and Pereira, 2023) is a FOND planner that generalizes A* (Hart et al., 1968) for FOND planning. It searches for a solution policy by performing an explicit heuristic search on the policy space of the FOND task. In this paper, we study and improve the performance of the policy-space search performed by AND*. We present a polynomial-time procedure that constructs a solution policy given just the set of states that should be mapped. This procedure, together with a better understanding of the structure of FOND policies, allows us to present three concepts of equivalences between policies. We use policy equivalences to prune part of the policy search space, making AND* substantially more effective in solving FOND tasks. We also study the impact of taking into account structural state-space symmetries to strengthen the detection of equivalence policies and the impact of performing the search with satisficing techniques. We apply a recent technique from the group theory literature to better compute structural state-space symmetries. Finally, we present a solution compressor that, given a policy defined over complete states, finds a policy that unambiguously represents it using the minimum number of partial states. AND* with the introduced techniques generates, on average, two orders of magnitude fewer policies to solve FOND tasks. These techniques allow explicit policy-space search to be competitive in terms of both coverage and solution compactness with other state-of-the-art FOND planners.

Language models have demonstrated impressive ability in context understanding and generative performance. Inspired by the recent success of language foundation models, in this paper, we propose LMTraj (Language-based Multimodal Trajectory predictor), which recasts the trajectory prediction task into a sort of question-answering problem. Departing from traditional numerical regression models, which treat the trajectory coordinate sequence as continuous signals, we consider them as discrete signals like text prompts. Specially, we first transform an input space for the trajectory coordinate into the natural language space. Here, the entire time-series trajectories of pedestrians are converted into a text prompt, and scene images are described as text information through image captioning. The transformed numerical and image data are then wrapped into the question-answering template for use in a language model. Next, to guide the language model in understanding and reasoning high-level knowledge, such as scene context and social relationships between pedestrians, we introduce an auxiliary multi-task question and answering. We then train a numerical tokenizer with the prompt data. We encourage the tokenizer to separate the integer and decimal parts well, and leverage it to capture correlations between the consecutive numbers in the language model. Lastly, we train the language model using the numerical tokenizer and all of the question-answer prompts. Here, we propose a beam-search-based most-likely prediction and a temperature-based multimodal prediction to implement both deterministic and stochastic inferences. Applying our LMTraj, we show that the language-based model can be a powerful pedestrian trajectory predictor, and outperforms existing numerical-based predictor methods. Code is publicly available at https://github.com/inhwanbae/LMTrajectory .

Mitigating the disparate impact of statistical machine learning methods is crucial for ensuring fairness. While extensive research aims to reduce disparity, the effect of using a \emph{finite dataset} -- as opposed to the entire population -- remains unclear. This paper explores the statistical foundations of fair binary classification with two protected groups, focusing on controlling demographic disparity, defined as the difference in acceptance rates between the groups. Although fairness may come at the cost of accuracy even with infinite data, we show that using a finite sample incurs additional costs due to the need to estimate group-specific acceptance thresholds. We study the minimax optimal classification error while constraining demographic disparity to a user-specified threshold. To quantify the impact of fairness constraints, we introduce a novel measure called \emph{fairness-aware excess risk} and derive a minimax lower bound on this measure that all classifiers must satisfy. Furthermore, we propose FairBayes-DDP+, a group-wise thresholding method with an offset that we show attains the minimax lower bound. Our lower bound proofs involve several innovations. Experiments support that FairBayes-DDP+ controls disparity at the user-specified level, while being faster and having a more favorable fairness-accuracy tradeoff than several baselines.

This work focuses on developing an effective meta-heuristic approach to protect against simultaneous attacks on nodes of a network modeled using a graph. Specifically, we focus on the $k$-strong Roman domination problem, a generalization of the well-known Roman domination problem on graphs. This general problem is about assigning integer weights to nodes that represent the number of field armies stationed at each node in order to satisfy the protection constraints while minimizing the total weights. These constraints concern the protection of a graph against any simultaneous attack consisting of $k \in \mathbb{N}$ nodes. An attack is considered repelled if each node labeled 0 can be defended by borrowing an army from one of its neighboring nodes, ensuring that the neighbor retains at least one army for self-defense. The $k$-SRD problem has practical applications in various areas, such as developing counter-terrorism strategies or managing supply chain disruptions. The solution to this problem is notoriously difficult to find, as even checking the feasibility of the proposed solution requires an exponential number of steps. We propose a variable neighborhood search algorithm in which the feasibility of the solution is checked by introducing the concept of quasi-feasibility, which is realized by careful sampling within the set of all possible attacks. Extensive experimental evaluations show the scalability and robustness of the proposed approach compared to the two exact approaches from the literature. Experiments are conducted with random networks from the literature and newly introduced random wireless networks as well as with real-world networks. A practical application scenario, using real-world networks, involves applying our approach to graphs extracted from GeoJSON files containing geographic features of hundreds of cities or larger regions.

Temporal Graph Neural Networks (TGNNs), crucial for modeling dynamic graphs with time-varying interactions, face a significant challenge in explainability due to their complex model structure. Counterfactual explanations, crucial for understanding model decisions, examine how input graph changes affect outcomes. This paper introduces two novel counterfactual explanation methods for TGNNs: GreeDy (Greedy Explainer for Dynamic Graphs) and CoDy (Counterfactual Explainer for Dynamic Graphs). They treat explanations as a search problem, seeking input graph alterations that alter model predictions. GreeDy uses a simple, greedy approach, while CoDy employs a sophisticated Monte Carlo Tree Search algorithm. Experiments show both methods effectively generate clear explanations. Notably, CoDy outperforms GreeDy and existing factual methods, with up to 59\% higher success rate in finding significant counterfactual inputs. This highlights CoDy's potential in clarifying TGNN decision-making, increasing their transparency and trustworthiness in practice.

Recently, a simple but powerful language for expressing and learning general policies and problem decompositions (sketches) has been introduced in terms of rules defined over a set of Boolean and numerical features. In this work, we consider three extensions of this language aimed at making policies and sketches more flexible and reusable: internal memory states, as in finite state controllers; indexical features, whose values are a function of the state and a number of internal registers that can be loaded with objects; and modules that wrap up policies and sketches and allow them to call each other by passing parameters. In addition, unlike general policies that select state transitions rather than ground actions, the new language allows for the selection of such actions. The expressive power of the resulting language for policies and sketches is illustrated through a number of examples.

Team Coordination on Graphs with Risky Edges (TCGRE) is a recently emerged problem, in which a robot team collectively reduces graph traversal cost through support from one robot to another when the latter traverses a risky edge. Resembling the traditional Multi-Agent Path Finding (MAPF) problem, both classical and learning-based methods have been proposed to solve TCGRE, however, they lacked either computation efficiency or optimality assurance. In this paper, we reformulate TCGRE as a constrained optimization and perform rigorous mathematical analysis. Our theoretical analysis shows the NP-hardness of TCGRE by reduction from the Maximum 3D Matching problem and that efficient decomposition is a key to tackle this combinatorial optimization problem. Further more, we design three classes of algorithms to solve TCGRE, i.e., Joint State Graph (JSG) based, coordination based, and receding-horizon sub-team based solutions. Each of these proposed algorithms enjoy different provable optimality and efficiency characteristics that are demonstrated in our extensive experiments.