Lane detection is a fundamental task in autonomous driving. While the problem is typically formulated as the detection of continuous boundaries, we study the problem of detecting lane boundaries that are sparsely marked by 2D points with many false positives. This problem arises in the Formula Student Driverless (FSD) competition and is challenging due to its inherent ambiguity. Previous methods are inefficient and unable to find long-horizon solutions. We propose a deterministic algorithm called CLC that uses backtracking graph search with a learned likelihood function to overcome these limitations. We impose geometric constraints on the lane candidates to guarantee a geometrically sound lane. Our exhaustive search leads to finding the global optimum in 45% of instances, and the algorithm is overall robust to up to 50% false positives. Our algorithm runs in less than 15 ms on a single CPU core, meeting the low latency requirements of autonomous racing. We extensively evaluate our method on real data and realistic racetrack layouts, and show that it outperforms the state-of-the-art by detecting long lanes over 100 m with few (0.6%) critical failures. This allows our autonomous racecar to drive close to its physical limits on a previously unknown racetrack without being limited by perception. We release our dataset with realistic Formula Student racetracks to enable further research.

This paper considers the distributed convex-concave minimax optimization under the second-order similarity. We propose stochastic variance-reduced optimistic gradient sliding (SVOGS) method, which takes the advantage of the finite-sum structure in the objective by involving the mini-batch client sampling and variance reduction. We prove SVOGS can achieve the $\varepsilon$-duality gap within communication rounds of ${\mathcal O}(\delta D^2/\varepsilon)$, communication complexity of ${\mathcal O}(n+\sqrt{n}\delta D^2/\varepsilon)$, and local gradient calls of $\tilde{\mathcal O}(n+(\sqrt{n}\delta+L)D^2/\varepsilon\log(1/\varepsilon))$, where $n$ is the number of nodes, $\delta$ is the degree of the second-order similarity, $L$ is the smoothness parameter and $D$ is the diameter of the constraint set. We can verify that all of above complexity (nearly) matches the corresponding lower bounds. For the specific $\mu$-strongly-convex-$\mu$-strongly-convex case, our algorithm has the upper bounds on communication rounds, communication complexity, and local gradient calls of $\mathcal O(\delta/\mu\log(1/\varepsilon))$, ${\mathcal O}((n+\sqrt{n}\delta/\mu)\log(1/\varepsilon))$, and $\tilde{\mathcal O}(n+(\sqrt{n}\delta+L)/\mu)\log(1/\varepsilon))$ respectively, which are also nearly tight. Furthermore, we conduct the numerical experiments to show the empirical advantages of proposed method.

Network interdiction problems are combinatorial optimization problems involving two players: one aims to solve an optimization problem on a network, while the other seeks to modify the network to thwart the first player's objectives. Such problems typically emerge in an attacker-defender context, encompassing areas such as military operations, disease spread analysis, and communication network management. The primary bottleneck in network interdiction arises from the high time complexity of using conventional exact solvers and the challenges associated with devising efficient heuristic solvers. GNNs, recognized as a cutting-edge methodology, have shown significant effectiveness in addressing single-level CO problems on graphs, such as the traveling salesman problem, graph matching, and graph edit distance. Nevertheless, network interdiction presents a bi-level optimization challenge, which current GNNs find difficult to manage. To address this gap, we represent network interdiction problems as Mixed-Integer Linear Programming (MILP) instances, then apply a multipartite GNN with sufficient representational capacity to learn these formulations. This approach ensures that our neural network is more compatible with the mathematical algorithms designed to solve network interdiction problems, resulting in improved generalization. Through two distinct tasks, we demonstrate that our proposed method outperforms theoretical baseline models and provides advantages over traditional exact solvers.

It's a puzzle that can keep most people entertained for hours. But the Rubik's Cube is light work for one robot, which has officially broken the Guinness World Record for the fastest robot to solve a rotating puzzle cube. The bot can complete the puzzle in just 0.305 seconds - so it's safe to say that if you blink, you'll miss it! That's around 10 times faster than the quickest human, who is able to solve the puzzle in an impressive 3.13 seconds. It's a puzzle that can keep most people entertained for hours. But the Rubik's Cube is light work for one robot, which has officially broken the Guinness World Record for the fastest robot to solve a rotating puzzle cube The'fastest robot to solve a rotating puzzle cube' record has been popular for years.

As the trend of moving away from high-precision maps gradually emerges in the autonomous driving industry,traditional planning algorithms are gradually exposing some problems. To address the high real-time, high precision, and high trajectory quality requirements posed by the automatic parking task under real-time perceived local maps,this paper proposes an improved automatic parking planning algorithm based on the A* algorithm, and uses Model Predictive Control (MPC) as the control module for automatic parking.The algorithm enhances the planning real-time performance by optimizing heuristic functions, binary heap optimization, and bidirectional search; it calculates the passability of narrow areas by dynamically loading obstacles and introduces the vehicle's own volume during planning; it improves trajectory quality by using neighborhood expansion and Bezier curve optimization methods to meet the high trajectory quality requirements of the parking task. After obtaining the output results of the planning algorithm, a loss function is designed according to the characteristics of the automatic parking task under local maps, and the MPC algorithm is used to output control commands to drive the car along the planned trajectory. This paper uses the perception results of real driving environments converted into maps as planning inputs to conduct simulation tests and ablation experiments on the algorithm. Experimental results show that the improved algorithm proposed in this paper can effectively meet the special requirements of automatic parking under local maps and complete the automatic parking planning and control tasks.

Automated Valet Parking (AVP) is a crucial component of advanced autonomous driving systems, focusing on the endpoint task within the "human-vehicle interaction" process to tackle the challenges of the "last mile".The perception module of the automated parking algorithm has evolved from local perception using ultrasonic radar and global scenario precise map matching for localization to a high-level map-free Birds Eye View (BEV) perception solution.The BEV scene places higher demands on the real-time performance and safety of automated parking planning tasks. This paper proposes an improved automated parking algorithm based on the A* algorithm, integrating vehicle kinematic models, heuristic function optimization, bidirectional search, and Bezier curve optimization to enhance the computational speed and real-time capabilities of the planning algorithm.Numerical optimization methods are employed to generate the final parking trajectory, ensuring the safety of the parking path. The proposed approach is experimentally validated in the commonly used industrial CARLA-ROS joint simulation environment. Compared to traditional algorithms, this approach demonstrates reduced computation time with more challenging collision-risk test cases and improved performance in comfort metrics.

Local Bayesian optimization is a promising practical approach to solve the high dimensional black-box function optimization problem. Among them is the approximated gradient class of methods, which implements a strategy similar to gradient descent. These methods have achieved good experimental results and theoretical guarantees. However, given the distributional properties of the Gaussian processes applied on these methods, there may be potential to further exploit the information of the Gaussian processes to facilitate the BO search. In this work, we develop the relationship between the steps of the gradient descent method and one that minimizes the Upper Confidence Bound (UCB), and show that the latter can be a better strategy than direct gradient descent when a Gaussian process is applied as a surrogate. Through this insight, we propose a new local Bayesian optimization algorithm, MinUCB, which replaces the gradient descent step with minimizing UCB in GIBO. We further show that MinUCB maintains a similar convergence rate with GIBO. We then improve the acquisition function of MinUCB further through a look ahead strategy, and obtain a more efficient algorithm LA-MinUCB. We apply our algorithms on different synthetic and real-world functions, and the results show the effectiveness of our method. Our algorithms also illustrate improvements on local search strategies from an upper bound perspective in Bayesian optimization, and provides a new direction for future algorithm design.

The multidimensional knapsack problem (MKP) is an NP-hard combinatorial optimization problem whose solution is determining a subset of maximum total profit items that do not violate capacity constraints. Due to its hardness, large-scale MKP instances are usually a target for metaheuristics, a context in which effective feasibility maintenance strategies are crucial. In 1998, Chu and Beasley proposed an effective heuristic repair that is still relevant for recent metaheuristics. However, due to its deterministic nature, the diversity of solutions such heuristic provides is insufficient for long runs. As a result, the search for new solutions ceases after a while. This paper proposes an efficiency-based randomization strategy for the heuristic repair that increases the variability of the repaired solutions without deteriorating quality and improves the overall results.

In this paper, we introduce a local search algorithm for hierarchical clustering. For the local step, we consider a tree re-arrangement operation, known as the {\em interchange}, which involves swapping two closely positioned sub-trees within a tree hierarchy. The interchange operation has been previously used in the context of phylogenetic trees. As the objective function for evaluating the resulting hierarchies, we utilize the revenue function proposed by Moseley and Wang (NIPS 2017.) In our main result, we show that any locally optimal tree guarantees a revenue of at least $\frac{n-2}{3}\sum_{i < j}w(i,j)$ where is $n$ the number of objects and $w: [n] \times [n] \rightarrow \mathbb{R}^+$ is the associated similarity function. This finding echoes the previously established bound for the average link algorithm as analyzed by Moseley and Wang. We demonstrate that this alignment is not coincidental, as the average link trees enjoy the property of being locally optimal with respect to the interchange operation. Consequently, our study provides an alternative insight into the average link algorithm and reveals the existence of a broader range of hierarchies with relatively high revenue achievable through a straightforward local search algorithm. Furthermore, we present an implementation of the local search framework, where each local step requires $O(n)$ computation time. Our empirical results indicate that the proposed method, used as post-processing step, can effectively generate a hierarchical clustering with substantial revenue.

Large Language Models (LLMs) can generate useful code, but often the code they generate cannot be trusted to be sound. In this paper, we present VerMCTS, an approach to begin to resolve this issue by generating verified programs in Dafny and Coq. VerMCTS uses a logical verifier in concert with an LLM to guide a modified Monte Carlo Tree Search (MCTS). This approach leverages the verifier to gain intermediate feedback inside the search algorithm by checking partial programs at each step to estimate an upper bound on the value function. To measure the performance of VerMCTS, we develop a new suite of multi-step verified programming problems in Dafny and Coq. In terms of pass@T, a new metric which computes the pass rate given a budget of T tokens sampled from the LLM, VerMCTS leads to more than a 30% absolute increase in average pass@5000 across the suite over repeated sampling from the base language model.