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Search and recommendation systems are essential in many services, and they are often developed separately, leading to complex maintenance and technical debt. In this paper, we present a unified deep learning model that efficiently handles key aspects of both tasks., Comment: 3 pages, 1 figure

Human-aware navigation is a complex task for mobile robots, requiring an autonomous navigation system capable of achieving efficient path planning together with socially compliant behaviors. Social planners usually add costs or constraints to the objective function, leading to intricate tuning processes or tailoring the solution to the specific social scenario. Machine Learning can enhance planners' versatility and help them learn complex social behaviors from data. This work proposes an adaptive social planner, using a Deep Reinforcement Learning agent to dynamically adjust the weighting parameters of the cost function used to evaluate trajectories. The resulting planner combines the robustness of the classic Dynamic Window Approach, integrated with a social cost based on the Social Force Model, and the flexibility of learning methods to boost the overall performance on social navigation tasks. Our extensive experimentation on different environments demonstrates the general advantage of the proposed method over static cost planners.

Motivated by applications to matrix multiplication algorithms, Pratt asked (ITCS'24) how large a subset of $[n] \times [n]$ could be without containing a skew-corner: three points $(x,y), (x,y+h),(x+h,y')$ with $h \ne 0$. We prove any skew corner-free set has size at most $\exp(-\Omega(\log^{1/12} n))\cdot n^2$, nearly matching the best known lower bound of $\exp(-O(\sqrt{\log n}))\cdot n^2$ by Beker (arXiv'24). Our techniques generalize those of Kelley and Meka's recent breakthrough on three-term arithmetic progression (FOCS'23), answering a question of Beker (arXiv'24). We note that a similar bound was obtained concurrently and independently by Mili\'cevi\'c (arXiv'24)., Comment: 23 pages, comments welcome

Autonomous navigation is the foundation of agricultural robots. This paper focuses on developing an advanced autonomous navigation system for a rover operating within row-based crops. A position-agnostic system is proposed to address the challenging situation when standard localization methods, like GPS, fail due to unfavorable weather or obstructed signals. This breakthrough is especially vital in densely vegetated regions, including areas covered by thick tree canopies or pergola vineyards. This work proposed a novel system that leverages a single RGB-D camera and a Non-linear Model Predictive Control strategy to navigate through entire rows, adapting to various crop spacing. The presented solution demonstrates versatility in handling diverse crop densities, environmental factors, and multiple navigation tasks to support agricultural activities at an extremely cost-effective implementation. Experimental validation in simulated and real vineyards underscores the system's robustness and competitiveness in both standard row traversal and target objects approach.

Segmentation-based autonomous navigation has recently been presented as an appealing approach to guiding robotic platforms through crop rows without requiring perfect GPS localization. Nevertheless, current techniques are restricted to situations where the distinct separation between the plants and the sky allows for the identification of the row's center. However, tall, dense vegetation, such as high tree rows and orchards, is the primary cause of GPS signal blockage. In this study, we increase the overall robustness and adaptability of the control algorithm by extending the segmentation-based robotic guiding to those cases where canopies and branches occlude the sky and prevent the utilization of GPS and earlier approaches. An efficient Deep Neural Network architecture has been used to address semantic segmentation, performing the training with synthetic data only. Numerous vineyards and tree fields have undergone extensive testing in both simulation and real-world to show the solution's competitive benefits., Comment: arXiv admin note: text overlap with arXiv:2304.08988

Spurred by the influential work of Viola (Journal of Computing 2012), the past decade has witnessed an active line of research into the complexity of (approximately) sampling distributions, in contrast to the traditional focus on the complexity of computing functions. We build upon and make explicit earlier implicit results of Viola to provide superconstant lower bounds on the locality of Boolean functions approximately sampling the uniform distribution over binary strings of particular Hamming weights, both exactly and modulo an integer, answering questions of Viola (Journal of Computing 2012) and Filmus, Leigh, Riazanov, and Sokolov (RANDOM 2023). Applications to data structure lower bounds and quantum-classical separations are discussed., Comment: Minor updates to better reflect past literature. No technical material has been changed

The log-rank conjecture, a longstanding problem in communication complexity, has persistently eluded resolution for decades. Consequently, some recent efforts have focused on potential approaches for establishing the conjecture in the special case of XOR functions, where the communication matrix is lifted from a boolean function, and the rank of the matrix equals the Fourier sparsity of the function, which is the number of its nonzero Fourier coefficients. In this note, we refute two conjectures. The first has origins in Montanaro and Osborne (arXiv'09) and is considered in Tsang et al. (FOCS'13), and the second one is due to Mande and Sanyal (FSTTCS'20). These conjectures were proposed in order to improve the best-known bound of Lovett (STOC'14) regarding the log-rank conjecture in the special case of XOR functions. Both conjectures speculate that the set of nonzero Fourier coefficients of the boolean function has some strong additive structure. We refute these conjectures by constructing two specific boolean functions tailored to each., Comment: Added additional background and intuition

Efficiently counting or detecting defective items is a crucial task in various fields ranging from biological testing to quality control to streaming algorithms. The \emph{group testing estimation problem} concerns estimating the number of defective elements $d$ in a collection of $n$ total within a given factor. We primarily consider the classical query model, in which a query reveals whether the selected group of elements contains a defective one. We show that any non-adaptive randomized algorithm that estimates the value of $d$ within a constant factor requires $\Omega(\log n)$ queries. This confirms that a known $O(\log n)$ upper bound by Bshouty (2019) is tight and resolves a conjecture by Damaschke and Sheikh Muhammad (2010). Additionally, we prove similar matching upper and lower bounds in the threshold query model., Comment: This work is a merger of arXiv:2309.09613 and arXiv:2309.10286

Service robotics is recently enhancing precision agriculture enabling many automated processes based on efficient autonomous navigation solutions. However, data generation and infield validation campaigns hinder the progress of large-scale autonomous platforms. Simulated environments and deep visual perception are spreading as successful tools to speed up the development of robust navigation with low-cost RGB-D cameras. In this context, the contribution of this work is twofold: a synthetic dataset to train deep semantic segmentation networks together with a collection of virtual scenarios for a fast evaluation of navigation algorithms. Moreover, an automatic parametric approach is developed to explore different field geometries and features. The simulation framework and the dataset have been evaluated by training a deep segmentation network on different crops and benchmarking the resulting navigation., Comment: Accepted at the 14th European Conference on Precision Agriculture (ECPA) 2023

Segmentation-based autonomous navigation has recently been proposed as a promising methodology to guide robotic platforms through crop rows without requiring precise GPS localization. However, existing methods are limited to scenarios where the centre of the row can be identified thanks to the sharp distinction between the plants and the sky. However, GPS signal obstruction mainly occurs in the case of tall, dense vegetation, such as high tree rows and orchards. In this work, we extend the segmentation-based robotic guidance to those scenarios where canopies and branches occlude the sky and hinder the usage of GPS and previous methods, increasing the overall robustness and adaptability of the control algorithm. Extensive experimentation on several realistic simulated tree fields and vineyards demonstrates the competitive advantages of the proposed solution.

Liu, Hong, Gu, and Lai proved if the second largest eigenvalue of the adjacency matrix of graph $G$ with minimum degree $\delta \ge 2m+2 \ge 4$ satisfies $\lambda_2(G) < \delta - \frac{2m+1}{\delta+1}$, then $G$ contains at least $m+1$ edge-disjoint spanning trees, which verified a generalization of a conjecture by Cioab\u{a} and Wong. We show this bound is essentially the best possible by constructing $d$-regular graphs $\mathcal{G}_{m,d}$ for all $d \ge 2m+2 \ge 4$ with at most $m$ edge-disjoint spanning trees and $\lambda_2(\mathcal{G}_{m,d}) < d-\frac{2m+1}{d+3}$. As a corollary, we show that a spectral inequality on graph rigidity by Cioab\u{a}, Dewar, and Gu is essentially tight., Comment: 13 pages, 2 figures

The design of revenue-maximizing auctions with strong incentive guarantees is a core concern of economic theory. Computational auctions enable online advertising, sourcing, spectrum allocation, and myriad financial markets. Analytic progress in this space is notoriously difficult; since Myerson's 1981 work characterizing single-item optimal auctions, there has been limited progress outside of restricted settings. A recent paper by D\"utting et al. circumvents analytic difficulties by applying deep learning techniques to, instead, approximate optimal auctions. In parallel, new research from Ilvento et al. and other groups has developed notions of fairness in the context of auction design. Inspired by these advances, in this paper, we extend techniques for approximating auctions using deep learning to address concerns of fairness while maintaining high revenue and strong incentive guarantees.

The \textit{toughness} $t(G)$ of a graph $G$ is a measure of its connectivity that is closely related to Hamiltonicity. Brouwer proved the lower bound $t(G) > \ell / \lambda - 2$ on the toughness of any connected $\ell$-regular graph, where $ \lambda$ is the largest nontrivial eigenvalue of the adjacency matrix. He conjectured that this lower bound can be improved to $\ell / \lambda-1$ and this conjecture is still open. Brouwer also observed that many families of graphs (in particular, those achieving equality in the Hoffman ratio bound for the independence number) have toughness exactly $\ell / \lambda$. Cioab\u{a} and Wong confirmed Brouwer's observation for several families of graphs, including Kneser graphs $K(n,2)$ and their complements, with the exception of the Petersen graph $K(5,2)$. In this paper, we extend these results and determine the toughness of Kneser graphs $K(n,k)$ when $k\in \{3,4\}$ and $n\geq 2k+1$ as well as for $k\geq 5$ and sufficiently large $n$ (in terms of $k$). In all these cases, the toughness is attained by the complement of a maximum independent set and we conjecture that this is the case for any $k\geq 5$ and $n\geq 2k+1$., Comment: 17 pages

Learning-to-Rank (LTR) models trained from implicit feedback (e.g. clicks) suffer from inherent biases. A well-known one is the position bias -- documents in top positions are more likely to receive clicks due in part to their position advantages. To unbiasedly learn to rank, existing counterfactual frameworks first estimate the propensity (probability) of missing clicks with intervention data from a small portion of search traffic, and then use inverse propensity score (IPS) to debias LTR algorithms on the whole data set. These approaches often assume the propensity only depends on the position of the document, which may cause high estimation variance in applications where the search context (e.g. query, user) varies frequently. While context-dependent propensity models reduce variance, accurate estimations may require randomization or intervention on a large amount of traffic, which may not be realistic in real-world systems, especially for long tail queries. In this work, we employ heterogeneous treatment effect estimation techniques to estimate position bias when intervention click data is limited. We then use such estimations to debias the observed click distribution and re-draw a new de-biased data set, which can be used for any LTR algorithms. We conduct simulations with varying experiment conditions and show the effectiveness of the proposed method in regimes with long tail queries and sparse clicks., Comment: 9 pages; to be published in SIGIR eCom'20