"how come leverage score initialization gives no improvement on the bounds of Theorem 3.6 and 3.7..." Thank you for the comment. The reason is that both bounds in Theorem 3.6, 3.7 come from two parts: 1) "presentation need to improve..more discussion..." Thank you for the advice. "undefined notations and typos" RE: Thank you for pointing out. We will address these issues in the final version. "no experiments are provided in this paper ..." Thank you for the comment.

-- This paper presents a novel robust online calibration framework for Ultra-Wideband (UWB) anchors in UWB-aided Visual-Inertial Navigation Systems (VINS). Accurate anchor positioning, a process known as calibration, is crucial for integrating UWB ranging measurements into state estimation. While several prior works have demonstrated satisfactory results by using robot-aided systems to autonomously calibrate UWB systems, there are still some limitations: 1) these approaches assume accurate robot localization during the initialization step, ignoring localization errors that can compromise calibration robustness, and 2) the calibration results are highly sensitive to the initial guess of the UWB anchors' positions, reducing the practical applicability of these methods in real-world scenarios. T o further enhance the robustness of the calibration results against initialization errors, we propose a tightly-coupled Schmidt Kalman Filter (SKF)-based online refinement method, making the system suitable for practical applications. Simulations and real-world experiments validate the improved accuracy and robustness of our approach. Visual-inertial navigation system (VINS) is favored in robot state estimation due to its accuracy, reliability, and lightweight design [1], [2]. Nevertheless, VINS suffers from cumulative drift due to inherent limitations in visual-based localization methods.

In combinatorial causal bandits (CCB), the learning agent chooses a subset of variables in each round to intervene and collects feedback from the observed variables to minimize expected regret or sample complexity. Previous works study this problem in both general causal models and binary generalized linear models (BGLMs). However, all of them require prior knowledge of causal graph structure. This paper studies the CCB problem without the graph structure on binary general causal models and BGLMs. We first provide an exponential lower bound of cumulative regrets for the CCB problem on general causal models. To overcome the exponentially large space of parameters, we then consider the CCB problem on BGLMs. We design a regret minimization algorithm for BGLMs even without the graph skeleton and show that it still achieves $O(\sqrt{T}\ln T)$ expected regret. This asymptotic regret is the same as the state-of-art algorithms relying on the graph structure. Moreover, we sacrifice the regret to $O(T^{\frac{2}{3}}\ln T)$ to remove the weight gap covered by the asymptotic notation. At last, we give some discussions and algorithms for pure exploration of the CCB problem without the graph structure.

In combinatorial causal bandits (CCB), the learning agent chooses at most $K$ variables in each round to intervene, collects feedback from the observed variables, with the goal of minimizing expected regret on the target variable $Y$. We study under the context of binary generalized linear models (BGLMs) with a succinct parametric representation of the causal models. We present the algorithm BGLM-OFU for Markovian BGLMs (i.e. no hidden variables) based on the maximum likelihood estimation method, and show that it achieves $O(\sqrt{T}\log T)$ regret, where $T$ is the time horizon. For the special case of linear models with hidden variables, we apply causal inference techniques such as the do-calculus to convert the original model into a Markovian model, and then show that our BGLM-OFU algorithm and another algorithm based on the linear regression both solve such linear models with hidden variables. Our novelty includes (a) considering the combinatorial intervention action space and the general causal models including ones with hidden variables, (b) integrating and adapting techniques from diverse studies such as generalized linear bandits and online influence maximization, and (c) avoiding unrealistic assumptions (such as knowing the joint distribution of the parents of $Y$ under all interventions) and regret factors exponential to causal graph size in prior studies.

Motivated by cognitive radios, stochastic Multi-Player Multi-Armed Bandits has been extensively studied in recent years. In this setting, each player pulls an arm, and receives a reward corresponding to the arm if there is no collision, namely the arm was selected by one single player. Otherwise, the player receives no reward if collision occurs. In this paper, we consider the presence of malicious players (or attackers) who obstruct the cooperative players (or defenders) from maximizing their rewards, by deliberately colliding with them. We provide the first decentralized and robust algorithm RESYNC for defenders whose performance deteriorates gracefully as $\tilde{O}(C)$ as the number of collisions $C$ from the attackers increases. We show that this algorithm is order-optimal by proving a lower bound which scales as $\Omega(C)$. This algorithm is agnostic to the algorithm used by the attackers and agnostic to the number of collisions $C$ faced from attackers.

Artificial Bee Colony (ABC) algorithm is a Swarm Intelligence optimization algorithm inspired by the functioning of honey bees trying to find the best nectar resources surrounding their bee hive. Derviş Kara-Bogaz first proposed this algorithm in 2005. This algorithm has been used in many forms of optimization of complex non-linear functions. As you will see soon, this algorithm is dependent on the randomness of the situation, it is a great domain for applying better strategies to find the optimal point even faster. You will also notice that if the algorithm has a hint that the point is somehow a local minimum, it has a strategy to even discard it.

Bandit problems are pervasive in various fields of research and are also present in several practical applications. Examples, including dynamic pricing and assortment and the design of auctions and incentives, permeate a large number of sequential treatment experiments. Different applications impose distinct levels of restrictions on viable actions. Some favor diversity of outcomes, while others require harmful actions to be closely monitored or mainly avoided. In this paper, we extend one of the most popular bandit solutions, the original $\epsilon_t$-greedy heuristics, to high-dimensional contexts. Moreover, we introduce a competing exploration mechanism that counts with searching sets based on order statistics. We view our proposals as alternatives for cases where pluralism is valued or, in the opposite direction, cases where the end-user should carefully tune the range of exploration of new actions. We find reasonable bounds for the cumulative regret of a decaying $\epsilon_t$-greedy heuristic in both cases and we provide an upper bound for the initialization phase that implies the regret bounds when order statistics are considered to be at most equal but mostly better than the case when random searching is the sole exploration mechanism. Additionally, we show that end-users have sufficient flexibility to avoid harmful actions since any cardinality for the higher-order statistics can be used to achieve an stricter upper bound. We illustrate the algorithms proposed in this paper both with simulated and real data.

In recent years, multi-dimensional online decision making has been playing a crucial role in many practical applications such as online recommendation and digital marketing. To solve it, we introduce stochastic low-rank tensor bandits, a class of bandits whose mean rewards can be represented as a low-rank tensor. We propose two learning algorithms, tensor epoch-greedy and tensor elimination, and develop finite-time regret bounds for them. We observe that tensor elimination has an optimal dependency on the time horizon, while tensor epoch-greedy has a sharper dependency on tensor dimensions. Numerical experiments further back up these theoretical findings and show that our algorithms outperform various state-of-the-art approaches that ignore the tensor low-rank structure.

Motivated by cognitive radios, stochastic multi-player multi-armed bandits gained a lot of interest recently. In this class of problems, several players simultaneously pull arms and encounter a collision -- with 0 reward -- if some of them pull the same arm at the same time. While the cooperative case where players maximize the collective reward (obediently following some fixed protocol) has been mostly considered, robustness to malicious players is a crucial and challenging concern. Existing approaches consider only the case of adversarial jammers whose objective is to blindly minimize the collective reward. We shall consider instead the more natural class of selfish players whose incentives are to maximize their individual rewards, potentially at the expense of the social welfare. We provide the first algorithm robust to selfish players (a.k.a. Nash equilibrium) with a logarithmic regret, when the arm reward is observed. When collisions are also observed, Grim Trigger type of strategies enable some implicit communication-based algorithms and we construct robust algorithms in two different settings: in the homogeneous case (with a regret comparable to the centralized optimal one) and in the heterogeneous case (for an adapted and relevant notion of regret). We also provide impossibility results when only the reward is observed or when arm means vary arbitrarily among players.