We introduce an adaptive nearest neighbor classification rule.

Gaussian process upper confidence bound (GP-UCB) is a theoretically established algorithm for Bayesian optimization (BO), where we assume the objective function $f$ follows GP. One notable drawback of GP-UCB is that the theoretical confidence parameter $\beta$ increased along with the iterations is too large. To alleviate this drawback, this paper analyzes the randomized variant of GP-UCB called improved randomized GP-UCB (IRGP-UCB), which uses the confidence parameter generated from the shifted exponential distribution. We analyze the expected regret and conditional expected regret, where the expectation and the probability are taken respectively with $f$ and noises and with the randomness of the BO algorithm. In both regret analyses, IRGP-UCB achieves a sub-linear regret upper bound without increasing the confidence parameter if the input domain is finite. Finally, we show numerical experiments using synthetic and benchmark functions and real-world emulators.

Level set estimation (LSE), the problem of identifying the set of input points where a function takes value above (or below) a given threshold, is important in practical applications. When the function is expensive-to-evaluate and black-box, the \textit{straddle} algorithm, which is a representative heuristic for LSE based on Gaussian process models, and its extensions having theoretical guarantees have been developed. However, many of existing methods include a confidence parameter $\beta^{1/2}_t$ that must be specified by the user, and methods that choose $\beta^{1/2}_t$ heuristically do not provide theoretical guarantees. In contrast, theoretically guaranteed values of $\beta^{1/2}_t$ need to be increased depending on the number of iterations and candidate points, and are conservative and not good for practical performance. In this study, we propose a novel method, the \textit{randomized straddle} algorithm, in which $\beta_t$ in the straddle algorithm is replaced by a random sample from the chi-squared distribution with two degrees of freedom. The confidence parameter in the proposed method has the advantages of not needing adjustment, not depending on the number of iterations and candidate points, and not being conservative. Furthermore, we show that the proposed method has theoretical guarantees that depend on the sample complexity and the number of iterations. Finally, we confirm the usefulness of the proposed method through numerical experiments using synthetic and real data.

Deep neural networks (DNNs) can easily be cheated by some imperceptible but purposeful noise added to images, and erroneously classify them. Previous defensive work mostly focused on retraining the models or detecting the noise, but has either shown limited success rates or been attacked by new adversarial examples. Instead of focusing on adversarial images or the interior of DNN models, we observed that adversarial examples generated by different algorithms can be identified based on the output of DNNs (logits). Logit can serve as an exterior feature to train detectors. Then, we propose HOLMES (Hierarchically Organized Light-weight Multiple dEtector System) to reinforce DNNs by detecting potential adversarial examples to minimize the threats they may bring in practical. HOLMES is able to distinguish \textit{unseen} adversarial examples from multiple attacks with high accuracy and low false positive rates than single detector systems even in an adaptive model. To ensure the diversity and randomness of detectors in HOLMES, we use two methods: training dedicated detectors for each label and training detectors with top-k logits. Our effective and inexpensive strategies neither modify original DNN models nor require its internal parameters. HOLMES is not only compatible with all kinds of learning models (even only with external APIs), but also complementary to other defenses to achieve higher detection rates (may also fully protect the system against various adversarial examples).

Among various acquisition functions (AFs) in Bayesian optimization (BO), Gaussian process upper confidence bound (GP-UCB) and Thompson sampling (TS) are well-known options with established theoretical properties regarding Bayesian cumulative regret (BCR). Recently, it has been shown that a randomized variant of GP-UCB achieves a tighter BCR bound compared with GP-UCB, which we call the tighter BCR bound for brevity. Inspired by this study, this paper first shows that TS achieves the tighter BCR bound. On the other hand, GP-UCB and TS often practically suffer from manual hyperparameter tuning and over-exploration issues, respectively. To overcome these difficulties, we propose yet another AF called a probability of improvement from the maximum of a sample path (PIMS). We show that PIMS achieves the tighter BCR bound and avoids the hyperparameter tuning, unlike GP-UCB. Furthermore, we demonstrate a wide range of experiments, focusing on the effectiveness of PIMS that mitigates the practical issues of GP-UCB and TS.

Gaussian process upper confidence bound (GP-UCB) is a theoretically promising approach for black-box optimization; however, the confidence parameter $\beta$ is considerably large in the theorem and chosen heuristically in practice. Then, randomized GP-UCB (RGP-UCB) uses a randomized confidence parameter, which follows the Gamma distribution, to mitigate the impact of manually specifying $\beta$. This study first generalizes the regret analysis of RGP-UCB to a wider class of distributions, including the Gamma distribution. Furthermore, we propose improved RGP-UCB (IRGP-UCB) based on a two-parameter exponential distribution, which achieves tighter Bayesian regret bounds. IRGP-UCB does not require an increase in the confidence parameter in terms of the number of iterations, which avoids over-exploration in the later iterations. Finally, we demonstrate the effectiveness of IRGP-UCB through extensive experiments.

Robots such as autonomous vehicles and assistive manipulators are increasingly operating in dynamic environments and close physical proximity to people. In such scenarios, the robot can leverage a human motion predictor to predict their future states and plan safe and efficient trajectories. However, no model is ever perfect -- when the observed human behavior deviates from the model predictions, the robot might plan unsafe maneuvers. Recent works have explored maintaining a confidence parameter in the human model to overcome this challenge, wherein the predicted human actions are tempered online based on the likelihood of the observed human action under the prediction model. This has opened up a new research challenge, i.e., \textit{how to compute the future human states online as the confidence parameter changes?} In this work, we propose a Hamilton-Jacobi (HJ) reachability-based approach to overcome this challenge. Treating the confidence parameter as a virtual state in the system, we compute a parameter-conditioned forward reachable tube (FRT) that provides the future human states as a function of the confidence parameter. Online, as the confidence parameter changes, we can simply query the corresponding FRT, and use it to update the robot plan. Computing parameter-conditioned FRT corresponds to an (offline) high-dimensional reachability problem, which we solve by leveraging recent advances in data-driven reachability analysis. Overall, our framework enables online maintenance and updates of safety assurances in human-robot interaction scenarios, even when the human prediction model is incorrect. We demonstrate our approach in several safety-critical autonomous driving scenarios, involving a state-of-the-art deep learning-based prediction model.

We present an approach geared toward estimating task execution confidence for robotic bin-picking applications. This requires estimating execution confidence for all constituent subtasks including part recognition and pose estimation, singulation, transport, and fine positioning. This paper is focussed on computing associated confidence parameters for the part recognition and pose estimation subtask. In particular, our approach allows a robot to evaluate how good the part recognition and pose estimation is, based on a confidence-measure, and thereby determine whether to proceed with the task execution (part singulation) or to request help from a human in order to resolve the associated failure. The value of a mean-square distance metric at a local minimum where the part matching solution is found is used as a surrogate for the confidence parameter. Experiments with a Baxter robot are used illustrate our approach.