We extend the traditional worst-case, minimax analysis of stochastic convex optimization by introducing a localized form of minimax complexity for individual functions. Our main result gives function-specific lower and upper bounds on the number of stochastic subgradient evaluations needed to optimize either the function or its "hardest local alternative" to a given numerical precision. The bounds are expressed in terms of a localized and computational analogue of the modulus of continuity that is central to statistical minimax analysis. We show how the computational modulus of continuity can be explicitly calculated in concrete cases, and relates to the curvature of the function at the optimum. We also prove a superefficiency result that demonstrates it is a meaningful benchmark, acting as a computational analogue of the Fisher information in statistical estimation. The nature and practical implications of the results are demonstrated in simulations.

We extend the traditional worst-case, minimax analysis of stochastic convex optimization by introducing a localized form of minimax complexity for individual functions. Our main result gives function-specific lower and upper bounds on the number of stochastic subgradient evaluations needed to optimize either the function or its "hardest local alternative" to a given numerical precision. The bounds are expressed in terms of a localized and computational analogue of the modulus of continuity that is central to statistical minimax analysis. We show how the computational modulus of continuity can be explicitly calculated in concrete cases, and relates to the curvature of the function at the optimum. We also prove a superefficiency result that demonstrates it is a meaningful benchmark, acting as a computational analogue of the Fisher information in statistical estimation. The nature and practical implications of the results are demonstrated in simulations.

Spoof localization, also called segment-level detection, is a crucial task that aims to locate spoofs in partially spoofed audio. The equal error rate (EER) is widely used to measure performance for such biometric scenarios. Although EER is the only threshold-free metric, it is usually calculated in a point-based way that uses scores and references with a pre-defined temporal resolution and counts the number of misclassified segments. Such point-based measurement overly relies on this resolution and may not accurately measure misclassified ranges. To properly measure misclassified ranges and better evaluate spoof localization performance, we upgrade point-based EER to range-based EER. Then, we adapt the binary search algorithm for calculating range-based EER and compare it with the classical point-based EER. Our analyses suggest utilizing either range-based EER, or point-based EER with a proper temporal resolution can fairly and properly evaluate the performance of spoof localization.

Agile flights of autonomous quadrotors in cluttered environments require constrained motion planning and control subject to translational and rotational dynamics. Traditional model-based methods typically demand complicated design and heavy computation. In this paper, we develop a novel deep reinforcement learning-based method that tackles the challenging task of flying through a dynamic narrow gate. We design a model predictive controller with its adaptive tracking references parameterized by a deep neural network (DNN). These references include the traversal time and the quadrotor SE(3) traversal pose that encourage the robot to fly through the gate with maximum safety margins from various initial conditions. To cope with the difficulty of training in highly dynamic environments, we develop a reinforce-imitate learning framework to train the DNN efficiently that generalizes well to diverse settings. Furthermore, we propose a binary search algorithm that allows online adaption of the SE(3) references to dynamic gates in real-time. Finally, through extensive high-fidelity simulations, we show that our approach is robust to the gate's velocity uncertainties and adaptive to different gate trajectories and orientations.

Algorithms are an essential aspect of programming. In this article, we will cover one such cool algorithm that can be used to efficiently find the location of a specific element in a list or array. We will cover the binary search algorithm in complete detail and try to implement it with python. In mathematics and computer science, an algorithm is a finite sequence of well-defined, computer-implementable instructions, typically to solve a class of problems or to perform a computation. One such algorithm that we will cover in this article is the binary search algorithm.

I used to live in a building that had a communal kitchen for over 100 students. As you might imagine, there were almost always dishes that weren't washed in the sink. A group at my school pitched the idea to put up a Nest Cam to catch culprits and call them out on it using the Nest Cam feed. To illustrate my point, let's say you found dirty dishes at 12 pm, and you hadn't been in the kitchen for a day. Think about the way that you would search for the person who left the dishes.

We extend the traditional worst-case, minimax analysis of stochastic convex optimization by introducing a localized form of minimax complexity for individual functions. Our main result gives function-specific lower and upper bounds on the number of stochastic subgradient evaluations needed to optimize either the function or its ``hardest local alternative'' to a given numerical precision. The bounds are expressed in terms of a localized and computational analogue of the modulus of continuity that is central to statistical minimax analysis. We show how the computational modulus of continuity can be explicitly calculated in concrete cases, and relates to the curvature of the function at the optimum. We also prove a superefficiency result that demonstrates it is a meaningful benchmark, acting as a computational analogue of the Fisher information in statistical estimation. The nature and practical implications of the results are demonstrated in simulations.