The Kullback-Leibler (KL) divergence is widely used in state-of-the-art Bayesian Neural Networks (BNNs) to approximate the posterior distribution of weights. However, the KL divergence is unbounded and asymmetric, which may lead to instabilities during optimization or may yield poor generalizations. To overcome these limitations, we examine the Jensen-Shannon (JS) divergence that is bounded, symmetric, and more general. Towards this, we propose two novel loss functions for BNNs. The first loss function uses the geometric JS divergence (JS-G) that is symmetric, unbounded, and offers an analytical expression for Gaussian priors. The second loss function uses the generalized JS divergence (JS-A) that is symmetric and bounded. We show that the conventional KL divergence-based loss function is a special case of the two loss functions presented in this work. To evaluate the divergence part of the loss we use analytical expressions for JS-G and use Monte Carlo methods for JS-A. We provide algorithms to optimize the loss function using both these methods. The proposed loss functions offer additional parameters that can be tuned to control the degree of regularisation. The regularization performance of the JS divergences is analyzed to demonstrate their superiority over the state-of-the-art. Further, we derive the conditions for better regularization by the proposed JS-G divergence-based loss function than the KL divergence-based loss function. Bayesian convolutional neural networks (BCNN) based on the proposed JS divergences perform better than the state-of-the-art BCNN, which is shown for the classification of the CIFAR data set having various degrees of noise and a histopathology data set having a high bias.

This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its reconstruction error via connections to higher-order singular values. Specifically, we introduce a novel Tucker packing problem, which we prove is NP-hard, and give a polynomial-time approximation scheme based on a reduction to the 2-dimensional knapsack problem with a matroid constraint. We also generalize our techniques to tree tensor network decompositions. We implement our algorithm using an integer programming solver, and show that its solution quality is competitive with (and sometimes better than) the greedy algorithm that uses the true Tucker decomposition loss at each step, while also running up to 1000x faster.

Selecting period values for tasks is a very important step in the design process of a real-time system, especially due to the significance of its impact on system schedulability. It is well known that, under RMS, the utilization bound for a harmonic task set is 100%. Also, polynomial-time algorithms have been developed for response-time analysis of harmonic task sets. In practice, the largest acceptable value for the period of a task is determined by the performance and safety requirements of the application. In this paper, we address the problem of assigning harmonic periods to a task set such that every task gets assigned an integer period less than or equal to its application specified upper bound and the task utilization of every task is less than 1. We focus on integer solutions given the discrete nature of time in real-time computer systems. We first express this problem of assigning harmonic periods to a task set as a discrete piecewise optimization problem. We then present the 'Discrete Piecewise Harmonic Search' (DPHS) algorithm that outputs an optimal harmonic task assignment. We then define conditions for a metric to be rational for harmonization. We show that commonly used metrics like, the total percentage error (TPE), total system utilization (TSU), first order error (FOE), and maximum percentage error (MPE), are rational. We next prove that the DPHS algorithm finds the optimal feasible assignment, if one exists, for these rational metrics. We apply the DPHS algorithm to harmonize task sets used in real-world applications to highlight its benefits. We compare the performance of the DPHS algorithm against a brute-force search and find that the DPHS searches up to 94\% fewer task sets than the brute-force search that obtains the optimal solution.

How should we leverage such an extra modality of feedback along with the typical reward signal in CBs? We study contextual bandit (CB) problems, While prior works have developed hybrid models such as where the user can sometimes respond with the learning with feedback graphs (e.g., (Mannor & Shamir, best action in a given context. Such an interaction 2011; Caron et al., 2012; Alon et al., 2017)) to capture a arises, for example, in text prediction or autocompletion continuum between supervised and CB learning, such settings settings, where a poor suggestion is simply are not a natural fit here. A key challenge in the ignored and the user enters the desired text feedback structure is that the extra supervised signal is only instead. Crucially, this extra feedback is usertriggered available on a subset of the contexts, which are chosen by on only a subset of the contexts. We develop the user as some unknown function of the algorithm's recommended a new framework to leverage such signals,

We consider a class of assortment optimization problems in an offline data-driven setting. A firm does not know the underlying customer choice model but has access to an offline dataset consisting of the historically offered assortment set, customer choice, and revenue. The objective is to use the offline dataset to find an optimal assortment. Due to the combinatorial nature of assortment optimization, the problem of insufficient data coverage is likely to occur in the offline dataset. Therefore, designing a provably efficient offline learning algorithm becomes a significant challenge. To this end, we propose an algorithm referred to as Pessimistic ASsortment opTimizAtion (PASTA for short) designed based on the principle of pessimism, that can correctly identify the optimal assortment by only requiring the offline data to cover the optimal assortment under general settings. In particular, we establish a regret bound for the offline assortment optimization problem under the celebrated multinomial logit model. We also propose an efficient computational procedure to solve our pessimistic assortment optimization problem. Numerical studies demonstrate the superiority of the proposed method over the existing baseline method.

Electric city bus gains popularity in recent years for its low greenhouse gas emission, low noise level, etc. Different from a passenger car, the weight of a city bus varies significantly with different amounts of onboard passengers. After analyzing the importance of battery aging and passenger load effects on an optimal energy management strategy, this study introduces the passenger load prediction into the hybrid-electric city buses energy management problem, which is not well studied in the existing literature. The average model, Decision Tree, Gradient Boost Decision Tree, and Neural Networks models are compared in the passenger load prediction. The Gradient Boost Decision Tree model is selected due to its best accuracy and high stability. Given the predicted passenger load, a dynamic programming algorithm determines the optimal power demand for supercapacitor and battery by optimizing the battery aging and energy usage leveraging cloud techniques. Then, rule extraction is conducted on dynamic programming results, and the rule is real-time loaded to the vehicle onboard controller to handle prediction errors and uncertainties. The proposed cloud-based Dynamic Programming and rule extraction framework with the passenger load prediction show 4% and 11% lower bus operating costs in off-peak and peak hours, respectively. The operating cost by the proposed framework is less than 1% of the dynamic programming with the true passenger load information.

There is a lack of consensus within the literature as to how `fairness' of algorithmic systems can be measured, and different metrics can often be at odds. In this paper, we approach this task by drawing on the ethical frameworks of utilitarianism and John Rawls. Informally, these two theories of distributive justice measure the `good' as either a population's sum of utility, or worst-off outcomes, respectively. We present a parameterized class of objective functions that interpolates between these two (possibly) conflicting notions of the `good'. This class is shown to represent a relaxation of the Rawlsian `veil of ignorance', and its sequence of optimal solutions converges to both a utilitarian and Rawlsian optimum. Several other properties of this class are studied, including: 1) a relationship to regularized optimization, 2) feasibility of consistent estimation, and 3) algorithmic cost. In several real-world datasets, we compute optimal solutions and construct the tradeoff between utilitarian and Rawlsian notions of the `good'. Empirically, we demonstrate that increasing model complexity can manifest strict improvements to both measures of the `good'. This work suggests that the proper degree of `fairness' can be informed by a designer's preferences over the space of induced utilitarian and Rawlsian `good'.

This survey focuses on categorizing and evaluating the methods of supernet optimization in the field of Neural Architecture Search (NAS). Supernet optimization involves training a single, over-parameterized network that encompasses the search space of all possible network architectures. The survey analyses supernet optimization methods based on their approaches to spatial and temporal optimization. Spatial optimization relates to optimizing the architecture and parameters of the supernet and its subnets, while temporal optimization deals with improving the efficiency of selecting architectures from the supernet. The benefits, limitations, and potential applications of these methods in various tasks and settings, including transferability, domain generalization, and Transformer models, are also discussed.

With the development of robotics, ground robots are no longer limited to planar motion. Passive height variation due to complex terrain and active height control provided by special structures on robots require a more general navigation planning framework beyond 2D. Existing methods rarely considers both simultaneously, limiting the capabilities and applications of ground robots. In this paper, we proposed an optimization-based planning framework for ground robots considering both active and passive height changes on the z-axis. The proposed planner first constructs a penalty field for chassis motion constraints defined in R3 such that the optimal solution space of the trajectory is continuous, resulting in a high-quality smooth chassis trajectory. Also, by constructing custom constraints in the z-axis direction, it is possible to plan trajectories for different types of ground robots which have z-axis degree of freedom. We performed simulations and realworld experiments to verify the efficiency and trajectory quality of our algorithm.

The use of Agent-Based and Activity-Based modeling in transportation is rising due to the capability of addressing complex applications such as disruptive trends (e.g., remote working and automation) or the design and assessment of disaggregated management strategies. Still, the broad adoption of large-scale disaggregate models is not materializing due to the inherently high complexity and computational needs. Activity-based models focused on behavioral theory, for example, may involve hundreds of parameters that need to be calibrated to match the detailed socio-economical characteristics of the population for any case study. This paper tackles this issue by proposing a novel Bayesian Optimization approach incorporating a surrogate model in the form of an improved Random Forest, designed to automate the calibration process of the behavioral parameters. The proposed method is tested on a case study for the city of Tallinn, Estonia, where the model to be calibrated consists of 477 behavioral parameters, using the SimMobility MT software. Satisfactory performance is achieved in the major indicators defined for the calibration process: the error for the overall number of trips is equal to 4% and the average error in the OD matrix is 15.92 vehicles per day.