We study best arm identification in a variant of the multi-armed bandit problem where the learner has limited precision in arm selection. The learner can only sample arms via certain exploration bundles, which we refer to as boxes. In particular, at each sampling epoch, the learner selects a box, which in turn causes an arm to get pulled as per a box-specific probability distribution. The pulled arm and its instantaneous reward are revealed to the learner, whose goal is to find the best arm by minimising the expected stopping time, subject to an upper bound on the error probability. We present an asymptotic lower bound on the expected stopping time, which holds as the error probability vanishes. We show that the optimal allocation suggested by the lower bound is, in general, non-unique and therefore challenging to track. We propose a modified tracking-based algorithm to handle non-unique optimal allocations, and demonstrate that it is asymptotically optimal. We also present non-asymptotic lower and upper bounds on the stopping time in the simpler setting when the arms accessible from one box do not overlap with those of others.
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Nowadays, the deployment of deep learning models on edge devices for addressing real-world classification problems is becoming more prevalent. Moreover, there is a growing popularity in the approach of early classification, a technique that involves classifying the input data after observing only an early portion of it, aiming to achieve reduced communication and computation requirements, which are crucial parameters in edge intelligence environments. While early classification in the field of time series analysis has been broadly researched, existing solutions for multivariate time series problems primarily focus on early classification along the temporal dimension, treating the multiple input channels in a collective manner. In this study, we propose a more flexible early classification pipeline that offers a more granular consideration of input channels and extends the early classification paradigm to the channel dimension. To implement this method, we utilize reinforcement learning techniques and introduce constraints to ensure the feasibility and practicality of our objective. To validate its effectiveness, we conduct experiments using synthetic data and we also evaluate its performance on real datasets. The comprehensive results from our experiments demonstrate that, for multiple datasets, our method can enhance the early classification paradigm by achieving improved accuracy for equal input utilization.
We study a dynamic allocation problem in which $T$ sequentially arriving divisible resources are to be allocated to a number of agents with linear utilities. The marginal utilities of each resource to the agents are drawn stochastically from a known joint distribution, independently and identically across time, and the central planner makes immediate and irrevocable allocation decisions. Most works on dynamic resource allocation aim to maximize the utilitarian welfare, i.e., the efficiency of the allocation, which may result in unfair concentration of resources on certain high-utility agents while leaving others' demands under-fulfilled. In this paper, aiming at balancing efficiency and fairness, we instead consider a broad collection of welfare metrics, the H\"older means, which includes the Nash social welfare and the egalitarian welfare. To this end, we first study a fluid-based policy derived from a deterministic surrogate to the underlying problem and show that for all smooth H\"older mean welfare metrics it attains an $O(1)$ regret over the time horizon length $T$ against the hindsight optimum, i.e., the optimal welfare if all utilities were known in advance of deciding on allocations. However, when evaluated under the non-smooth egalitarian welfare, the fluid-based policy attains a regret of order $\Theta(\sqrt{T})$. We then propose a new policy built thereupon, called Backward Infrequent Re-solving with Thresholding ($\mathsf{BIRT}$), which consists of re-solving the deterministic surrogate problem at most $O(\log\log T)$ times. We prove the $\mathsf{BIRT}$ policy attains an $O(1)$ regret against the hindsight optimal egalitarian welfare, independently of the time horizon length $T$. We conclude by presenting numerical experiments to corroborate our theoretical claims and to illustrate the significant performance improvement against several benchmark policies.
Integrated circuit verification has gathered considerable interest in recent times. Since these circuits keep growing in complexity year by year, pre-Silicon (pre-SI) verification becomes ever more important, in order to ensure proper functionality. Thus, in order to reduce the time needed for manually verifying ICs, we propose a machine learning (ML) approach, which uses less simulations. This method relies on an initial evaluation set of operating condition configurations (OCCs), in order to train Gaussian process (GP) surrogate models. By using surrogate models, we can propose further, more difficult OCCs. Repeating this procedure for several iterations has shown better GP estimation of the circuit's responses, on both synthetic and real circuits, resulting in a better chance of finding the worst case, or even failures, for certain circuit responses. Thus, we show that the proposed approach is able to provide OCCs closer to the specifications for all circuits and identify a failure (specification violation) for one of the responses of a real circuit.
This paper investigates the best arm identification (BAI) problem in stochastic multi-armed bandits in the fixed confidence setting. The general class of the exponential family of bandits is considered. The existing algorithms for the exponential family of bandits face computational challenges. To mitigate these challenges, the BAI problem is viewed and analyzed as a sequential composite hypothesis testing task, and a framework is proposed that adopts the likelihood ratio-based tests known to be effective for sequential testing. Based on this test statistic, a BAI algorithm is designed that leverages the canonical sequential probability ratio tests for arm selection and is amenable to tractable analysis for the exponential family of bandits. This algorithm has two key features: (1) its sample complexity is asymptotically optimal, and (2) it is guaranteed to be $\delta-$PAC. Existing efficient approaches focus on the Gaussian setting and require Thompson sampling for the arm deemed the best and the challenger arm. Additionally, this paper analytically quantifies the computational expense of identifying the challenger in an existing approach. Finally, numerical experiments are provided to support the analysis.
The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad--Shafranov equation. The presence of uncertainty in the model parameters introduces the need to quantify the variability in the predictions. This is often done by computing a large number of model solutions on a computational grid for an ensemble of parameter values and then obtaining estimates for the statistical properties of solutions. In this study, we explore the savings that can be obtained using multilevel Monte Carlo methods, which reduce costs by performing the bulk of the computations on a sequence of spatial grids that are coarser than the one that would typically be used for a simple Monte Carlo simulation. We examine this approach using both a set of uniformly refined grids and a set of adaptively refined grids guided by a discrete error estimator. Numerical experiments show that multilevel methods dramatically reduce the cost of simulation, with cost reductions typically on the order of 60 or more and possibly as large as 200. Adaptive gridding results in more accurate computation of geometric quantities such as x-points associated with the model.
This paper investigates a hitherto unaddressed aspect of best arm identification (BAI) in stochastic multi-armed bandits in the fixed-confidence setting. Two key metrics for assessing bandit algorithms are computational efficiency and performance optimality (e.g., in sample complexity). In stochastic BAI literature, there have been advances in designing algorithms to achieve optimal performance, but they are generally computationally expensive to implement (e.g., optimization-based methods). There also exist approaches with high computational efficiency, but they have provable gaps to the optimal performance (e.g., the $\beta$-optimal approaches in top-two methods). This paper introduces a framework and an algorithm for BAI that achieves optimal performance with a computationally efficient set of decision rules. The central process that facilitates this is a routine for sequentially estimating the optimal allocations up to sufficient fidelity. Specifically, these estimates are accurate enough for identifying the best arm (hence, achieving optimality) but not overly accurate to an unnecessary extent that creates excessive computational complexity (hence, maintaining efficiency). Furthermore, the existing relevant literature focuses on the family of exponential distributions. This paper considers a more general setting of any arbitrary family of distributions parameterized by their mean values (under mild regularity conditions). The optimality is established analytically, and numerical evaluations are provided to assess the analytical guarantees and compare the performance with those of the existing ones.
The robot operating system is the de-facto standard for designing and implementing robotics applications. Several previous works deal with the integration of heterogeneous accelerators into ROS-based applications. One of these approaches is ReconROS, which enables nodes to be completely mapped to hardware. The follow-up work fpgaDDS extends ReconROS by an intra-FPGA data distribution service to process topic-based communication between nodes entirely in hardware. However, the application of this approach is strictly limited to communication between nodes implemented in hardware only. This paper introduces gateways to close the gap between topic communication in hardware and software. Gateways aim to reduce data transfers between hardware and software by synchronizing a hardware-and software-mapped topic. As a result, data must be transferred only once compared to a separate data transmission for each subscribing hardware node in the baseline. Our measurements show significant speedups in multi-subscriber scenarios with large message sizes. From the conclusions of these measurements, we present a methodology for the communication mapping of ROS 2 computation graphs. In the evaluation, an autonomous driving real-world example benefits from the gateway and achieves a speedup of 1.4.
Multiple solutions mainly originate from the existence of redundant degrees of freedom in the robot arm, which may cause difficulties in inverse model learning but they can also bring many benefits, such as higher flexibility and robustness. Current multi-solution inverse model learning methods rely on conditional deep generative models, yet they often fail to achieve sufficient precision when learning multiple solutions. In this paper, we propose Conditional Embodied Self-Supervised Learning (CEMSSL) for robot arm multi-solution inverse model learning, and present a unified framework for high-precision multi-solution inverse model learning that is applicable to other conditional deep generative models. Our experimental results demonstrate that our framework can achieve a significant improvement in precision (up to 2 orders of magnitude) while preserving the properties of the original method. The related code will be available soon.
In this study, we have developed an incremental machine learning (ML) method that efficiently obtains the optimal model when a small number of instances or features are added or removed. This problem holds practical importance in model selection, such as cross-validation (CV) and feature selection. Among the class of ML methods known as linear estimators, there exists an efficient model update framework called the low-rank update that can effectively handle changes in a small number of rows and columns within the data matrix. However, for ML methods beyond linear estimators, there is currently no comprehensive framework available to obtain knowledge about the updated solution within a specific computational complexity. In light of this, our study introduces a method called the Generalized Low-Rank Update (GLRU) which extends the low-rank update framework of linear estimators to ML methods formulated as a certain class of regularized empirical risk minimization, including commonly used methods such as SVM and logistic regression. The proposed GLRU method not only expands the range of its applicability but also provides information about the updated solutions with a computational complexity proportional to the amount of dataset changes. To demonstrate the effectiveness of the GLRU method, we conduct experiments showcasing its efficiency in performing cross-validation and feature selection compared to other baseline methods.
With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.
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