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This paper studies sample average approximation (SAA) and its simple regularized variation in solving convex or strongly convex stochastic programming problems. Under heavy-tailed assumptions and comparable regularity conditions as in the typical SAA literature, we show — perhaps for the first time — that the sample complexity can be completely free from any complexity measure (e.g., logarithm of the covering number) of the feasible region. As a result, our new bounds can be more advantageous than the state-of-the-art in terms of the dependence on the problem dimensionality. 

Abstract Objective. UNet-based deep-learning (DL) architectures are promising dose engines for traditional linear accelerator (Linac) models. Current UNet-based engines, however, were designed differently with various strategies, making it challenging to fairly compare the results from different studies. The objective of this study is to thoroughly evaluate the performance of UNet-based models on magnetic-resonance (MR)-Linac-based intensity-modulated radiation therapy (IMRT) dose calculations.Approach. The UNet-based models, including the standard-UNet, cascaded-UNet, dense-dilated-UNet, residual-UNet, HD-UNet, and attention-aware-UNet, were implemented. The model input is patient CT and IMRT field dose in water, and the output is patient dose calculated by DL model. The reference dose was calculated by the Monaco Monte Carlo module. Twenty training and ten test cases of prostate patients were included. The accuracy of the DL-calculated doses was measured using gamma analysis, and the calculation efficiency was evaluated by inference time.Results. All the studied models effectively corrected low-accuracy doses in water to high-accuracy patient doses in a magnetic field. The gamma passing rates between reference and DL-calculated doses were over 86% (1%/1 mm), 98% (2%/2 mm), and 99% (3%/3 mm) for all the models. The inference times ranged from 0.03 (graphics processing unit) to 7.5 (central processing unit) seconds. Each model demonstrated different strengths in calculation accuracy and efficiency; Res-UNet achieved the highest accuracy, HD-UNet offered high accuracy with the fewest parameters but the longest inference, dense-dilated-UNet was consistently accurate regardless of model levels, standard-UNet had the shortest inference but relatively lower accuracy, and the others showed average performance. Therefore, the best-performing model would depend on the specific clinical needs and available computational resources.Significance. The feasibility of using common UNet-based models for MR-Linac-based dose calculations has been explored in this study. By using the same model input type, patient training data, and computing environment, a fair assessment of the models’ performance was present. 

Abstract Objective . Deep-learning (DL)-based dose engines have been developed to alleviate the intrinsic compromise between the calculation accuracy and efficiency of the traditional dose calculation algorithms. However, current DL-based engines typically possess high computational complexity and require powerful computing devices. Therefore, to mitigate their computational burdens and broaden their applicability to a clinical setting where resource-limited devices are available, we proposed a compact dose engine via knowledge distillation (KD) framework that offers an ultra-fast calculation speed with high accuracy for prostate Volumetric Modulated Arc Therapy (VMAT). Approach . The KD framework contains two sub-models: a large pre-trained teacher and a small to-be-trained student. The student receives knowledge transferred from the teacher for better generalization. The trained student serves as the final engine for dose calculation. The model input is patient computed tomography and VMAT dose in water, and the output is DL-calculated patient dose. The ground-truth \dose was computed by the Monte Carlo module of the Monaco treatment planning system. Twenty and ten prostate cases were included for model training and assessment, respectively. The model’s performance (teacher/student/student-only) was evaluated by Gamma analysis and inference efficiency. Main results . The dosimetric comparisons (input/DL-calculated/ground-truth doses) suggest that the proposed engine can effectively convert low-accuracy doses in water to high-accuracy patient doses. The Gamma passing rate (2%/2 mm, 10% threshold) between the DL-calculated and ground-truth doses was 98.64 ± 0.62% (teacher), 98.13 ± 0.76% (student), and 96.95 ± 1.02% (student-only). The inference time was 16 milliseconds (teacher) and 11 milliseconds (student/student-only) using a graphics processing unit device, while it was 936 milliseconds (teacher) and 374 milliseconds (student/student-only) using a central processing unit device. Significance . With the KD framework, a compact dose engine can achieve comparable accuracy to that of a larger one. Its compact size reduces the computational burdens and computing device requirements, and thus such an engine can be more clinically applicable. 

High-dimensional statistical learning (HDSL) has wide applications in data analysis, operations research, and decision making. Despite the availability of multiple theoretical frameworks, most existing HDSL schemes stipulate the following two conditions: (a) the sparsity and (b) restricted strong convexity (RSC). This paper generalizes both conditions via the use of the folded concave penalty (FCP). More specifically, we consider an M-estimation problem where (i) (conventional) sparsity is relaxed into the approximate sparsity and (ii) RSC is completely absent. We show that the FCP-based regularization leads to poly-logarithmic sample complexity; the training data size is only required to be poly-logarithmic in the problem dimensionality. This finding can facilitate the analysis of two important classes of models that are currently less understood: high-dimensional nonsmooth learning and (deep) neural networks (NNs). For both problems, we show that poly-logarithmic sample complexity can be maintained. In particular, our results indicate that the generalizability of NNs under overparameterization can be theoretically ensured with the aid of regularization.