We further significantly improve sample quality with'double guidance'.

First-order optimization (FOO) algorithms are pivotal in numerous computational domains, such as reinforcement learning and deep learning. However, their application to complex tasks often entails significant optimization inefficiency due to their need of many sequential iterations for convergence. In response, we introduce first-order opt imization ex pedited with approximately parallelized iterations (OptEx), the first general framework that enhances the optimization efficiency of FOO by leveraging parallel computing to directly mitigate its requirement of many sequential iterations for convergence. To achieve this, OptEx utilizes a kernelized gradient estimation that is based on the history of evaluated gradients to predict the gradients required by the next few sequential iterations in FOO, which helps to break the inherent iterative dependency and hence enables the approximate paral-lelization of iterations in FOO. We further establish theoretical guarantees for the estimation error of our kernelized gradient estimation and the iteration complexity of SGD-based OptEx, confirming that the estimation error diminishes to zero as the history of gradients accumulates and that our SGD-based OptEx enjoys an effective acceleration rate of Θ( N) over standard SGD given parallelism of N, in terms of the sequential iterations required for convergence. Finally, we provide extensive empirical studies, including synthetic functions, reinforcement learning tasks, and neural network training on various datasets, to underscore the substantial efficiency improvements achieved by OptEx in practice. Our implementation is available at https://github.com/youyve/OptEx .

Cleaning missing values: The human-generated questions may be unanswerable. Thus, we remove the Q&A items that lack available answers. Additionally, documents lacking any valid Q&A pairs are also removed.

Models (LLMs) in collaborating with external data, yet significant challenges exist in real-world scenarios. In areas such as academic literature and finance question answering, data are often found in raw text and tables in HTML or PDF formats, which can be lengthy and highly unstructured.

Based on our large-scale study, we summarize our key findings as follows: Key findings.

We compare our method with four competing methods in Table 1 of the main paper. We also use the score reported by [5]. We found that the corner-based methods, e.g., HEA T and RoomFormer, fail to reconstruct the correct floorplans and are easily affected by the irregular Heat: Holistic edge attention transformer for structured reconstruction. Real-world perception for embodied agents.