Abstract. Low-rank matrix approximation plays an important role in various applications such as image processing, signal processing, and data analysis. The existing methods require a guess of the ranks of matrices that represent images or involve additional costs to determine the ranks. A novel efficient orthogonal decomposition with automatic basis extraction (EOD-ABE) is proposed to compute the optimal low-rank matrix approximation with adaptive identification of the optimal rank. By introducing a randomized basis extraction mechanism, EOD-ABE eliminates the need for additional rank determination steps and can compute a rank-revealing approximation to a low-rank matrix. With a computational complexity of [Formula: see text], where [Formula: see text] and [Formula: see text] are the dimensions of the matrix and [Formula: see text] is its computed numerical rank, EOD-ABE achieves significant speedups compared to the state-of-the-art methods. Experimental results demonstrate the superior speed, accuracy, and robustness of EOD-ABE and indicate that EOD-ABE is a powerful tool for fast image compression and reconstruction and hyperspectral image dimensionality reduction in large-scale applications.

Most existing LTR approaches follow a supervised learning paradigm from offline data collected from the online system. However, it has been noticed that previous LTR models can have good performances over offline validation data but have poor online performances, which implies a possible large inconsistency between the offline and online evaluation. We investigate and confirm in this paper that such inconsistency exists and can have a significant impact on AliExpress Search. Reasons for the inconsistency include the ignorance of item context. Therefore, this paper proposes an evaluator-generator framework for LTR with item context. The framework consists of an evaluator that generalizes to evaluate recommendations involving the context, and a generator that maximizes the evaluator score by reinforcement learning, and a discriminator that ensures the generalization of the evaluator. Extensive experiments in simulation environments and AliExpress Search online system show that, firstly, the classic data-based metrics on the offline dataset can show significant inconsistency with online performance. Secondly, the proposed evaluator score is significantly more consistent with the online performance than common ranking metrics. Finally, as the consequence, our method achieves a significant improvement in terms of Conversion Rate over the industrial-level fine-tuned model in online A/B tests.

Contrastive unsupervised learning gives remarkable promise for sample-efficiency improvement in reinforcement learning, especially for high-dimensional observations by extracting latent features from raw inputs. However, prior works scarcely take sequential information and the knowledge of dynamic transitions into consideration when constructing contrastive samples. In this paper, we propose Sequential and Dynamic constraint Contrastive Reinforcement Learning (SDCRL) to improve the sample efficiency in high-dimensional inputs (e.g., images) setting. We firstly construct a sequential contrastive module to extract latent features with sequential information from raw correlated image inputs. Furthermore, we add a dynamic transition classification module to extract the knowledge of state transitions. We validate the proposed method in low sample regime (few interactions). Our algorithm surpasses prior pixel-based approaches on complex tasks in Deepmind Control Suite and even achieves or exceeds the performance of the method that uses state-based features as inputs on 11 out of 15 tasks. In Atari2600 games, SDCRL also outperforms strong baselines and achieves state-of-the-art performance on 7 out of 26 games.