We thank all reviewers for valuable comments. Entropy is used to measure sufficiency, compactness and uniqueness . The usage of variance to approximate entropy was discussed in L203. Therefore, the performance deteriorates dramatically. We will run our algorithm in more environments and provide the results in Appendix.

In contrast to the independent sampling assumed in classical matrix completion literature, the observed entries, which arise from past matching data, are constrained by matching capacity. This matching-induced dependence poses new challenges for both estimation and inference in the matrix completion framework. We propose a non-convex algorithm based on Grassmannian gradient descent and establish near-optimal entrywise convergence rates for three canonical mechanisms, i.e., one-to-one matching, one-to-many matching with one-sided random arrival, and two-sided random arrival. To facilitate valid uncertainty quantification and hypothesis testing on matching decisions, we further develop a general debiasing and projection framework for arbitrary linear forms of the reward matrix, deriving asymptotic normality with finite-sample guarantees under matching-induced dependent sampling. Our empirical experiments demonstrate that the proposed approach provides accurate estimation, valid confidence intervals, and efficient evaluation of matching policies.

We thank all reviewers for valuable comments. Entropy is used to measure sufficiency, compactness and uniqueness . The usage of variance to approximate entropy was discussed in L203. Therefore, the performance deteriorates dramatically. We will run our algorithm in more environments and provide the results in Appendix.

Reward decomposition, which aims to decompose the full reward into multiple sub-rewards, has been proven beneficial for improving sample efficiency in reinforcement learning. Existing works on discovering reward decomposition are mostly policy dependent, which constrains diverse or disentangled behavior between different policies induced by different sub-rewards. In this work, we propose a set of novel reward decomposition principles by constraining uniqueness and compactness of different state features/representations relevant to different sub-rewards. Our principles encourage sub-rewards with minimal relevant features, while maintaining the uniqueness of each sub-reward. We derive a deep learning algorithm based on our principle, and term our method as RD 2, since we learn reward decomposition and representation decomposition jointly.

The progress of humanity is driven by those successful discoveries accompanied by countless failed experiments. Researchers often seek the potential research directions by reading and then verifying them through experiments. The process imposes a significant burden on researchers. In the past decade, the data-driven black-box deep learning method demonstrates its effectiveness in a wide range of real-world scenarios, which exacerbates the experimental burden of researchers and thus renders the potential successful discoveries veiled. Therefore, automating such a research and development (R&D) process is an urgent need. In this paper, we serve as the first effort to formalize the goal by proposing a Real-world Data-centric automatic R&D Benchmark, namely RD2Bench. RD2Bench benchmarks all the operations in data-centric automatic R&D (D-CARD) as a whole to navigate future work toward our goal directly. We focuses on evaluating the interaction and synergistic effects of various model capabilities and aiding to select the well-performed trustworthy models. Although RD2Bench is very challenging to the state-of-the-art (SOTA) large language model (LLM) named GPT-4, indicating ample research opportunities and more research efforts, LLMs possess promising potential to bring more significant development to D-CARD: They are able to implement some simple methods without adopting any additional techniques. We appeal to future work to take developing techniques for tackling automatic R&D into consideration, thus bringing the opportunities of the potential revolutionary upgrade to human productivity.

We study the parameter estimation problem for a varying index coefficient model in high dimensions. Unlike the most existing works that simultaneously estimate the parameters and link functions, based on the generalized Stein's identity, we propose computationally efficient estimators for the high dimensional parameters without estimating the link functions. We consider two different setups where we either estimate each sparse parameter vector individually or estimate the parameters simultaneously as a sparse or low-rank matrix. For all these cases, our estimators are shown to achieve optimal statistical rates of convergence (up to logarithmic terms in the low-rank setting). Moreover, throughout our analysis, we only require the covariate to satisfy certain moment conditions, which is significantly weaker than the Gaussian or elliptically symmetric assumptions that are commonly made in the existing literature. Finally, we conduct extensive numerical experiments to corroborate the theoretical results.