DeepSeek Proposes Tensor Decomposition-Based Surrogate Modeling for Discrete Black-Box Optimization

Summary:DeepSeek has introduced a tensor decomposition-based surrogate modeling approach for discrete black-box optimization. This method captures the structure of discrete search spaces while directly integrating feasibility information, significantly improving search efficiency. Experiments on both synthetic and real-world benchmarks, including a pressure vessel design task, demonstrate that the proposed method effectively guides the search away from infeasible regions, enhancing overall performance.

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Core Breakthrough

The DeepSeek team has proposed a tensor decomposition-based surrogate modeling approach for discrete black-box optimization. The key innovations include:

• Capturing Discrete Search Space Structure: The surrogate model leverages tensor decomposition to effectively capture the structural characteristics of discrete search spaces.
• Integrating Feasibility Information: The method directly integrates feasibility information, such as logical constraints, into the modeling process to prevent the search from entering infeasible regions.
• Optimizing the Training Process: The surrogate model training is formulated as a constrained polynomial optimization problem, and a relaxed formulation is solved using a differentiable penalty term derived from T-norms.

Experimental Results

The research team validated the method's effectiveness through multiple benchmarks, including:

• Synthetic Datasets: Experiments on synthetic datasets showed that the method can effectively reduce the number of invalid attempts in the search space.
• Pressure Vessel Design Task: In the real-world pressure vessel design task, the method significantly improved sample efficiency, successfully guiding the search away from infeasible regions.

Technical Highlights

• Innovative Application of Tensor Decomposition: This is the first time tensor decomposition has been applied to discrete black-box optimization problems, demonstrating its potential in handling complex constraints.
• Use of Differentiable Penalty Terms: The introduction of differentiable penalty terms allows for a softened treatment of constraints, making the optimization process more efficient.

Industry Impact and Developer Recommendations

This method provides a new solution for discrete black-box optimization problems, particularly applicable to industrial design, supply chain optimization, and other fields with complex constraints. For developers, it is recommended to consider integrating tensor decomposition techniques into existing optimization algorithms to enhance search efficiency and result quality. Additionally, this method offers new perspectives on the application of AI in complex system modeling.

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Source: ArXiv Machine Learning (cs.LG) (2026-09-10)

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Tags: #DeepSeek #Tensor Decomposition #Black-Box Optimization #AI Research #Discrete Optimization