Optimizing Rank-based Metrics with Blackbox Differentiation (1912.03500v2)

Abstract: Rank-based metrics are some of the most widely used criteria for performance evaluation of computer vision models. Despite years of effort, direct optimization for these metrics remains a challenge due to their non-differentiable and non-decomposable nature. We present an efficient, theoretically sound, and general method for differentiating rank-based metrics with mini-batch gradient descent. In addition, we address optimization instability and sparsity of the supervision signal that both arise from using rank-based metrics as optimization targets. Resulting losses based on recall and Average Precision are applied to image retrieval and object detection tasks. We obtain performance that is competitive with state-of-the-art on standard image retrieval datasets and consistently improve performance of near state-of-the-art object detectors. The code is available at https://github.com/martius-lab/blackbox-backprop

• The paper introduces a blackbox backpropagation technique to efficiently compute gradients for rank-based metrics like AP and mAP.
• It leverages mini-batch gradient descent and combinatorial solvers to overcome non-differentiability in key computer vision tasks.
• Experimental results show competitive performance with state-of-the-art methods, offering practical improvements and theoretical advancements.

Optimizing Rank-Based Metrics with Blackbox Differentiation

The paper, "Optimizing Rank-Based Metrics with Blackbox Differentiation," presents a novel method for differentiating rank-based metrics in computer vision applications. The authors address the longstanding challenge posed by the non-differentiable and non-decomposable nature of rank-based metrics, which are ubiquitously employed for evaluating the performance of machine learning models in various computer vision tasks, such as image retrieval and object detection.

Methodology

The authors propose an efficient method using mini-batch gradient descent to optimize rank-based metrics like Average Precision (AP) and mean Average Precision (mAP). This approach leverages blackbox backpropagation, which reduces the optimization problem to a combinatorial one by redefining ranking as a linear combinatorial objective. This allows the use of existing efficient blackbox combinatorial solvers for backpropagation. The technique offers a principled interpolation of piecewise constant functions, inherited from the blackbox approach, with strong mathematical guarantees.

Key Contributions

• Theoretical Foundation: They effectively formalize rank-based metrics, providing a novel link between ranking operations and combinatorial solvers. This connection allows them to apply blackbox differentiation to compute gradients efficiently.
• Practical Implementation: The proposed method achieves competitive performance on standard image retrieval datasets and improves near-state-of-the-art object detectors. This makes it a compelling option for improving rank-based metrics in machine learning systems.

Numerical Results and Implications

The experiments conducted demonstrate the competitiveness of the proposed methodology. The numerical results assert that their technique achieves performance on par with state-of-the-art methods on retrieval tasks on datasets like CUB-200-2011, Stanford Online Products, and In-shop Clothes. Additionally, there are consistent improvements in object detection performance over standard baselines.

Implications

The implications of this work are twofold:

1. Practical Impact: It offers a viable solution for applying rank-based loss functions directly, potentially boosting the performance of image retrieval and object detection models used in real-world applications.
2. Theoretical Advancements: The paper contributes a substantive advancement in the field by unveiling a method that effectively integrates non-differentiable operations into neural network training using blackbox solvers.

Future Directions

The authors indicate opportunities for future work, particularly the potential to optimize large-scale ranking metrics with sequences containing millions of elements efficiently. This direction could enhance the scalability and applicability of rank-based optimization in more complex AI systems.

In summary, the paper provides a well-founded method for the optimization of rank-based metrics, demonstrating both theoretical innovation and practical viability. The results and approach present new avenues for robust, scalable machine learning models in computer vision and beyond.