Adaptive Proximal Gradient Optimizer: Addressing Gradient Inexactness in Predict+Optimize Framework

ICLR 2025 Conference Submission652 Authors

Keywords: Predict+optimize, Inexact gradient, Proximal gradient descent, Optimizer

TL;DR: We propose the Adaptive Proximal Gradient Optimizer (AProx) to address the underexplored inexact gradient problem existing in the Predict+Optimize framework.

Abstract:

To achieve end-to-end optimization in the Predict+Optimize (P+O) framework, efforts have been focused on constructing surrogate loss functions to replace the non-differentiable decision regret.
While these surrogate functions are effective in forwarding training, the backpropagation of the gradient introduces a significant but unexplored problem: the inexactness of the surrogate gradient, which often destabilizes the training process. To address this challenge, we propose the Adaptive Proximal Gradient Optimizer (AProx), the first gradient descent optimizer designed to handle the inexactness of surrogate gradient backpropagation within the P+O framework.
Instead of explicitly solving proximal operations, AProx uses subgradients to approximate the proximal operator, simplifying the computational complexity and making proximal gradient descent feasible within the P+O framework. We prove that the surrogate gradients of three major types of surrogate functions are subgradients, allowing efficient application of AProx to end-to-end optimization.
Additionally, AProx introduces momentum and novel strategies for adaptive weight decay and parameter smoothing, which together enhance both training stability and convergence speed.
Through experiments on several classical combinatorial optimization benchmarks using different surrogate functions, AProx demonstrates superior performance in stabilizing the training process and reducing the optimality gap under predicted parameters.

Primary Area: optimization

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Submission Number: 652