arXiv subjects

Jiatai Tong

Publications and source records attributed to Jiatai Tong.

3 recordsLinked to original sources

arXiv2026

Optimization over Trained (and Sparse) Neural Networks: A Surrogate within a Surrogate

In constraint learning, we use a neural network as a surrogate for part of the constraints or of the objective function of an optimization model. However, the tractability of the resulting model is heavily influenced by the size of the neural network used as a surrogate. One way to obtain a more tractable surrogate is by pruning the neural network first. In this work, we consider how to approach the setting in which the neural network is actually a given: how can we solve an optimization model embedding a large and predetermined neural network? We propose surrogating the neural network itself by pruning it, which leads to a sparse and more tractable optimization model, for which we hope to still obtain good solutions with respect to the original neural network. For network verification and function maximization models, that indeed leads to better solutions within a time limit, especially -- and surprisingly -- if we skip the standard retraining step known as finetuning. Hence, a pruned network with worse inference for lack of finetuning can be a better surrogate.

math.OC↗

arXiv2026

Optimization over Trained Neural Networks: Going Large with Gradient-Based Algorithms

When optimizing a nonlinear objective, one can employ a neural network as a surrogate for the nonlinear function. However, the resulting optimization model can be time-consuming to solve globally with exact methods. As a result, local search that exploits the neural-network structure has been employed to find good solutions within a reasonable time limit. For such methods, a lower per-iteration cost is advantageous when solving larger models. The contribution of this paper is two-fold. First, we propose a gradient-based algorithm with lower per-iteration cost than existing methods. Second, we further adapt this algorithm to exploit the piecewise-linear structure of neural networks that use Rectified Linear Units (ReLUs). In line with prior research, our methods become competitive with -- and then dominant over -- other local search methods as the optimization models become larger.

math.OC↗

arXiv2024

Optimization Over Trained Neural Networks: Taking a Relaxing Walk

Besides training, mathematical optimization is also used in deep learning to model and solve formulations over trained neural networks for purposes such as verification, compression, and optimization with learned constraints. However, solving these formulations soon becomes difficult as the network size grows due to the weak linear relaxation and dense constraint matrix. We have seen improvements in recent years with cutting plane algorithms, reformulations, and an heuristic based on Mixed-Integer Linear Programming (MILP). In this work, we propose a more scalable heuristic based on exploring global and local linear relaxations of the neural network model. Our heuristic is competitive with a state-of-the-art MILP solver and the prior heuristic while producing better solutions with increases in input, depth, and number of neurons.

math.OC↗