[Paper Review] Deep Learning for Explicitly Modeling Optimization Landscapes

Shumeet Baluja|arXiv (Cornell University)|Mar 21, 2017

Machine Learning and Data Classification30 references5 citations

TL;DR

This paper proposes a deep learning-based method to explicitly model optimization landscapes by training deep neural networks (DNNs) to approximate the evaluation function of complex, high-dimensional problems. By using 'deep-network inversion' to generate high-quality initial solutions, the approach improves local search performance across diverse domains—including combinatorial, discrete, and continuous optimization problems—demonstrating significant gains over standard stochastic search methods like genetic algorithms.

ABSTRACT

In all but the most trivial optimization problems, the structure of the solutions exhibit complex interdependencies between the input parameters. Decades of research with stochastic search techniques has shown the benefit of explicitly modeling the interactions between sets of parameters and the overall quality of the solutions discovered. We demonstrate a novel method, based on learning deep networks, to model the global landscapes of optimization problems. To represent the search space concisely and accurately, the deep networks must encode information about the underlying parameter interactions and their contributions to the quality of the solution. Once the networks are trained, the networks are probed to reveal parameter combinations with high expected performance with respect to the optimization task. These estimates are used to initialize fast, randomized, local search algorithms, which in turn expose more information about the search space that is subsequently used to refine the models. We demonstrate the technique on multiple optimization problems that have arisen in a variety of real-world domains, including: packing, graphics, job scheduling, layout and compression. The problems include combinatoric search spaces, discontinuous and highly non-linear spaces, and span binary, higher-cardinality discrete, as well as continuous parameters. Strengths, limitations, and extensions of the approach are extensively discussed and demonstrated.

Motivation & Objective

• To develop a method that explicitly models the structure of optimization landscapes using deep neural networks.
• To improve stochastic optimization by using trained DNNs to generate high-quality initial solutions for local search.
• To reduce reliance on random perturbations in local search by leveraging learned parameter interactions from the DNN.
• To explore the integration of deep learning with traditional optimization heuristics such as hill-climbing and genetic algorithms.
• To evaluate the method across diverse problem types, including combinatorial, discontinuous, and non-linear search spaces.

Proposed method

• Train a deep feedforward neural network to approximate the true evaluation function of the optimization problem using sampled solutions.
• Use 'deep-network inversion'—a differentiable sampling technique—to generate new candidate solutions with high expected performance from the trained DNN.
• Initialize fast, randomized local search algorithms (e.g., NASH) with these DNN-generated candidates to explore promising regions of the search space.
• Iteratively refine the DNN model by collecting new evaluation results from the local search and retraining the network with updated data.
• Apply early stopping and regularization to prevent overfitting during incremental training on evolving data.
• Use the DNN as a surrogate evaluation function to accelerate search, reducing reliance on expensive real evaluations.

Experimental results

Research questions

• RQ1 Can deep neural networks effectively model complex, high-dimensional optimization landscapes with minimal prior problem-specific design?
• RQ2 Does using DNN-generated initial solutions improve the performance of local search algorithms compared to random initialization?
• RQ3 How does the integration of deep learning with stochastic optimization affect convergence speed and solution quality across diverse problem types?
• RQ4 Can the DNN model generalize across similar optimization problems, enabling transfer learning and reduced retraining?
• RQ5 What are the key hyperparameters and training strategies that influence the robustness and scalability of the method?

Key findings

• The Deep-Opt-GA approach achieved a mean performance of 5131 on the graph-based constraints problem, significantly outperforming standard GA with population sizes of 50 and 100, which achieved 4817 and 4825 respectively, winning all 20 instantiations.
• The method demonstrated consistent improvements across multiple domains, including packing, graphics, job scheduling, layout, and compression, despite varying problem types and search space characteristics.
• The use of deep-network inversion to generate high-quality initial solutions led to faster convergence and higher-quality solutions in local search procedures.
• The approach showed robustness with minimal architectural tuning, using the same 5- and 10-layer feedforward networks across all problems without problem-specific modifications.
• The method reduced reliance on random exploration by encoding parameter interactions and dependencies learned from previous evaluations, enabling more intelligent search direction.
• The study identified that network retraining from scratch was necessary when new samples could not be accommodated, suggesting sensitivity to weight scaling and the need for regularization in incremental training.