Learning to Optimize: A Primer and A Benchmark

Chen, Tianlong; Chen, Xiaohan; Chen, Wuyang; Heaton, Howard; Liu, Jialin; Wang, Zhangyang; Yin, Wotao

doi:10.48550/arxiv.2103.12828

Cited by 31 publications

(45 citation statements)

References 61 publications

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“…Learning to optimize. Learning to optimize (L2O) applies deep learning to learn from past optimization experience to optimize future problems more effectively and faster; see [Chen et al, 2021] for a survey. Model-free L2O uses recurrent neural networks to discover new optimizers suitable for similar problems [Andrychowicz et al, 2016, Li andMalik, 2016].…”

Section: Related Workmentioning

confidence: 99%

“…An advantage of our representation is that it can represent arbitrary number of solutions (Figure C.5) and can handle the case when the solution set is continuous (Figure C.2). This highlights the difference between our setup and that of existing L2O methods [Chen et al, 2021]: at test time, we do not need access to {f ω } ω∈Ω or their gradients, which can be costly to evaluate or unavailable; instead we only need ω (e.g. in the case of object detection, ω is an image).…”

Section: Extracting Solutionsmentioning

confidence: 99%

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Learning Proximal Operators to Discover Multiple Optima

Li¹,

Aigerman²,

Kim³

et al. 2022

Preprint

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Finding multiple solutions of non-convex optimization problems is a ubiquitous yet challenging task. Typical existing solutions either apply single-solution optimization methods from multiple random initial guesses or search in the vicinity of found solutions using ad hoc heuristics. We present an end-to-end method to learn the proximal operator across a family of non-convex problems, which can then be used to recover multiple solutions for unseen problems at test time. Our method only requires access to the objectives without needing the supervision of ground truth solutions. Notably, the added proximal regularization term elevates the convexity of our formulation: by applying recent theoretical results, we show that for weakly-convex objectives and under mild regularity conditions, training of the proximal operator converges globally in the over-parameterized setting. We further present a benchmark for multi-solution optimization including a wide range of applications and evaluate our method to demonstrate its effectiveness.

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Section: Related Workmentioning

confidence: 99%

Section: Extracting Solutionsmentioning

confidence: 99%

Learning Proximal Operators to Discover Multiple Optima

Li¹,

Aigerman²,

Kim³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Learning to optimise. Learning to optimise (L2O) combines the flexible data-driven learning procedure and interpretable rule-based optimisation [8]. Algorithmic unrolling is one main approach of L2O [26].…”

Section: Related Workmentioning

confidence: 99%

“…To address the above limitations, we propose a novel functional learning framework to learn a mapping from node observations to the underlying graph topology with desired structural property. Our framework is inspired by the emerging field of learning to optimise (L2O) [8,26]. Specifically, as shown in Figure 1, we first unroll an iterative algorithm for solving the aforementioned regularised graph learning objective.…”

Section: Introductionmentioning

confidence: 99%

Learning to Learn Graph Topologies

Pu¹,

Cao²,

Zhang³

et al. 2021

Preprint

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Learning a graph topology to reveal the underlying relationship between data entities plays an important role in various machine learning and data analysis tasks. Under the assumption that structured data vary smoothly over a graph, the problem can be formulated as a regularised convex optimisation over a positive semidefinite cone and solved by iterative algorithms. Classic methods require an explicit convex function to reflect generic topological priors, e.g. the 1 penalty for enforcing sparsity, which limits the flexibility and expressiveness in learning rich topological structures. We propose to learn a mapping from node data to the graph structure based on the idea of learning to optimise (L2O). Specifically, our model first unrolls an iterative primal-dual splitting algorithm into a neural network. The key structural proximal projection is replaced with a variational autoencoder that refines the estimated graph with enhanced topological properties. The model is trained in an end-to-end fashion with pairs of node data and graph samples. Experiments on both synthetic and real-world data demonstrate that our model is more efficient than classic iterative algorithms in learning a graph with specific topological properties.

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“…Machine learning techniques have been used to design optimization methods (e.g., [15], [16]). There are fewer works that develop embedded-ML methods specifically for distributed optimization algorithms.…”

Section: Introductionmentioning

confidence: 99%

A Reinforcement Learning Approach to Parameter Selection for Distributed Optimal Power Flow

Zeng¹,

Kody²,

Kim³

et al. 2021

Preprint

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With the increasing penetration of distributed energy resources, distributed optimization algorithms have attracted significant attention for power systems applications due to their potential for superior scalability, privacy, and robustness to a single point-of-failure. The Alternating Direction Method of Multipliers (ADMM) is a popular distributed optimization algorithm; however, its convergence performance is highly dependent on the selection of penalty parameters, which are usually chosen heuristically. In this work, we use reinforcement learning (RL) to develop an adaptive penalty parameter selection policy for the AC optimal power flow (ACOPF) problem solved via ADMM with the goal of minimizing the number of iterations until convergence. We train our RL policy using deep Q-learning, and show that this policy can result in significantly accelerated convergence (up to a 59% reduction in the number of iterations compared to existing, curvature-informed penalty parameter selection methods). Furthermore, we show that our RL policy demonstrates promise for generalizability, performing well under unseen loading schemes as well as under unseen losses of lines and generators (up to a 50% reduction in iterations). This work thus provides a proof-of-concept for using RL for parameter selection in ADMM for power systems applications.

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Learning to Optimize: A Primer and A Benchmark

Cited by 31 publications

References 61 publications

Learning Proximal Operators to Discover Multiple Optima

Learning Proximal Operators to Discover Multiple Optima

Learning to Learn Graph Topologies

A Reinforcement Learning Approach to Parameter Selection for Distributed Optimal Power Flow

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