# Meta-Learning for Black-box Optimization

## TL;DR

This paper introduces RNN-Opt, a meta-learning approach using RNNs trained with a regret-based loss function to effectively optimize real-valued black-box functions under practical constraints.

## Contribution

It proposes a novel training method for RNN-based optimizers using synthetic functions and regret minimization, improving black-box optimization performance under constraints.

## Key findings

- RNN-Opt outperforms existing methods on synthetic benchmarks.
- RNN-Opt effectively handles unknown value ranges and constraints.
- Demonstrated success on industrial constrained optimization problems.

## Abstract

Recently, neural networks trained as optimizers under the "learning to learn" or meta-learning framework have been shown to be effective for a broad range of optimization tasks including derivative-free black-box function optimization. Recurrent neural networks (RNNs) trained to optimize a diverse set of synthetic non-convex differentiable functions via gradient descent have been effective at optimizing derivative-free black-box functions. In this work, we propose RNN-Opt: an approach for learning RNN-based optimizers for optimizing real-parameter single-objective continuous functions under limited budget constraints. Existing approaches utilize an observed improvement based meta-learning loss function for training such models. We propose training RNN-Opt by using synthetic non-convex functions with known (approximate) optimal values by directly using discounted regret as our meta-learning loss function. We hypothesize that a regret-based loss function mimics typical testing scenarios, and would therefore lead to better optimizers compared to optimizers trained only to propose queries that improve over previous queries. Further, RNN-Opt incorporates simple yet effective enhancements during training and inference procedures to deal with the following practical challenges: i) Unknown range of possible values for the black-box function to be optimized, and ii) Practical and domain-knowledge based constraints on the input parameters. We demonstrate the efficacy of RNN-Opt in comparison to existing methods on several synthetic as well as standard benchmark black-box functions along with an anonymized industrial constrained optimization problem.