Practical tradeoffs between memory, compute, and performance in learned optimizers (2203.11860v3)

Abstract: Optimization plays a costly and crucial role in developing machine learning systems. In learned optimizers, the few hyperparameters of commonly used hand-designed optimizers, e.g. Adam or SGD, are replaced with flexible parametric functions. The parameters of these functions are then optimized so that the resulting learned optimizer minimizes a target loss on a chosen class of models. Learned optimizers can both reduce the number of required training steps and improve the final test loss. However, they can be expensive to train, and once trained can be expensive to use due to computational and memory overhead for the optimizer itself. In this work, we identify and quantify the design features governing the memory, compute, and performance trade-offs for many learned and hand-designed optimizers. We further leverage our analysis to construct a learned optimizer that is both faster and more memory efficient than previous work. Our model and training code are open source.

• The paper demonstrates that learned optimizers achieve lower meta-losses through dynamic, meta-learned designs that replace static hyperparameters.
• It details tradeoffs such as increased computational overhead and memory usage versus improved training performance compared to traditional counterparts like SGD and Adam.
• A novel small_fc_lopt architecture is proposed, emphasizing resource efficiency and generalization across diverse neural network tasks.

Practical Tradeoffs Between Memory, Compute, and Performance in Learned Optimizers

Introduction

The paper investigates the practical constraints and tradeoffs encountered with learned optimizers in machine learning. It argues that while learned optimizers can enhance both training efficiency and model performance compared to traditional hand-designed optimizers like Adam or SGD, they come with their own set of challenges. Learned optimizers substitute static hyperparameters with dynamic, parameterized functions optimized over several tasks. The emphasis of the paper is on understanding the impact of design choices on memory, computational efficiency, and performance tradeoffs, presenting a new learned optimizer architecture that achieves a balance of speed and efficiency.

Optimizer Design and Meta-Learning

Gradient-Based Optimizers

The paper dives into standard first-order gradient-based optimizers, which leverage gradient history to adjust model parameters. The core components include an Init function to initialize state and an Update function to compute parameter updates from gradients. Examples include Adam, which uses moment accumulators to adjust learning rates for parameters.

Meta-Learned Optimizers

Here, hyperparameters of optimizers become learnable parameters, typically encapsulated in neural networks. Various architectures for learned optimizers include hyperparameter controllers, per-parameter learned optimizers, and hierarchical optimizers. These approaches vary in computational and memory overhead and the complexity involved in training tasks using historical gradient information.

Training, Tasks, and Meta-Optimization

The training of learned optimizers is framed as a meta-optimization problem, where optimizers themselves are optimized. The paper outlines tasks using neural network training setups, particularly focusing on how the optimizer's design affects performance on different classes of tasks. Meta-optimization leverages algorithms like Persistent Evolution Strategies (PES) to refine optimizer parameters based on training loss.

Tradeoffs in Learned Optimizer Architectures

Compute, Memory, and Performance

The paper comprehensively evaluates the tradeoffs in compute, memory, and ultimate performance across different learned optimizers and compares them against hand-designed baselines like SGD and Adam. Learned optimizers prove to frequently achieve lower meta-losses but are more computationally expensive. The paper analyzes specific design choices like using multiple decay rates for momentum or second-moment accumulators, influencing computational overhead and performance.

Per-Parameter Learned Optimizer Details

An innovative learned optimizer architecture, termed small_fc_lopt, highlights the tradeoffs in more detail. This architecture is characterized by a memory-efficient structure with significantly fewer parameters, leveraging minimal momentum and adaptive factorized accumulator features to maintain balance against resource constraints.

Generalization and Scaling

A key insight is the learned optimizers' ability to generalize beyond specific training tasks, though meta-overfitting remains a concern. The transferability to new tasks is contingent on the target application and the balance between memory and computational requirements of the optimizer. The paper extends these comparisons to realistic tasks such as training ResNets and Transformer models on a TPUv2.

Implications and Future Work

The findings advocate for refined architectural designs of learned optimizers that can be tailored to maximize performance while minimizing computational costs. Future exploration is suggested to further paper the robustness of learned optimizers in diverse application contexts, deepen insights into meta-generalization capabilities, and reduce meta-overfitting tendencies.

Conclusion

The paper concludes by reiterating the necessity of strategic design in learned optimizers to address the multifaceted balance of computation, memory, and performance. This research lays groundwork for the ongoing development of effective, efficient optimizers and invites further investigation into advanced design frameworks, facilitating broader adoption in practice.