# Locally Optimal Descent for Dynamic Stepsize Scheduling

arXiv: https://arxiv.org/abs/2311.13877 · HTML: https://mlsanity.com/paper/2311.13877/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 49 references that are in the map.
- First posted on arXiv 23 Nov 2023.

## Builds on (most cited first, 30 of 34)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [In-Datacenter Performance Analysis of a Tensor Processing Unit](https://mlsanity.com/paper/1704.04760/) (2017)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [Shampoo: Preconditioned Stochastic Tensor Optimization](https://mlsanity.com/paper/1802.09568/) (2018)
- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Lookahead Optimizer: k steps forward, 1 step back](https://mlsanity.com/paper/1907.08610/) (2019)
- [Deep Learning Recommendation Model for Personalization and Recommendation Systems](https://mlsanity.com/paper/1906.00091/) (2019)
- [Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training](https://mlsanity.com/paper/2305.14342/) (2023)
- [AdaGrad stepsizes: Sharp convergence over nonconvex landscapes](https://mlsanity.com/paper/1806.01811/) (2018)
- [On the Convergence of Stochastic Gradient Descent with Adaptive Stepsizes](https://mlsanity.com/paper/1805.08114/) (2018)
- [Coin Betting and Parameter-Free Online Learning](https://mlsanity.com/paper/1602.04128/) (2016)
- [Sequence-to-Sequence Learning as Beam-Search Optimization](https://mlsanity.com/paper/1606.02960/) (2016)
- [Black-Box Reductions for Parameter-free Online Learning in Banach Spaces](https://mlsanity.com/paper/1802.06293/) (2018)
- [Painless Stochastic Gradient: Interpolation, Line-Search, and Convergence Rates](https://mlsanity.com/paper/1905.09997/) (2019)
- [Online Learning Rate Adaptation with Hypergradient Descent](https://mlsanity.com/paper/1703.04782/) (2017)
- [Learning-Rate-Free Learning by D-Adaptation](https://mlsanity.com/paper/2301.07733/) (2023)
- [DoG is SGD's Best Friend: A Parameter-Free Dynamic Step Size Schedule](https://mlsanity.com/paper/2302.12022/) (2023)
- [Understanding Short-Horizon Bias in Stochastic Meta-Optimization](https://mlsanity.com/paper/1803.02021/) (2018)
- [The Complexity of Finding Stationary Points with Stochastic Gradient Descent](https://mlsanity.com/paper/1910.01845/) (2019)
- [Parameter-free online learning via model selection](https://mlsanity.com/paper/1801.00101/) (2017)
- [SGD with AdaGrad Stepsizes: Full Adaptivity with High Probability to Unknown Parameters, Unbounded Gradients and Affine Variance](https://mlsanity.com/paper/2302.08783/) (2023)

## Abstract (arXiv)

We introduce a novel dynamic learning-rate scheduling scheme grounded in theory with the goal of simplifying the manual and time-consuming tuning of schedules in practice. Our approach is based on estimating the locally-optimal stepsize, guaranteeing maximal descent in the direction of the stochastic gradient of the current step. We first establish theoretical convergence bounds for our method within the context of smooth non-convex stochastic optimization, matching state-of-the-art bounds while only assuming knowledge of the smoothness parameter. We then present a practical implementation of our algorithm and conduct systematic experiments across diverse datasets and optimization algorithms, comparing our scheme with existing state-of-the-art learning-rate schedulers. Our findings indicate that our method needs minimal tuning when compared to existing approaches, removing the need for auxiliary manual schedules and warm-up phases and achieving comparable performance with drastically reduced parameter tuning.